N NAVIGA ATION NAL PA

N NAVIGA ATION NAL PA
NAVIGA
ATION
NAL PA
ATH AN
NALYS
SIS OF
F MOBIILE
ROB
BOT IN
N VAR
RIOUS ENVIR
E
RONME
ENTS
Mukkesh Kum
mar Singgh
Navigational Path Analys
A
sis of Mobile
M
Robott in
V
Various
s Envirronmeents
Thesiis Submittted to the
Depaartment off Mechan
nical Engiineering
Nation
nal Institu
ute of Tecchnology, Rourkelaa
For aw
ward of th
he degree
of
Doctoor of Phiilosophyy
by
Mukessh Kum
mar Singh
h
Undeer the guiddance of
Prof. Dayal R.
R Parhii
Departm
ment of Mechan
nical En
ngineering
National
N
l Institutte of Technologgy Rourk
kela
Orissaa (India))-7690088
Novemberr 2009
Declaration
I hereby declare that this submission is my own work and that, to the best of my
knowledge and belief, it contains no material previously published or written by another person
nor material which to a substantial extent has been accepted for the award of any other degree
or diploma of the university or other institute of higher learning, except where due
acknowledgement has been made in the text.
(Mukesh Kumar Singh)
Date: 16/11/2009
NATION
NAL IN
NSTITU
UE OF TECH
HNOLO
OGY
ROUR
RKELA
A -7690008, OR
RISSA, INDIA
I
.
Certificaate
This is to ceertify that thhe thesis enttitled, “Naviigational Paath Analysiss of Mobile robot in
varioous Environ
nment”, beiing submitteed by Mr. Mukesh
M
Kum
mar Singh too the Departtment of
Mechanical Eng
gineering, Naational Instiitute of Techhnology, Rouurkela, for thhe partial fulfillment
of aw
ward of the degree Docctor of Philoosophy, is a record of bona
b
fide ressearch workk carried
out by
b him underr my superviision and guuidance.
This thesis in
i my opinioon, is worthyy of considerration for aw
ward of the degree of Doctor
D
of
Philoosophy in acccordance with
w the reguulation of thee institute. To
T the best off my knowleedge, the
results embodied
d in this thessis have nott been submiitted to any other Univeersity or Insttitute for
the award
a
of anyy degree or diploma.
d
Sup
pervisor
Datee: 16/11/2009
(Dayal R.
R Parhi)
Prrofessor,
Departtment of
Mecchanical Enggineering
N
National
Insttitute of Tecchnology
R
Rourkela,
Orrissa, India- 769008.
7
------------------------------------------------------------------------------------------------------------------------Web: http///www.nitrkl.ac.in, Phone: 0661-2462031, 2462021, 2472050, Fax:
F 91-661-2462039, 2462999.
Acknowledgements
I extend my deep sense of indebtedness and gratitude to Prof. Dayal R. Parhi for his
kindness in providing me an opportunity to work under his supervision and guidance. He
played a crucial role in the process of my research work. First of all, he allowed me to join his
research group, even three scholars were working under him. His advice to harmonize theory
and applications help me a lot in my research. He showed me different ways to approach a
research problem and the need to be persistent to accomplish my goal. His keen interest,
invaluable guidance and immense help have helped me for the successful completion of the
thesis.
I am thankful to Prof. Sunil Kumar Sarangi, Director of National Institute of Technology,
for giving me an opportunity to work under the supervision of Prof. Parhi. Special thank goes
to him, without his support it was not possible to choose such a sincere guide. I am thankful to
Prof. R.K. Sahoo, Head of the Department, Mechanical Engineering, for his moral support and
valuable suggestions regarding the research work.
Besides my advisors, I would like to thank Mr. Maheshwar Das, for helping me to
complete the robot controller circuit for experimental validation as well as the challenging
research that lie behind it. I am also thankful of all lab mates Mr. Jayata Kumar Pothal, Mr. B.
Mohan, Soumitri Rai Jagdev and Miss Subhshri Kundu for their valuable support and
maintaining a nice research environment in the laboratory.
I wish to extend special thanks to Prof. P. Rath, Prof. B.K. Singh, Prof. S. Bhowmik and
Scientist S.K. Kashyap, for their valuable suggestions and cordial environment in NIT Campus.
Special thanks go to Prof. S.K. Mahapatra who shared tennis with me throughout the semester
to make life enjoyable apart from academics. The beautiful weather of NIT Campus, kept me in
good health and high spirits throughout the research period.
Special thanks go to my wife, ‘Karuna’ for all her support at every stage of this research. I
hope she knows that there is no one in the world as beautiful and inspiring as she is. During this
period I cannot forget the telephonic voice of my lovely son ‘Mintu’.
ii
Synopsis
This dissertation describes work in the area of an autonomous mobile robot. The objective
is navigation of mobile robot in a real world dynamic environment avoiding structured and
unstructured obstacles either they are static or dynamic. The shapes and position of obstacles
are not known to robot prior to navigation. The mobile robot has sensory recognition of specific
objects in the environments. This sensory-information provides local information of robots
immediate surroundings to its controllers. The information is dealt intelligently by the robot to
reach the global objective (the target). Navigational paths as well as time taken during
navigation by the mobile robot can be expressed as an optimisation problem and thus can be
analyzed and solved using AI techniques. The optimisation of path as well as time taken is
based on the kinematic stability and the intelligence of the robot controller. A successful way of
structuring the navigation task deals with the issues of individual behaviour design and action
coordination of the behaviours. The navigation objective is addressed using fuzzy logic, neural
network, adaptive neuro-fuzzy inference system and different other AI technique. The research
also addresses distributed autonomous systems using multiple robots.
The proposed research work aims to broaden the development in the area of navigational
path analysis of mobile robot in various (known and unknown) environments by avoiding static
as well as dynamic obstacles. This research also addresses distributed autonomous systems
using multiple robots which are superior in control strategy to single mobile robots in terms of
reliability, expandability, and flexibility. In contrast to a single robot system; they provide
increased robustness by taking advantage of inherent parallelism and redundancy. Research in
autonomous multi-robot systems often focuses on mechanisms to enhance the efficiency of the
group through some form of cooperation among the individual agents. An intelligent controller
enables the robot to cope with its real world environment. This research is related to design of
an intelligent controller for single as well as multiple mobile robots using AI techniques (i.e.
Fuzzy, neural, adaptive neuro-fuzzy, heuristic rule base network) so that mobile robot able to
navigate in real word dynamic environments. The current investigation focuses on optimisation
of robot path as well as time taken during navigation to reach the specified targets by avoiding
static as well as dynamic obstacles.
iii
Table of Contents
Declaration ...................................................................................................................................i
Certificate ................................................................................................................................... ii
Acknowledgements ................................................................................................................... iii
Synopsis ......................................................................................................................................iv
Contents ....................................................................................................................................... v
List of Tables ..............................................................................................................................ix
List of Figures ............................................................................................................................. x
List of Symbols .......................................................................................................................xxiv
1 Introduction........................................................................................................................... 1 1.1 Background and Motivation .......................................................................................... 1 1.2 Aims and Objectives of this Research ........................................................................... 4 1.3 Outline of the Research Work ....................................................................................... 6 2 Literature Review ................................................................................................................. 7 2.1 Introduction.................................................................................................................... 7 2.2 Navigation of Mobile Robots ........................................................................................ 8 2.2.1 Indoor Navigation ................................................................................................. 8 2.2.2 Outdoor Navigation .............................................................................................. 9 2.3 Kinematics of Mobile Robot ....................................................................................... 11 2.4 Fuzzy Logic Controller for Mobile Robot ................................................................... 15 2.5 Neural Controller for Mobile Robot ............................................................................ 20 2.6 Adaptive Neuro-Fuzzy Controller for Mobile Robot .................................................. 25 2.7 Heuristic Rule Base Neural Controller for Mobile Robot ........................................... 28 2.8 Summary ...................................................................................................................... 31 3 Kinematic Analysis of Mobile Robots ............................................................................... 32 3.1 Introduction.................................................................................................................. 32 3.2 Type of Wheels used in Mobile Robot ........................................................................ 33 3.3 Analysis of Wheel Kinematic Constraints ................................................................... 35 3.4 Motion Control ............................................................................................................ 37 3.4.1 Open Loop Control ............................................................................................. 37 3.4.2 Feedback Control ................................................................................................ 37 iv
3.5 3.6 3.7 3.8 Problem Statement ....................................................................................................... 38 Kinematic Analysis of Mobile Robot .......................................................................... 39 Dynamic Analysis of Mobile Robot ............................................................................ 42 Motion Control of Mobile Robot ................................................................................. 44 3.8.1 The control Law .................................................................................................. 45 3.8.2 Local Stability Issue ........................................................................................... 47 3.9 Summary ...................................................................................................................... 48 4 Analysis of Fuzzy Logic Controller for Mobile Robot .................................................... 49 4.1 Introduction.................................................................................................................. 49 4.2 Fuzzy Logic Behaviour for Control Technique ........................................................... 51 4.3 Behavioural Architecture ............................................................................................. 54 4.3.1 Obstacle Avoidance ............................................................................................ 55 4.3.2 Wall Following Behaviour ................................................................................. 58 4.3.3 Target seeking Behaviour ................................................................................... 60 4.4 Simulation Results and Discussion .............................................................................. 62 4.5 Experimental results .................................................................................................... 64 4.6 Summary ...................................................................................................................... 66 5 Analysis of Neural Controller for Mobile Robot ............................................................. 68 5.1 Introduction.................................................................................................................. 68 5.2 Analysis of Neural Network for Navigation ................................................................ 69 5.3 Simulation Results and Discussions ............................................................................ 75 5.4 Experimental results .................................................................................................... 80 5.5 Summary ...................................................................................................................... 84 6 Adaptive Neuro-Fuzzy Controller for Navigation of Mobile Robots ............................ 85 6.1 Introduction.................................................................................................................. 85 6.2 Analysis of ANFIS ...................................................................................................... 87 6.3 Simulation Results ....................................................................................................... 91 6.4 Experimental Results ................................................................................................... 95 6.5 Summary ...................................................................................................................... 97 7 Heuristic Rule Base Neural Controller for Mobile Robot .............................................. 99 7.1 7.2 7.3 7.4 7.5 Introduction.................................................................................................................. 99 Perception Based Heuristic Rule ............................................................................... 100 Back Propagation Algorithms (BPA) ........................................................................ 108 Petri Net Model (PNM) ............................................................................................. 108 Simulation Results and Discussion ............................................................................ 110 v
7.6 Experimental Results with Real Mobile Robot ......................................................... 114 7.6.1 Implementation of HRBN Controller on Khepera robot .................................. 114 7.6.2 Implementation of HRBN Controller on Koala robot ...................................... 116 7.7 Summary .................................................................................................................... 119 8 Results and Discussion ..................................................................................................... 120 8.1 Kinematics and Dynamic Stability of Mobile Robot ................................................ 120 8.2 Intelligent Controller of Mobile Robots .................................................................... 121 9 Conclusions and Future Works ....................................................................................... 126 9.1 Conclusions................................................................................................................ 126 9.2 Future Works ............................................................................................................. 127 Appendix-A ............................................................................................................................. 128 Appendix-B .............................................................................................................................. 130 Appendix-C ............................................................................................................................. 134 References ................................................................................................................................ 138 Published and Accepted Papers ............................................................................................ 156 Bibliography ............................................................................................................................ 158 vi
List of Tables
Table 4.1. Parameter for variables ............................................................................................. 52
Table 4.2. List of rules for obstacle avoidance .......................................................................... 56
Table 4.3. List of rules for wall following behaviour ................................................................ 59
Table 4.4. List of rules for target seeking and map localisation ................................................ 61
Table 4.5. Time taken by robots in simulation and experiment to reach targets ....................... 66
Table 5.1. Some of the training pattern of neural controller...................................................... 72
Table 5.2. Reactive behaviours adopted by mobile robot during navigation ............................ 74
Table 5.3 Time taken by robots in simulation and experiment to reach targets ....................... 81
Table 5.4. Simulation results comparison between the fuzzy controllers developed by
Pradhan et al. [213] and the current developed neural controller ............................. 83
Table 6.1 Time taken by robots in simulation and experiment to reach targets. ...................... 95
Table 7.1. Heuristic rule formulation for obstacle and target located in the left side of the
robot. ....................................................................................................................... 102
Table 7.2 Heuristic rule formulation for obstacle and target located in the right side of
the robot. ................................................................................................................. 103
Table 7.3. Heuristic rule formation for obstacle present front of the robot and target
located in right side of the robot. ............................................................................ 103
Table 7.4. Perception based heuristic rule formation for obstacle avoidance Fig. 7.3(a)........ 104
Table 7.5. Perception based heuristic rule formation for obstacle avoidance (Fig.7.3(b)) ...... 105
Table 7.6. Human perception based heuristic rule formation for wall following Fig.
7.4(a) ....................................................................................................................... 106
Table 7.7. Perception based heuristic rule formation for wall following (Fig. 7.4 (b))........... 107
Table 7.8 Total path traveled and time taken by robots during simulation and
experimental environment by proposed method..................................................... 116
Table 7.9. Total path traveled and time taken by robots during simulation and
experimental environment by proposed method..................................................... 118
Table 8.1. Results deviation of travelled path and time taken during simulation and
experimental mode.................................................................................................. 124
vii
List of Figures
Figure 1.1. General control scheme of autonomous mobile robot system. ................................ 3 Figure 2.1. Flow diagram of the horizontal decomposition method for robot navigation. ...... 10 Figure 2.2. Flow diagram of the vertical decomposition method for robot navigation. .......... 11 Figure 2.3. Schematic diagram of the fuzzy logic controller for mobile robot. ....................... 17 Figure 2.4. Schematic view of the neural networks used for the navigation of mobile
robots, the output of the Kohonen network is fed into the feed forward
network as a regression. ......................................................................................... 24 Figure 3.1. (a) Schematic view of conventional wheel and (b) Ball wheel used in mobile
robots. .................................................................................................................... 34 Figure 3.2. Kinematic parameters of (a) Standard wheel (b) Ball wheel. ................................ 35 Figure 3.3. Kinematic control of a mobile robot, (a) Open-loop control based on straight
lines and circular trajectory segments, (b) Typical situation for feedback
control of a mobile robot. ...................................................................................... 38 Figure 3.4. Kinematic analysis of mobile robot ....................................................................... 39 Figure 3.5. Resulting paths of the robot at initially on the unit circle in X-Y plane. ............... 46 Figure 4.1. Simulation resulting paths of mobile robot. .......................................................... 52 Figure 4.2. Fuzzy membership functions used to design fuzzy logic controller...................... 55 Figure 4.3. Schematic diagram of the fuzzy logic for navigation of mobile robots. ............... 57 Figure 4.4. The surface view of the fuzzy logic for navigation of mobile robots. ................... 57 Figure 4.5. (a) Static as well as dynamic obstacle avoidance (b) Obstacle avoidance and
motion control behaviour. ...................................................................................... 58 Figure 4.6. (a) Robot in indefinite loop in concave trap (b) Wall following behaviour. ......... 60 Figure 4.7. (a) Escape from dead ends and find the target (b) Target seeking behaviour. ...... 61 Figure 4.8. (a) Mobile robot reference trajectories by Das et al. [86] (b) Mobile robot
reference trajectories by proposed controller. ....................................................... 62 Figure 4.9. (a) Mobile robot trajectories with different number by Zhu et al. [154] (b)
Mobile robot trajectories with different number by purposed method. ................. 63 Figure 4.10. Experimental results of mobile robot to reach the target successfully. ................. 65 Figure 4.11. Experimental results validation with simulation mode. ........................................ 66 viii
Figure 5.1. Four-layer neural network for robot navigation. ................................................... 71 Figure 5.2. Example of training patterns. ................................................................................. 71 Figure 5.3. Hyperbolic tangent function used for activation function. .................................... 72 Figure 5.4. Static as well as dynamic obstacle avoidance behaviour (a) At initial
position before simulation (b) Navigational path during simulation. .................... 76 Figure 5.5. Robot with wall following behaviour (b) Robot escaping from dead end
obstacles. ................................................................................................................ 76 Figure 5.6. (a) Navigation of a mobile robot in unknown environment by Ray et al.
[216] (b) Navigation of a mobile robot in unknown environment using a
developed controller. ............................................................................................. 77 Figure 5.7. (a) Experimental result of planned path by Hamel et al. [194] (b) Navigation
of mobile robot using developed controller. .......................................................... 78 Figure 5.8. (a) Static and dynamic experimental result by Sanchis et al. [214] (b) Static
and dynamic simulation result by developed neural controller. ............................ 79 Figure 5.9. The chassis of the KHEPERA-III robot. ............................................................... 80 Figure 5.10. Experimental results during target seeking by the mobile robot in various
environments.......................................................................................................... 82 Figure 5.11. Comparison of experimental results with simulation results. ................................ 83 Figure 6.1. Six-layers ANFIS architecture for robot navigation. ............................................. 88 Figure 6.2. Bell shaped membership function used for fuzzy inference system...................... 88 Figure 6.3. (a) Static as well as dynamic obstacle avoidance behaviour (b) Target
seeking behaviour of mobile robot. ....................................................................... 91 Figure 6.4. (a) Navigation path of mobile robot by purposed ANFIS (b) Escaping from
dead end by purposed ANFIS methodology. ......................................................... 92 Figure 6.5. (a) Results of Abdessemed et al. [90] during vehicle controlled motion with
a cluttered obstacle environment from two different starting points. (b)
Results of proposed ANFIS approach during vehicle controlled motion with
a cluttered obstacle environment from two different goal and starting points. ..... 93 Figure 6.6. (a) Path traced by the robot embedded with Arkin’s[211] controller, (b) Path
traced by the robot embedded with proposed ANFIS controller. .......................... 93 Figure 6.7. Comparison results of Camilo et al. [221] proposed approach (i) in a double
U shape environment (ii) in a large and recursive U-shape environment (b)
ix
Results of proposed ANFIS approach (i) in a double U shape environment
(ii) in a large and recursive U-shape environment................................................. 94 Figure 6.8. Experimental results of purposed ANFIS method. ................................................ 96 Figure 6.9. Paths followed by mobile robots using ANFIS method. ....................................... 96 Figure 6.10. Experimental results validation in simulation mode. ............................................ 97 Figure 7.1. Position of wheels and sensors in Khepera-III mobile robot, infrared (1-11)
and ultrasonic sensors (U1-U5). .......................................................................... 101 Figure 7.2. Position of wheels and sensors in koala mobile robot. ........................................ 101 Figure 7.3. Perception based rule formation for obstacle avoidance in different
environments........................................................................................................ 104 Figure 7.4. Perception based rule formation for wall following behaviour in different
environments........................................................................................................ 106 Figure 7.5. Four-layer heuristic rule neural network for robot navigation. ........................... 109 Figure 7.6. Petri net model to avoid inter collision among robots during navigation............ 109 Figure 7.7. Simulation result of inter robot collision avoidance among robots via petri
net model (a) Initial position of mobile robots (b) After simulation result. ....... 111 Figure 7.8. Simulation result of wall following behaviour in different environments. ......... 111 Figure 7.9. (a) Simulation result of target searching behaviour of mobile robots (b)
target searching behaviour. .................................................................................. 111 Figure 7.10. (a) Simulation results of Ayari et al. [220] collision free goal reaching in
learned environment (b) Simulation results of proposed method collision
free goal reaching. ............................................................................................... 112 Figure 7.11. (a) Simulation results comparisons with Yang et al. [88] (b) Simulation
results of proposed method. ................................................................................. 113 Figure 7.12. Experimental validation of simulation result on Khepera robots ........................ 115 Figure 7.13. Traced paths of mobile robots during experiment ............................................... 115 Figure 7.14. Path optimization of target tracker robot (TR) avoiding static as well as
dynamic obstacle with experimental validation. ................................................. 116 Figure 7.15. (a) Experimental result with Koala mobile robot to start moving towards
target and (b) Finally robot tracks the target following optimal path. ................. 117 Figure 7.16. Experimental result validation with simulation mode. ........................................ 118 x
Figure 8.1. Comparison of results between Fuzzy, Neural, ANFIS and HRBN
controller. ............................................................................................................. 125 Figure A.1. The Typical Screen of ROBNAV Software used for Navigation of Mobile
Robots. ................................................................................................................. 128 Figure A.2. The obstacles into the software............................................................................ 129 Figure A.3. (i) The number of robot into the software (ii) The target into the software. ....... 129 Figure B.1. A Simple Petri Net Model. .................................................................................. 130 Figure B.2. The Input and Output arcs. .................................................................................. 132 Figure B.3. Firing of Petri Net Model. ................................................................................... 132 Figure C.1. (a) Chassis of the robot (b) Working model of NITR Mobile Robot. ................. 134 Figure C.2. KHEPERA-II mobile robot. ................................................................................ 135 Figure C.3. KHEPERA-III mobile robot. ............................................................................... 136 Figure C.4. Koala mobile robot. ............................................................................................. 137 xi
List of Symbols
Left-obs
=
Left obstacle distance
Right-obs
=
Right obstacle distance
Front-obs
=
Front obstacle distance
Head-ang
=
Heading angle
Tar-ang
=
Target angle
Left-v
=
Velocity of left wheel
Right-v
=
Velocity of right wheel
=
Angle between local coordinate x-axis to robot reference frame
=
Angle of the wheel plane relative to the chassis
=
Angle of rotation w.r.t. global coordinate
P
=
Position in polar coordinates
R
=
Radius of the wheel
V
=
Linear velocity
ω
=
Angular velocity
t
=
Time taken by a robot to move from a distance
K
=
Control matrix
w
=
Axel length (left and right driving wheels distance)
C
=
Center of gravity point of the mobile robot
V
=
Linear tangential velocity
V
=
Linear velocity of right wheel
V
=
Linear velocity of left wheel
ω
=
Angular tangential velocity
q
=
The position of global coordinate frame
SA
=
Steering angle of the robot
M(q)
=
A symmetric, positive definite inertia matrix
=
Torque of right wheel
=
Torque of left wheel
λ
=
Vector of Lagrange multipliers
µ
=
Fuzzy membership function
xii
R3nx3n
z
=
Centroid distance of the firing area
Med
=
Medium
y
=
Left obstacle distance from the robot
y
=
Front obstacle distance from the robot
y
=
Right obstacle distance from the robot
y
=
Target bearing of the robot
θ
=
Desired output from the neural network
θ
=
Actual output from the neural network
f(.)
=
Activation function
=
Weight of the neuron connection from i in layer j
=
Error gradient
a , b , and c =
The parameters for the fuzzy membership function
L
=
Layer of the network
PN
=
Petri net structure
=
Distance between the center of the robot’s wheel axel and the target
position
xiii
1 Introduction
The work described in this thesis has been carried out in the context of the navigation of
various environments with mobile robots. This chapter introduces the basic concept and an
overview of the research areas concerning the work carried out in this thesis. In the first part
background information and motivation of research has been discussed and the aims and
objective of the research have been discussed in the second part. An outline of current research
work has been explained in the third part of this chapter.
1.1 Background and Motivation
Current research and development of mobile robot have attracted the attention of
researchers in the areas of engineering, computer science, biology, mining and others. Mobile
robots have a high potential in several applications. These include automatic freeway driving,
guidance of the blind and disabled, explorations of dangerous regions and mechanical parts
transfer in flexible assembly system. Progress in the field of mobile robot navigation has been
slower than might have been expected from the excitement and relatively rapid advances of the
early days of research. Systems where a robot is acting independently in complicated
surroundings have often been proven only in very limited trials, or have not produced actions
which could be thought of as particularly.
Autonomous mobile robots are intelligent agents which can perform desired tasks in
various (known and unknown) environments without continuous human guidance. Many kinds
of robots are autonomous to some degree. One important area of robotics research is to enable
the robot to cope with its environment whether this is on land, underwater, in the air,
underground or in space. A fully autonomous robot in the real world has the ability to:
¾ Gain information about the environment.
¾ Travel from one point to another point, without human navigation assistance.
¾ Avoid situations that are harmful to people, property or itself.
¾ Repair itself without outside assistance.
1
A robot may also be able to learn autonomously. Autonomous learning includes the ability to:
¾ Learn or gain new capabilities without outside assistance.
¾ Adjust strategies based on the surroundings.
¾ Adapt to surroundings without outside assistance.
Autonomous mobile robotics is a challenging research topic for several reasons. First, a
mobile robot should able to identify features, detect obstacles, patterns and target, learn from
experience, find a path and build maps, and navigate. These abilities of mobile robot require the
simultaneous application of many research disciplines (e.g. Engineering and computer science).
Secondly, autonomous mobile robots are the closest approximation of intelligent agents.
For centuries people have been interested in building machines that can think and make
decisions based on the environment around them. To satisfy this goal mobile robotics research
has increasingly incorporated artificial intelligence enabling the machines to mimic living
beings.
Thirdly, there are many applications for mobile robots. Transportation, surveillance,
inspection, cleaning and entertainment, military operations in complex hazardous
environments, hostile environments such as Mars trigger even more unusual locomotion
mechanisms, are just some examples. Other commercial robots operate not where humans
cannot go, but rather share space with humans in human environments. These robots are
compelling not for reasons of mobility but because of their autonomy, and so their ability to
maintain a sense of position and to navigate without human intervention is paramount.
The design of mobile robots involves the integration of many different bodies of
knowledge. To solve locomotion problems, the mobile robot must understand mechanism and
kinematics, dynamics and control theory. Localization and navigation demand knowledge of
computer algorithms, information theory, artificial intelligence, and probability theory. A
general control scheme of autonomous mobile robot system has been illustrated in Fig.1.1.
To be sure, some form of high-level control is required to ensure that the robots do not
harm any humans being or equipment or other robots. In effect, this high level of control
implies an implementation of Asimov’s laws (1950).
2
Goal command
Position
global map
Cognition Path
planning
Path
Environment model local map
Path
Execution
Actuator
Raw data
Sensors
Action
Motion control
Information
extraction
Perception
Knowledge base
Localization
Map Building
Real World
Environment
Figure 1.1. General control scheme of autonomous mobile robot system.
After introducing the original three laws, Asimov detected as early as 1950, a need to
extend the first law, which protected individual humans, so that it would protect humanity as a
whole. Thus, his calculating machines “have the good of humanity at heart through the
overwhelming force of the First Law of Robotics. The revised set of laws is shown in the
sidebar. There is a law that is greater than the First Law: “A robot may not injure humanity, or
through inaction, allow humanity to come to harm”.
Path analysis and planning is another exciting challenge in building autonomous mobile
robots. An autonomous robot must be able to learn its environment and programming itself
without assistance. It consists on finding a route from the origin of the robot to its target
destination. Path analysis and planning becomes more difficult when some static as well as
dynamic obstacles are added to the environment. When this occurs, it is necessary to find an
alternative route. This implies a process of adaptation to the environment. In addition to
avoiding collision, the other requirements are smoother motion, shorter traveling time, or more
clearance from the obstacle. Therefore, the path analysis and planning involves optimization
with respect to certain performance measures.
3
1.2 Aims and Objectives of this Research
The goal of autonomous mobile robotics is to build and control physical systems which
can move purposefully and without human intervention in real-world environments which have
not been specifically engineered for the robot. The development of techniques for autonomous
mobile robot operation constitutes one of the major trends in the current research and practice
in modern robotics. When we visit an unfamiliar place, like a new building, shopping mall or
theme park, we look for guiding information to guide us to our destinations in mind. This thesis
contributes towards design and development of control techniques those enables the robot to
navigate in a real world environment, avoiding static and dynamic obstacles especially in
crowded and unpredictably changing environment. The robot explores in the environments and
identifies human understandable guiding clues to find a way to the assigned destination. The
aim of this research is to idealize an existing autonomous mobile robot, on all levels. This
includes the kinematics, perception, cognition, sensor fusion, path analysis, path planning and
navigation. The following reactive behaviours are required to train the mobile robots to make
them capable of intelligent motion. The following behaviours are required during navigation of
mobile robots.
1.
Obstacle avoidance behaviour, so that the mobile robot able to avoid collisions with both
static obstacles and dynamic obstacles in various environments.
2.
Wall following behaviour, so that mobile robot cannot trap in loop as the mobile robot
detects an obstacle in the front while the target tracking control mode is on operation.
3.
Target searching behaviour, so that mobile robot quickly moves towards the target if there
are no obstacles around the robot.
Another objective is to determine the shortest path from the origin of the robot to its target
destination. Methods for finding the shortest path, even through obstacles, have traditionally
been based on one of several models, including static obstacles and moving obstacles. This
thesis purposes alternative ways for determining the best route a mobile robot can follow in any
environment from its origin to its target destination with the aim to reach a specified target. The
objective of a kinematic controller is to follow a trajectory described by its position and
velocity profiles as function of time. Many researchers have studied kinematic behaviour and
4
provided some adequate solutions for (kinematic) motion control of a mobile robot system.
Most of controllers of mobile robot are not considering the dynamics of the system.
If the robot is kinematical stable then another challenge is to design an intelligent
controller which may provide a general, robust, safe and optimised path so that mobile robot
navigate in real world dynamic environment. To design an intelligent controller fuzzy logic and
neural network play vital role. This is due to the fact that fuzzy if-then rules are well suited for
capturing the imprecise nature of human knowledge and reasoning processes. Fuzzy logic
modeling is primarily based on fuzzy sets and fuzzy if-then rules proposed by Zadeh (1965)
[55] which are closely related to perception and cognitive science. On the other hand the neural
networks tackle the same problems with a different strategy. The neural network is equipped
with a remarkable learning capability such that a desired input output mapping can be
discovered through learning by examples. These two innovative modeling approaches share
some common characteristics such as i) they assume parallel operations, ii) they are well
known for their fault tolerance capabilities and iii) they are often called model free modeling
approaches. As a result many researchers are trying to integrate these two schemes to generate
hybrid models that can take advantage of the strong points of both. This is also the motivation
for proposed research which aims at providing an integrate framework capable of using both
neural networks and fuzzy inference systems. This thesis also proposes two integrated models
Adaptive Neuro-Fuzzy Inference System (ANFIS) and Human Perception Based Heuristic Rule
Base Neural Network (HRBN). These purposed approaches are appropriate for designing of
intelligent controller. Petri nets model has been used to avoid inter collision among multiple
robots in purposed thesis.
A ROBNAV software using C++ has been developed to demonstrate the simulation test
(Appendix-A). NITR (Appendix-C.1) (developed and design in the laboratory), Khepera-II
(Appendix-C.2), Khepera-III (Appendix-C.3), and Koala (Appendix-C.4) mobile robots has
been used to obtained experimental results. A series of simulations and experimental results
shows the effectiveness of the proposed control scheme and the robustness of the fuzzy, neural,
ANFIS (Adaptive Neuro Fuzzy Inference System) and HRBN (Heuristic Rule Base Neural
network) controllers. This research is devoted to the design and development of some control
techniques for navigational path analysis of mobile robot in various environments.
5
1.3 Outline of the Research Work
The processes as outlined in this thesis are broadly divided into eight chapters. Following
the introduction, Chapter 2 provides a state of the art review of navigation, kinematics analysis,
fuzzy logic controller, neural controller, adaptive neuro-fuzzy controller and heuristic rule base
neural controller of mobile robot.
In Chapter 3 analyses the kinematics of mobile robots. A wheeled mobile robot is
considered for the kinematic analysis. It explains how a desired trajectory can be obtained
using kinematic stability during navigation.
Chapter 4 defines the concept of the fuzzy logic and outlines the methodology used to
design an intelligent fuzzy logic controller which enables the mobile robot to navigate
successfully in real world environment.
Chapter 5 discusses the neural network technique being used for navigation of mobile
robots. In Chapter 6 Navigation of mobile robots using Adaptive Network based Fuzzy
Inference System (ANFIS) has been described.
In Chapter 7 Human Perception Based Navigation control of Heuristic Rule Base Neural
network (HRBN) controller for mobile robot has been discussed. In Chapter 8 a detailed report
of results and discussion has been given. This chapter summarises the findings of all chapters
discussed before.
Finally in Chapter 9 conclusions of this research and future directions for further
investigation has been discussed.
The paper published related to the chapter has been listed in the last section of the chapter.
6
2 Literature Review
This chapter reviews the work related to the development of navigational path analysis and
planning of mobile robot in various environments. The progress made in past decades in the
field of navigational path analysis of mobile robot and techniques used to design the intelligent
controller has been described. This chapter presents a literature review of past and recent
developments in area of kinematics analysis and artificial intelligence techniques used for
navigation of mobile robots.
2.1 Introduction
A significant amount of research has been published in many aspects related to mobile
robots. A literature review cannot simply be a catalog of all the articles published on a subject,
the list would be much too long and could not be include each contribution. The alternative is
to include in this chapter only those contributions that cover to kinematics stability of mobile
robots which provides desired trajectory and artificial intelligence technique that helps to
design an intelligent controller for robot. A large number of researchers have used kinematic
models to develop motion control strategy for mobile robots. The ultimate goal of mobile
robotics research is to endow the robots with high intellectual ability, of which navigation in an
unknown environment is achieved by using on line sensory information. It summarizes the past
work, mostly in computational geometry and robotics, and discusses possible directions for
research.
Another challenge in literature review is that even the perception of what constitutes
progress varies widely in the research community. The representations would be difficult to
extend other scenarios where a robot may need to seek out optimal path and track the target in
the competing clutter environment on the basis of their semantic significance. Despite these
challenges, the next sections review in this article and highlights some of the more interesting,
important and experimental milestones. This chapter provides details survey report within
important aspects of what the researchers have worked in the area of navigational path analysis
and planning for mobile robot using fuzzy logic, neural network, adaptive neuro-fuzzy and
heuristic rule base neural network technique.
7
2.2 Navigation of Mobile Robots
The development of techniques for autonomous navigation in real-world environments
constitutes one of the major trends in the current research on robotics. One of the main
problems in mobile robot navigation is the determination of the robot position [1]. An
important problem in autonomous navigation is the need to cope with the large amount of
uncertainty that is inherent of natural environments [2]. Navigation of mobile robot is an active
area of research with many potential military and civilian applications. Yet, there are many
unsolved problems which probably either need a breakthrough in the current theories or a
completely new approach for the solution. Extraordinary abilities of humans in doing these
tasks without any measurement have inspired many researchers [3]. Navigation for mobile
robots can be well-defined in mathematical (geometrical) terms. It also involves many distinct
sensory inputs and computational processes. Elementary decisions like turn left, or turn right,
or run or stop is made on the basis of thousands of incoming signals [3-6]. Thus it is necessary
to define what navigation is and what the function of a navigation system? Navigation is
traditionally defined as the process of determining and maintaining a trajectory to a goal
location [5]. Biological navigation behaviours have been an important source of inspiration for
robotics in the past decade. According to Levitt and Lawton [7], navigation consists of
answering three questions: (a) “Where am I?” (b) “Where are other places with respect to me?”
and (c) “How do I get to other places from here?” However, biological systems do not
necessarily require all that knowledge to navigate, but they usually work on a “how do I reach
the goal?” basis. Most systems typically deal with different degrees of knowledge depending on
the circumstances. Navigation can be classified as two broad group indoor and outdoor
navigations.
2.2.1 Indoor Navigation
From the pioneering robotic vehicle work by Giralt et al. [8] in 1979, and later by
Moravec [9] in 1983, and Nilsson [10] in 1984, it became clear that, implicitly or explicitly,
meant for navigation to incorporate within it some knowledge of what the computer was
supposed to see. When sequences of images were used to represent space, the images taken
8
during navigation were submitted to some kind of appearance-based matching between the
perception and expectation. All of these and subsequent efforts fall into three broad groups.
¾
Map-Based Navigation: Map-Based Navigation is the systems that depend on user-
created geometric models or topological maps of the environment. In this method information
acquired from the robot's onboard sensors is compared to a map or world model of the
environment [11]. If features from the sensor-based map and the world model map match, then
the vehicle's absolute location can be estimated [12].
¾
Map-Building-Based Navigation: Map-Building-Based Navigation is the systems that
use sensors to construct their own geometric or topological models of the environment and then
use these models for navigation [13].
¾
Map less Navigation: Map less Navigation is the systems that use no explicit
representation at all about the space in which navigation is to take place, but rather resort to
recognizing objects found in the environment or to tracking those objects by generating
motions based on visual observations [14].
2.2.2 Outdoor Navigation
Outdoor Navigation usually involves obstacle-avoidance, landmark detection, map
building updating, and position estimation. Outdoor navigation can still be divided into two
classes according to their level of structure of the environment.
¾
Structured environment: Structured environment first reported in the literature is by
Tsugawa et al. [15] for a car that could drive autonomously. The navigation relied mostly on
obstacle avoidance. In general, outdoor navigation in structured environments requires some
sort of road-following. Road-following means an ability to recognise the lines that separate the
lanes or separate the road from the berm, the texture of the road surface, and the adjoining
surfaces etc. [16].
¾
Unstructured environment: An outdoor environment with no regular properties that
could be perceived and tracked for navigation may be referred to as unstructured environment
[17]. In such a situation the vision system can make use of at most a generic characterization of
the possible obstacles in the environment.
9
Reactive-based approaches are widely used in autonomous navigation. However, in
complex unknown environments, pure reactive-based navigation still poses a few challenges
since it can be easily trapped by a local minimum and may produce some extra maneuvers [18].
During the last decade, the research communities in mobile robotics have paid lot of attentions,
to the development of different control architectures for navigation of mobile robots. For this,
mainly two principle designs have been adopted. One is called the functional or horizontal
decomposition, Fig. 2.1; the other is the behavioural or vertical decomposition, Fig. 2.2. It is
found that the research for navigation of mobile robot has to be modified in many terms. Robot
localization with multiple sensors using interval analysis deals with the robot localization
problem in a nonlinear and global way and bypasses the data association step [19]. Research
may be done in finding out the optimal navigation technique for several mobile robots.
Technical details may be found out to achieve various interactive perceptions (e.g.
communications) between the robots and to recognise the obstacle ahead. Using the
environment information obtained at each instant of time‘t’, a strategy may be adopted
permitting the robot to reach the target position. At the same time, the robot should avoid the
different obstacles situated in the robot work place. The intelligent control provides conflict-
SENSING
MOTOR
EXECUTION
PLANNING
MODELLING
PERCEPTION
free shortest path, minimum time motion planning and deadlock avoidance [20].
ACTION
ENVIRONMENT
Figure 2.1.Flow diagram of the horizontal decomposition method for robot navigation.
10
BUILDING MAP
EXPLORE
WANDER
AVOID OBSTACLE
SENSING
ACTION
ENVIRONMENT
Figure 2.2.Flow diagram of the vertical decomposition method for robot navigation.
Keeping in view of the various research publications in the recent years in this field,
attempt has been made to summarise the various navigation techniques for mobile robots. For
reviewing the approaches for navigation of mobile robots, the investigation has been divided
into five main segments. In the first part effort has been made to find out the kinematic stability
of mobile robot. The next part mainly deals with various controllers being used for navigation
of mobile robot. These controllers are classified into four divisions as Fuzzy Logic Controller
(FLC), Neural Controller (NC), Adaptive Neuro Fuzzy Controller (ANFC) and Heuristic Rule
Base Network (HRBN) controller. The next section review the published paper in the area of
kinematics of mobile robot as well as techniques used in this thesis for navigation of mobile
robots.
2.3 Kinematics of Mobile Robot
This section provides a detailed survey report of kinematics of mobile robot. With
reference to the unicycle kinematics, this part review several control strategies for trajectory
tracking and posture stabilization in an environment free of obstacles. A kinematic
methodology is the first step towards achieving these goals.
11
Mobile robots are more energy efficient than legged or treaded robots on hard, smooth
surfaces, and will potentially be the fist to find widespread application in industry, because of
the hard, smooth plant floors in existing industrial environments [21]. Several mobility
configurations can be found in the applications as mentioned by Jones et al. [22]. The most
common for single-body robots are differential drive and synchro drive tricycle or car-like
drive, and omnidirectional steering [23]. Beyond the relevance in applications, the problem of
autonomous motion planning and control of mobile robot has attracted the interest of
researchers in view of its theoretical challenges [24]. The motion control of wheeled mobile
robots has drawn considerable attention over the past few years. The nonholonomic behaviour
in robotic systems is particularly interesting, because it implies that the mechanism can be
completely controlled with a reduced number of actuators. In particular, these systems are a
typical example of nonholonomic mechanisms due to the perfect rolling constraints on the
wheel motion [25]. Several controllers were proposed for mobile robots with nonholonomic
constraints, where the two main approaches to controlling mobile robots are posture
stabilization and trajectory tracking.
The aim of posture stabilization is to stabilize the robot to a reference point, while the aim
of trajectory tracking is to have the robot follow a reference trajectory. For mobile robots
trajectory tracking is easier to achieve than posture stabilization [26]. Path planning and
motion-planning involve finding a continuous path and trajectory, respectively, from the initial
position to the final position that avoids obstacles in the environment. The feedback
stabilization at a given posture cannot be achieved via smooth time-invariant control [27]. This
indicates that the problem is truly nonlinear; linear control is ineffective, even locally, and
innovative design techniques are needed. The motion control problem of wheeled mobile
robots in environments without obstacles with reference to the popular unicycle kinematics, the
dynamic feedback linearization is an efficient design tool leading to a solution simultaneously
valid for both trajectory tracking and set point regulation problems [28]. After a preliminary
attempt at designing local controllers, the trajectory tracking problem was globally solved in by
using a nonlinear feedback action [29]. A recursive technique for trajectory tracking of
nonholonomic systems in chained form can also be derived from the back stepping paradigm
[30]. As for posture stabilization, both discontinuous and time-varying feedback controllers can
be used. Smooth time-varying stabilization was pioneered by Samson [31], while discontinuous
12
control has been used in various forms [32] where dynamic feedback linearization has been
extended to the posture stabilization problem. Dynamics of wheeled mobile robots are
nonholonomic and pose is challenging problems for control design and stability analysis [33].
Under output-tracking control laws the dynamics can be formulated in terms of full-state
tracking errors which offers some properties that allow better understanding of the internal and
zero dynamics of the tracking-error system and more insights to the trajectory tracking stability
[34]. An ideal automatic driving control system should be able to comply with changes in slip
conditions so as to optimise the control performance.
Trajectory tracking is more natural for mobile robots. Usually, the reference trajectory is
obtained by using a reference robot; therefore, all the kinematic constraints are implicitly
considered by the reference trajectory [35]. A generic kinematic control, which is directly
applicable to any type of wheeled mobile robot, proposed by Gracia et al. [36]. The neural
kinematic controller is applied to compensate the uncertainties in the kinematic parameters of
the mobile robot. To analyze the stability of a general class of mobile robot path-tracking
algorithms taking into account explicitly the computation and communication delays in the
control loop. The delay problem can be solve directly the transcendental characteristic equation
that appears when the time delay is considered. This is applicable for straight paths and paths of
constant curvature [37]. The global stability of the neural network is guaranteed by qualitative
analysis and the Lyapunov stability theory [38]. Fierro and Lewis [24] developed an artificial
neural network-based controller by combining the feedback velocity control technique and
torque controller, using a multilayer feed forward neural network. But the controller structure
and the neural network-learning algorithm are very complicated and it is computationally
expensive [39]. The control approach for the mobile robot has the properties to quickly drive
the position error to zero and to indicate better smooth movement in the tracking control
process. These features are due to continuous online learning and adaptive capability of analog
neural networks [40]. The dynamic wave expansion neural network for path generation in a
dynamic environment for mobile robots is parameter-free, computationally efficient, and its
complexity does not explicitly depend on the dimensionality of the configuration space [41].
The autonomous navigation wheeled robots requires integrated kinematic and dynamic
control to perform trajectory tracking, path following and stabilization. The coupling effect
13
between linear and angular motion dynamics is considered in the fuzzy steering by building
appropriate linguistic rules [42]. A fuzzy logic approach can be used in order to minimise the
position and orientation errors caused by odometric problems. The fuzzy logic maps the inputs
heading and distance errors determined by the odometry readings to the outputs of translational
and rotational speed of the mobile robot [43]. Fuzzy inference mechanism extended that
compensation for environmental perturbations as variable friction. A fuzzy-neural control
algorithm realizes the obstacle avoidance of the mobile robot. Using the self location function,
the mobile robot could locate itself in a world coordinate system [44]. This indicates that the
problem is truly nonlinear; linear control is ineffective, even locally, and innovative design
techniques are needed. The existing approaches of sensor-based motion planning tend to deal
solely with kinematic and geometric issues, and ignore the system dynamics. Any nonlinear
optimal control requires a solution to a two-point-boundary-value problem that is salvable only
by numerical iteration. Consequently, an improved control can he obtained by modifying the
suboptimal control in such a way that the distance aforementioned is minimised as much as
possible in closed form [45]. The sensor with classical rangefinders allows the use of
practically unmodified Monte Carlo algorithms, with the additional advantage of being able to
easily detect occlusions caused by moving obstacles [46]. An iterative learning rule with both
predictive and current learning terms is used to overcome uncertainties and the disturbances in
the system [47].
The problem of terrain acquisition presents a special case of robot motion planning. The
harmonic drive system for non-linear controller to compensate for kinematic error in the
presence of flexibility in high-speed regulation and trajectory tracking application has been
proposed by Gandhi et al. [48]. In it, a robot that operates in an unfamiliar scene populated with
a finite number of objects of unknown shapes and dimensions is asked to cover the scene and
build its complete map using some sort of sensory feedback and generating as short a path
during operation as possible [49]. The behaviour of space robots with torque and attitude
controller has been discussed by Pathak et al. [50]. A dynamical local path-planning algorithm
of an autonomous mobile robot available for moving obstacle avoidance as well as stationary
obstacle avoidance using artificial pressure and nonlinear friction [51]. A receding horizon
controller is may used for tracking control of wheeled mobile robots subject to nonholonomic
constraint in the environments without obstacles. The control policy is derived from the
14
optimization of a quadratic cost function, which penalizes the tracking error and control
variables in each sampling time [52]. This methods, improve the domain of applicability of a
wide range of obstacle avoidance methods [53]. Basically, both trajectory tracking and posture
stabilization controllers can be implemented with on-board computing power.
2.4 Fuzzy Logic Controller for Mobile Robot
Fuzzy Logic technique plays an important role to design the intelligent controller for
mobile robot. This technique can be used for navigation of mobile robots. Fuzzy set theory
provides a mathematical framework for representing and treating uncertainty in the sense of
vagueness, imprecision, lack of information and partial truth. Fuzzy control systems employ a
mode of approximate reasoning that resembles the decision-making process of humans. A
fuzzy system is usually designed by interviewing an expert and formulating the implicit
knowledge of the underlying process into a set of linguistic variables and fuzzy rules. In
particular for complex control tasks, obtaining the fuzzy knowledge base from an expert is
often based on a tedious and unreliable trial and error approach [54]. Fuzzy set theory was
introduced by Lofti Zadeh in the mid sixties. In 1965 Lotfi Zadeh proposed fuzzy set theory,
and published a paper [55]. Fuzzy logic has been applied to diverse fields, from control theory
to artificial intelligence. This section presents a variety of fuzzy logic techniques which address
the challenges posed by autonomous robot navigation.
Autonomous mobile robot navigation in uncertain and dynamic environments demands
adaptation and perception capabilities. Reactive control strategies imply a strong dependency
on sensed information about the robot’s environment. Thus, imprecision and uncertainties in
perception from sensors have to be considered [56]. While the rules are based on qualitative
knowledge, the membership functions defining the linguistic terms provide a smooth interface
to the numerical process variables and the set-points [57]. Stability analysis of fuzzy systems is
a very important research field in fuzzy systems practically from the pioneer work of E.H.
Mamdani on fuzzy control applications [58]. A Mamdani controller is usually used as a
feedback controller. Since the rule base represents a static mapping between the antecedent and
the consequent variables, external dynamic filters must be used to obtain the desired dynamic
behaviour of the controller [59]. The control protocol is stored in the form of if-then rules in a
rule base which is a part of the knowledge base. While the rules are based on qualitative
15
knowledge, the membership functions defining the linguistic terms provide a smooth interface
to the numerical process variables and the set-points [60]. Intelligent control plays an important
role when employing mobile robots in unstructured, unknown, and dynamic environments. The
task complexity of intelligent control is greatly reduced by dividing the overall task into
subtasks. These subtasks are modeled as perception-action units, called behaviours. The
reduced task complexity in a behaviour-based approach increases responsiveness to
environmental dynamics [61]. Systems equipped with fuzzy logic controllers give rise to
nonlinear dynamic systems. This theory provides an overall perspective on the behaviour
modes of the system, which can be used as a guide for the search of concrete behaviours [62].
Fuzzy systems belong to the family of nonlinear systems and they can have, in general, a
complex analytical description [63]. It is not easy and time consuming for human experts to
examine all the input-output data from a mobile robot to find a number of proper rules for a
fuzzy controller. To copy with this difficulty, an intelligent mobile robot with automatic fuzzy
controller design approaches is necessary [64]. It should also be noticed that although the
operating range of the input is restricted by the saturation, the range of the other system
variables cannot be bounded. This is in fact the cause of the troubles with the nonlinear nature
of the saturation [65]. In this context, fuzzy logic is often adopted to overcome the difficulties
of modeling the unstructured, dynamically changing environment, which is difficult to express
using mathematical equation [66]. A class of fuzzy control laws can be formulated using the
Lyapunov’s direct method, which can guarantee the convergence of the steering errors [67].
The fuzzy controller can be optimised by using the schema co-evolutionary algorithm, which
finds an optimal solution [68]. The main problem in fuzzy control involves the design of the
fuzzy knowledge base. Various approaches to this problem have been proposed, including trial
and error. For a mobile robot to intermesh navigation in various environments using fuzzy logic
controller shown in Fig.2.3 represents significant progress for the entire research community.
In Fig.2.3,
Left-obs = Left obstacle distance, Right-obs = Right obstacle distance, Front-obs = Front
obstacle distance, Tar-ang= Target angle, Left-v = velocity of left wheel, Right-v = velocity of
right wheel and Med= Medium.
The fuzzy rules are if-then rule as: If (Antecedent) Then (consequent).
16
Inputs
Fuzzyfy
Front-obs
Left-obs
Right-obs
Tar-ang
Fuzzyfication
Interface
Module
Knowledge base
Fuzzy Interface
Engine
Fuzzy Rule Base
or Data Base
Defuzzyfy
Outputs
Defuzzyfication
Interface
Module
Left-v
Right-v
Figure 2.3. Schematic diagram of the fuzzy logic controller for mobile robot.
An adaptive-resonance theory based fuzzy controller, including an adaptive-resonance
theory based environment recogniser, a comparer, combined rule bases, and a fuzzy inferring
mechanism, is introduced for the purpose of the adaptive navigation of the quadruped robot
[69]. The adaptive fuzzy logic control based on physical properties of wheeled inverted
pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to
approximate the unknown dynamics [70]. Fuzzy adaptive extended information filtering is to
improve estimation accuracy and robustness for the localization system, while the system lacks
sufficient information of complete models or the process and measurement noise varies with
time [71]. The unmanned control of the steering wheel is, at present, one of the most important
challenges facing researchers in autonomous vehicles within the field of intelligent
transportation systems [72]. Once this control architecture has been implemented, installed, and
tuned, the resulting steering maneuvering is very similar to human driving, and the trajectory
errors from the reference route are reduced to a minimum. In the controller a rule base of
positive rules can be specified by an expert for directing the vehicle to the target in the absence
of obstacles, while a rule base of negative rules can be experimentally determined from expert
operation of the vehicle in the presence of obstacles [73].
Fuzzy logic system promises an efficient way for obstacle avoidance. However, it is
difficult to maintain the correctness, consistency, and completeness of a fuzzy rule base
constructed and tuned by a human expert. Reinforcement learning method is capable of
learning the fuzzy rules automatically [74]. Martinez et al. [75] have considered a problem
which is consisted of achieving sensor based motion control of mobile robot among obstacles
17
in structured and unstructured environments with collision-free motion. Sensor-based
navigation method, which utilised fuzzy logic and reinforcement learning for navigation of
mobile robot in uncertain environments, has been proposed by Boem et al. [76] they have
discussed about the navigation of mobile robot using fuzzy logic.
The concepts of car maneuvers, fuzzy logic control, and sensor-based behaviours are
merged to implement the human-like driving skills by an autonomous car-like mobile robot.
Four kinds of Fuzzy logic controller, fuzzy wall-following control, fuzzy corner control, fuzzy
garage-parking control, and fuzzy parallel-parking control, are synthesized to accomplish the
autonomous fuzzy behaviour control [77]. The architecture for the fuzzy controller is a
hierarchical scheme which combines seven modules working in series and in parallel [78]. The
scaling factors and the coefficients of the sliding surface for the control of the steering angle
and forward–backward velocity of a car-like mobile robot are adopted by that for the control of
two motors [79]. Wang [80] has used fuzzy systems to model higher levels of hierarchical
systems and design controllers for the hierarchical systems. Seraji’s [81] paper presents a new
strategy for behaviour- based navigation of field mobile robots on challenging terrain. Outdoor
environments are particularly challenging for mobile robots as they offer dynamic,
unstructured, and highly variable situations where the inconsistency of the terrain, the
irregularity of the product, and the open nature of the working environment result in complex
problems of identification, modeling, sensing, and control [82].
One important problem in autonomous robot navigation is the effective following of an
unknown path traced in the environment in compliance with the kinematic limits of the vehicle,
i.e., bounded linear and angular velocities and accelerations. In this case, the motion planning
must be implemented in real time and must be robust with respect to the geometric
characteristics of the unknown path, namely curvature and sharpness [83]. The stabilizing
controller is designed as a state optimal controller and second application is the optimization
method applied to the design of a fuzzy controller for vision-based mobile robot navigation
[84]. The fuzzy error correction control system can be used to navigate a robot along an easily
modifiable path in a well-structured environment. The fuzzy engine gives outputs commands
for the robot wheels. These commands determine the necessary angle of rotation to correct the
direction of travel in order for the robot to remain on the path [85]. Das et al. [86] have
18
assumed a control structure that makes possible the integration of a kinematic controller and an
adaptive fuzzy controller for trajectory tracking for nonholonomic mobile robots. The hybrid
controller is able to choose a better position according to the circumstances encountered [87].
The information about the global goal and the long-range sensory data are used by the first
layer of the planner to produce an intermediate goal, referred to as the way-point that gives a
favorable direction in terms of seeking the goal within the detected area. The second layer of
the planner takes this way-point as a sub goal and, using short-range sensory data, guides the
robot to reach the sub goal while avoiding collisions [88]. Designing the controller on account
of nonholonomic constraints gain more accurate position and velocity control, a self-organized
fuzzy controller can be used to find solutions of optimal fuzzy input and output membership
functions [89] and to determine a rule base process.
The fuzzy multi sensor data fusion scheme provides a novel mechanism to efficiently
integrate task scheduling, action planning and motion control in a unified framework. The
theoretical development of a complete navigation problem of an autonomous mobile robot is
the situation for which the vehicle tries to reach the endpoint is treated using a fuzzy logic
controller [90]. An efficient design methodology that allows starting with any kind of fuzzy
controller and subsequently transforming it until a system suitable for easy digital signal
processing implementation is obtained [91]. Navigation based on processing some analog
features of Radio Frequency Identification signal is a promising alternative to different types of
navigation methods in the state of the art. The main idea is to exploit the ability of a mobile
robot to navigate a priori unknown environments without a vision system and without building
an approximate map of the robot workspace, as is the case in most other navigation algorithms
[92]. In the soccer game strategy Radio Frequency data transmitter is used to communicate
among robot [93]. The development of the controllers is carried out by means of a
reconfigurable platform based on field-programmable gate arrays. This platform combines
specific hardware to implement fuzzy inference modules with a general-purpose processor, thus
allowing the realization of hybrid hardware/software solutions [94]. The merger method is
applied to fuzzy rule base simplification by automatically replacing the fuzzy sets
corresponding to a given cluster with that pertaining to cluster prototype [95]. Target tracking
requires team coordination to maintain a desired formation and to keep team-mates and target
together. Generally, distributed autonomous systems using multiple robots are considered
19
superior to others in terms of reliability, expandability, and flexibility. In contrast to a single
robot system; they provide increased robustness by taking advantage of inherent parallelism
and redundancy. Moreover, the versatility of a multi-robot system can provide the
heterogeneity of structures and functions required to undertake different missions in unknown
environmental conditions [96]. Research in autonomous multi-robot systems often focuses on
mechanisms to enhance the efficiency of the group through some form of cooperation among
the individual agents. One of the greatest challenges in robotics is to create machines that are
able to interact with unpredictable environments in real time [97]. Intriguingly, a similar
relationship between group size and efficiency has been documented in social robots.
2.5 Neural Controller for Mobile Robot
The human brain is very complex, nonlinear and parallel computer. There are billions of
neurons and trillions of connections between them. The interest in neural network stems from
the wish of understanding principles leading in some manner to the comprehension of the basic
human brain functions, and to building the machines that are able to perform complex tasks.
Neural network theory revolves around the idea that certain key properties of biological
neurons can be extracted and applied to simulations, thus creating a simulated brain. There is a
significant interest in autonomous mobile robots which may be defined as vehicles that are
capable of intelligent autonomous navigation.
Robots must be able to understand the structure of the environment [98]. To reach their
targets without collisions, the robots must be endowed with perception, data processing,
recognition, learning, reasoning, interpreting, and decision-making and action capacities. A
first wave of interest in neural networks emerged after the introduction of simplified neurons by
McCulloch and Pitts in 1943 [99]. In 1949 Hebb [100] formed the basis of ‘Hebbian learning’
which is now regarded as an important part of neural networks theory [101]. About this time of
neural network development, the digital computer became more widely available and its
availability proved to be of great practical value in the further investigation of neural networks
performance. Rosenblatt [102] constructed neuron models in hardware during 1957. These
models ultimately resulted in the concept of the Perceptron. This was an important
development and the underlying concept is still in wide use today. Widrow and Hoff [103]
were responsible for simplified artificial neuron development. When Minsky and Papert
20
published their book Perceptrons in 1969 [104] in which they showed the deficiencies of
perceptron models, most neural network funding was redirected and researchers left the field.
If human understand how an animal controls its behaviour, and comparable technology is
available, it should be possible to build a robot that behaves the same way. Recent advances in
both knowledge and technology have begun to make this possibility a realistic aim in
invertebrate neuroscience [105-107]. Neural circuit are capable of producing coordinated
patterns of high-dimensional rhythmic output signals while receiving only simple, lowdimensional, input signals [105]. There are now a growing number of studies in which
hypotheses for the behavioural function of neural circuits are tested by implementing them as
controllers for robots and evaluating the robot behaviour [108]. An artificial neural network is a
mathematical model or computational model that tries to simulate the structure and/or
functional aspects of biological neural networks [109]. It consists of an interconnected group of
artificial neurons and processes information using a connectionist approach to computation
[110]. They can be used to model complex relationships between inputs and outputs or to find
patterns in data [111]. However, generally, the evolved neural controllers could be fragile in
inexperienced environments, especially in real worlds, because the evolutionary optimization
processes would be executed in idealized simulators. This is known as the gap problem
between the simulated and real worlds. To overcome this, Kondo [112] has focused on an
evolving on-line learning ability instead of weight parameters in a simulated environment.
Basically, the control of a robot arm and the control of a mobile robot is similar the controller
[113]. First plans a path, the path is transformed from Cartesian domain to the joint or wheel
domain using the inverse kinematics of the system and finally a dynamic controller takes care
of the mapping from set points in this domain to actuator signals. However, in practice the
problems with mobile robots occur more with path-planning and navigation than with the
dynamics of the system. Recently, a new paradigm of cognitive science has been emerged
[114]. The hallmark of this new approach is the focus on the situated and embodied nature of
intelligence. Research in so-called behaviour-based artificial intelligence [115], embodied
neurobiology, and embodied cognitive science [116] has challenged the traditional view
according to which intelligence is an abstract, symbolic process independent of physical
implementation. The artificial life approach to evolutionary robotics is used as a fundamental
framework for the development of a modular neural control of autonomous mobile robots
21
[117]. The applied evolutionary technique is especially designed to grow different neural
structures with complex dynamical properties. This is due to a modular neuro dynamics
approach to cognitive systems, stating that cognitive processes are the result of interacting
dynamical neuro-modules [118]. Relevant brain centers, known as Mushroom Bodies and
Central Complex were recently identified in insects: though their functional details are not yet
fully understood, it is known that they provide secondary pathways allowing the emergence of
cognitive behaviours [119]. In recent years, mobile robots have been required to become more
and more autonomous in such a way that they are able to sense and recognise the threedimensional space in which they live or work [120]. Werbos et al. [106] have reviewed the
empirical results which fit the theory, and suggested important new directions for research,
within the scope of NSF's recent initiative on cognitive optimization and prediction.
The purpose of the learning rule is to train the network to perform some task. There are
many types of neural network learning rules [121]. They fall into three broad categories:
supervised learning, unsupervised learning and reinforcement learning. The mobile robot
navigation deals with application of back propagation algorithm in both, supervised and
reinforcement learning approaches [122]. A hybrid approach for the autonomous motion
control of robots in cluttered environments with unknown obstacles is introduced by Maravall
et al. [123]. Decision making system is the most important part of the robot soccer system
[124]. As the environment is dynamic and complex, one of the reinforcement learning methods
is employed in learning the decision-making strategy. Nelson et al. [125] have described the
evolutionary training of artificial neural network controllers for competitive team a game
playing behaviours by teams of real mobile robots. A neural network based machine vision
system, which is intended to act as a reconfigurable inspection tool, for use in manufacturing
environments [126, 127]. Discriminative training is accomplished in a supervised manner,
using gradient-descent method. The approach is suitable for navigation and for map learning
[128]. Many current machine learning paradigms has been used for this purpose, however,
result in opaque models that are difficult, if not impossible to analyze, which is an impediment
in safety-critical applications or application scenarios where humans and robots occupy the
same workspace [129]. The hybrid architecture using band pass filtering, cross-correlation and
recurrent neural networks can be used to develop a robust, accurate and fast sound-source
localisation model for a mobile robot [130]. The new approach in robotic learning systems has
22
been proposed by Burgsteiner et al. [131]. It provides a method to use a real-world device that
operates in real time, controlled through a simulated recurrent spiking neural network for
robotic experiments. Robot path-planning techniques can be divided into two categories. The
first, called local planning relies on information available from the current 'viewpoint' of the
robot. This planning is important, since it is able to deal with fast changes in the environment.
The second situation is called global path-planning, in which case the system uses global
knowledge from a topographic map previously stored into memory. Although global planning
permits optimal paths to be generated [132], it has its weakness. Spiking neural networks [133],
as the third generation of artificial neural networks, have unique advantages and are good
candidates for robot controllers. In the controller the integrated-and firing model can be used
and the Spiking neural network is trained by the Hebbian learning algorithm [134]. The
transportation using wheels is one of the most popular transportation mechanisms for mobile
robots because of its high energy efficiency, simple mechanisms and well-investigated control
systems [135]. Wheel type mobile systems are the most popular transportation mechanisms
because the energy efficiency is high, the mechanism is simple and the control system is well
investigated [136]. On the other hand, the wheel type mobile robots have difficulties in rough
terrain movement. Perception and behaviour are usually considered to be separate processes.
Behavioural learning, however, forms associations between perception and action, organized
by reinforcement, without regard for the construction of perception [137]. The behaviour is
organized as a dynamic hierarchy of independent schemas [138]. An incremental evolution
method for neural networks based on cellular automata and a method of combining several
evolved modules by a rule-based approach [139].
The problems of trajectory following and posture stabilization of the mobile robot with
nonholonomic constraints can be solve with the recurrent neural network with one hidden layer
which is trained on-line by back propagation optimization algorithm with an adaptive learning
rate[140]. A direct modified Elman neural networks based decentralized controller is proposed
by Chen et al. [141] to control the magnet. The dynamic model with model uncertainties and
the kinematic model represented by polar coordinates are considered to design a robust control
system [142]. A dynamic collision-free trajectory generation in a non-stationary environment is
studied using biologically inspired neural network approaches [143].
23
Feed Forward Network
Context Unit Feedback Loop
Kohonen Network
Winner
Range Image
Figure 2.4. Schematic view of the neural networks used for the navigation of mobile robots,
the output of the Kohonen network is fed into the feed forward network as a regression.
Hierarchical approach to solving sensor planning for the global localization of a mobile
robot consists of two subsystems: a lower layer and a higher layer [144]. The lower layer uses a
particle filter to evaluate the posterior probability of the localization. The higher layer uses a
Bayesian network for probabilistic inference. Tani et al. [145] have presented a novel scheme
for sensory-based navigation of a mobile robot. They have shown that their scheme constructs a
correct mapping from sensory inputs sequences to the maneuvering outputs through neural
adaptation, such that a hypothetical vector field that achieves the goal can be generated (Fig.
2.4). In general, the main focus of the research on robot mapping has been on representing the
geometry of the environment with high accuracy [146]. Janet et al. [147] have discussed about
the neural network technique for navigation of mobile robot. They have used Kohonen and
region-feature neural networks for this purpose.
24
2.6 Adaptive Neuro-Fuzzy Controller for Mobile Robot
In the field of artificial intelligence, Neuro-Fuzzy refers to combinations of artificial neural
networks and fuzzy logic. Fuzzy systems have the ability to make use of knowledge expressed
in the form of linguistic rules, thus they offer the possibility of implementing expert human
knowledge and experience. Usually, tuning parameters of membership functions is a time
consuming task. Neural network learning techniques can automate this process, significantly
reducing development time, and resulting in better performance. Neuro-fuzzy hybridization
results in a hybrid intelligent system that synergizes these two techniques by combining the
human-like reasoning style of fuzzy systems with the learning and connectionist structure of
neural networks.
Traditional robot control methods rely upon strong mathematical modeling, analysis, and
synthesis. However, operations in unstructured environments, such as in remote planets and
hazardous waste sites, require robots to perform more complex tasks without an adequate
analytical model [148]. Fuzzy systems and neural-networks are widely used techniques in
intelligent systems [149, 150]. A fuzzy logic system has been designed with three behaviours,
target seeking, obstacle avoidance and wall following [151]. The main drawback of fuzzy
controller is the lack of a systematic methodology for their design. Usually, tuning parameters
of membership functions is a time consuming task [152]. On the other hand neural network
modeling is based on artificial neural networks which are motivated by biological neural
systems and learning techniques can automate this process, significantly reducing development
time, and resulting in better performance. Neural-networks are adaptive systems that can be
trained and tuned from a set of samples. Once they are trained, neural-networks can deal with
new input data by generalizing the acquired knowledge [153]. A learning algorithm based on
neural network techniques is developed to tune the parameters of membership functions, which
smoothes the trajectory generated by the fuzzy logic system [154]. Neural network modeling
does not rely on human expertise. Instead, it employs a learning procedure and a given training
data set to evolve a set of parameters such that the required functional behaviour is achieved.
Nevertheless, it is very difficult to extract and understand that knowledge [153]. However,
neural network has some disadvantages such as the local minimum points, the slow
astringency, and fuzzy systems have a drawback when applied to different applications.
25
Moreover, the rules are often very difficult or even impossible to be determined [149]. It should
be emphasized that the weights in a neural network with hard limiter as its activation function
do have physical meanings the weights of a given node represent the coefficients of the hyperplane [150]. That partitions the input space into two regions with different output values.
Mobile robot local path planning in an unknown and dynamic environment with
uncertainties is one of the most challenging problems in robotics [155]. For real time
autonomous navigation, the robot should be capable of sensing its environment, interpreting the
sensed information to obtain the knowledge of its position and the environment, planning a
real-time route from an initial position to a target with obstacle avoidance, and controlling the
robot direction and velocity to reach the target [155]. The hybridisation of neural and fuzzy
techniques generates neuro- fuzzy architecture and that provides human like reasoning. In this
connection Ng et al. [156] have proposed a neural integrated fuzzy controller, which integrates
the fuzzy logic representation of human knowledge with the learning capability of neural
networks, to save nonlinear dynamic control problems. The problem of autonomous navigation
applied to mobile robots has well defined as a search process within a navigation environment
containing obstacles and targets by Crestani et al. [157]. Rutkowski et al. [158] have derived
flexible neuro-fuzzy inference Mamdani-type systems and they have stated that it is more
suitable for approximation problems. A fuzzy logic controller has been used to control the
robot and has been improved by using three different neuro-fuzzy approaches by Hui et al.
[159]. Fifth-order polynomial reference paths for three different size parking dimensions can be
used to generate the training data to solve car-like mobile robot parking [160]. The autonomous
mobile robot uses infrared and contact sensors for detecting targets and avoiding collisions.
Truck backer-upper problem is a typical benchmark for many control methods in nonlinear
system identification [161]. The control system is organized in a top-bottom hierarchy of
various tasks and behaviours. Rusu et al. [162] have discussed a neuro-fuzzy controller for
sensor-based mobile robot navigation in indoor environments. A neuro-fuzzy system
architecture for behaviour-based control of mobile robot in unknown environments has been
presented by Li et al. [163]. They acquired the range information by ultrasonic sensors. Garbi et
al. [164] have focused the detailed of an adaptive neuro-fuzzy inference system implemented in
structure of multi valued behaviours system for robotic vehicle navigation.
26
Adaptive Network based Fuzzy Inference System (ANFIS) is appropriate for nonlinear
modeling time series prediction and intelligent control. Under the control of ANFIS approach,
the mobile robots are able to avoid static and dynamic obstacles, and reach the target
successfully in various environments [165]. The evolvement of soft-computing paradigms have
provided a powerful tool to deal with mobile robot navigation process, which exhibits
incomplete and uncertain knowledge due to the inaccuracy and imprecision inherent from the
sensory system [166]. The systematic approach of soft computing techniques provides an
optimal design solution based on customized optimization criteria [167]. The artificial neural
network can be used as a universal learning paradigm for any smooth parameterized models,
including fuzzy inference system [150]. Direct adaptive control scheme for stable path tracking
of mobile robots using TSK-type recurrent neuro fuzzy system is developed by Lee et al. [168].
This study is addressed to improve the quality of the signal of the Adaptive-Network based
Fuzzy Inference System [169] reducing the level of fluctuations in the output due to periodical
disturbances.
Within the last decade, there has been an interest among the scientists and researchers to
coordinate multiple mobile robots. This interest has stemmed both from practical
considerations such as multiple robots are able to handle tasks that individual machine cannot
do, for instance carrying large, bulky and heavy loads and desire to create artificial systems that
mimic nature in particular by exhibiting some of the primary behaviours observed in human
societies [170]. Pham et al. [171] have focused on the development of intelligent multi-agent
robot teams that are capable of acting autonomously and of collaborating in a dynamic
environment to achieve team objectives. An assessment of different estimation and prediction
techniques applied to the tracking of multiple robots is proposed by Torres-Torriti et al. [172].
Cooperative control of multiple robots has received considerable attention in the last decade
due to a wide array of applications such as moving a large number of objects, environmental
monitoring, rescue missions, distributed transportation, and multipoint surveillance; such tasks
cannot be efficiently accomplished by a single robot [173]. In many applications, a group of
robots is required to follow a predefined trajectory while maintaining a desired spatial pattern,
which is the focus of this work. In 1990, high-MIQ consumer products employing fuzzy logic
began to grow in number and visibility. Somewhat later neural network techniques combined
with fuzzy logic begins to be employed in a wide variety of consumer product with the
27
capability to adopted and learn from experience [174]. Such neuro-fuzzy products are likely to
become ubiquitous in the years ahead. The same is likely to happen in the realm of robotics.
Industrial systems, process control and speed control of a switched reluctance motor [175]. The
design and implementation of a neural fuzzy controller suitable for real-time control of an
autonomous mobile robot using Generalized Dynamic Fuzzy Neural Networks learning
algorithm is well presented by Er et al. [176]. According to modular robot concept, the
integrated structure is constructed and its dynamic modeling is performed by Yangmin et al.
[177]. Control and sensor information between the robots and the control system is supplied
through radio communication [178]. The adaptive neuro-fuzzy hybrid force/motion controller
is presented by Zhijun et al. [179]. The dynamic analyses of flexible robotic manipulators have
been reported by Pieper [180] and Diwedi et al. [181]. The redundancy of a mobile modular
manipulator is investigated to avoid tipping over of the entire robot [182]. The problem of
minimum-time trajectory planning for a three degrees-of-freedom planar manipulator can be
solved using a hierarchical hybrid neuro-fuzzy system.
2.7 Heuristic Rule Base Neural Controller for Mobile Robot
This section introduces a control system for a mobile robot which provides heuristic
learning concretely. These learning methods are applied to design goal oriented driving
behaviours and static as well as dynamic obstacle avoidance and to optimise path as well as
time within the environment. The method is simple and fast in execution using the perception
based heuristic rule concept. The algorithm computes the paths for the individual robots in the
configuration-time space. Thereby it trades off the distance to static objects as well as with
other robots and the length of the path to be traveled. Useful heuristic rules are hybridized with
the artificial neural network to build the desired mapping between perception and motion.
When people make guidance on the route for the newcomers, one tells where the
destinations are and then tells which path follows from the landmarks to their destination [183].
The navigation problem involves how to reach a goal avoiding obstacles in dynamic
environments. These mechanisms allow the learning of both reactions and sequences of actions.
This learning process involves two main tasks: first, discrimination between rules and, second,
the discovery of new rules to obtain a successful operation in dynamic environments [184]. The
reactive rule base governing the robot behaviour is synthesized corresponding to the various
28
situations defined by the instant robot motion, environment and target information. Sensed
ranging and relative target position signals are input to the fuzzy controller while the steering
angle and the velocity change are inferred to drive the mobile robot [185]. A local navigation
algorithm for mobile robots combines rule-based and neural network approaches togather. The
global path environment has been classified into a number of basic local path environments to
which each module has been optimised with higher resolution and better generalization [186].
Navigation algorithms have been investigated by many researchers [187]. Their methods are
generally good for local navigation but may not be optimal in a global sense. To navigate in an
unknown or unstructured environment, it is more desirable for the mobile robot to take
intelligent decision based on its sensory information [188]. In order to adapt the robot’s
behaviour to any complex, and dynamic environment without further human intervention, it
should be able to extract information from the environment heuristically, to perceive, and act
within the environment [189]. As a result, designing of intelligent controller of a mobile robot
plays an important role in robotics [190-192]. Existing approaches plan an initial path based on
known information about the environment, then modify the plan locally as the robot travels or
reschedule the entire path as the robot discovers obstacles with its sensors, sacrificing
optimality or computational efficiency, respectively [191]. Reactive obstacle avoidance is one
of the most desirable characteristics of an autonomous mobile robot. It is important for the
robot to respond promptly to its surroundings, for instance, to avoid unexpected obstacles and
continue traveling toward the target [192]. Autonomous wheeled mobile robot needs
implementing velocity and path tracking control subject to complex dynamical constraints.
Conventionally, the control design is obtained by analysis and synthesis or by domain expert to
build control rules. An adaptive critic motion control design, which enables wheeled mobile
robot to autonomously generate the control ability by learning through trials, is proposed by
Lin et al. [193]. This searches for the most probable map such that the associated pose provides
the robot with the best localization information. The problem of determining a feedback control
law, robust with respect to localization errors, allowing a mobile robot to follow a prescribed
path [194]. Knowledge of this attractive domain allows us to compute easily a security margin
to guarantee obstacle avoidance during the path following process.
Real-time heuristic search methods interleave planning and plan executions and plan only
in the part of the domain around the current state of the agents. Approaches based on the
29
classical paradigms are not completely suitable for unpredictable and dynamic environments
[184]. One general principle that can reduce the planning time in nondeterministic domains is
interleaving planning and plan executions. Without interleaving planning and plan executions,
the agents have to find a large conditional plan that solves the planning task [195]. The mobile
robot is assumed to move in a two-dimensional workspace with continuous input from the
surrounding environment. The input is a signal that reflects the distance and position of an
obstacle momentarily. The neural network uses an original approach of hybrid instantaneous
reinforcement learning in addition to a long-term back propagation through time learning. The
second stage is to test the learned neural network with different obstacles than the ones used in
learning [196]. The approach is based on qualitative representations of variations in sensor
behaviour between adjacent regions in space. These representations are used to localize and
guide planning and reaction [197]. During execution, the robot controller integrates this map
into a reaction module.
In animals, there is evidence that the stronger their motivation for a task, the more they
tend to accept as relevant those stimuli to which they previously paid no attention. It is shown
how motivations and their reactivity threshold bring about perceptual generalizations that might
help animals to recognise more opportunities to act [198]. This process is likely to be useful in
uncertain environments, such as the real world. Designers interested in autonomous mobile
robots construct machines with flexible goal achievements [92]. In particular, these robots are
provided with specific motivational states that determine when to carry out a given task. In
addition, the goal-objects may vary in optimality; not all are always equally attractive in
relation to the same task. Multi-robot motion planning that is based on the concept of planning
within dynamic robot networks [199]. The system enables multiple mobile robots that have
limited ranges of sensing and communication to maneuver safely in dynamic, unstructured
environments [200]. The Kino dynamic randomized motion planning techniques has been used
to construct trajectories in real-time and has been discussed by Bennewitz et al. [201]. The
Radio Frequency Identification technology algorithm is capable of reaching a target point in its
a priori unknown workspace without vision system, as well as tracking a desired trajectory with
a high precision [202]. The general aim of automation is to avoid human interventions to
control and to supervise tasks. Ideally, it should be possible that robot can communicate with
technical systems in a similar way as they do with human assistants [203]. The interconnection
30
of the distributed intelligent subsystems is a key factor in the overall performance of the
system. The development of new multi-modal human machine interfaces and new navigation
systems are current research robotic trends towards human-oriented robotics [204]. The speed
function is proposed such that the minimum cost path between the starting and target locations
in the environment is the optimum planned path. The speed function is controlled by one
parameter, which takes one of three possible values to generate the safest, the shortest, or the
hybrid planned path [205]. The hybrid path is much safer than the shortest path, but shorter
than the safest one.
2.8 Summary
This chapter has extensively reviewed the various aspects of the progress made so far in the
navigation of mobile robot. First the kinematics and dynamic analysis of differential drive
mobile robot has been addressed and the problem of posture regulation, path following, and
trajectory tracking have been demonstrated. A stable control algorithm capable of dealing with
nonholonomic navigation problems, and that considers the complete dynamics of a mobile
robot. This chapter also provides a detailed review report which has been used in last decades
by many researchers in the area of new intelligent control technique. The working principle
and controllers for navigation of mobile robot using different intelligent controller i.e. Fuzzy
Logic controller, Neural Controller, Adaptive Neuro-Fuzzy Controller and Heuristic Rule Base
Neural Controller can be outlined for powerful cognition of the complex environment around
the robots to distinguish between targets, surrounding obstacles, other moving robots and for
cooperative behaviour. From the survey it has been noticed that the mobile robot navigation
can be controlled successfully in a complex, unknown and dynamic environments using the
above strategies.
™ Publications
1. “Various strategies of navigation of mobile robot: A review” International Journal of
Automation and Control, Inderscience, 3(2/3), 2009, 114-134.
2. “Design of Intelligent Controllers for Mobile Robot navigation: A Review” International
Conference on ETEE07, January12-14, 2007, Science City Kolkata, India.
3. “Navigational Path Analysis of Mobile Robot in various Environments: A survey”,
National Conference on ATENM-07, January 23-24, 2007, BIT Mesra, India.
31
3 Kinematic Analysis of Mobile Robots
Kinematics is the most basic study of how mechanical systems behave and it plays greater role
to follow a desired trajectory. In mobile robotics, it is necessary to understand the mechanical
behaviour of the robot both in order to design appropriate mobile robots for tasks and to
understand how to create control software of mobile robot hardware. This chapter provides a
detailed kinematic analysis of mobile robot.
3.1 Introduction
The kinematics of mobile robot focuses on design of mobile platforms to perform
intelligent tasks, rather than on the development of methodologies for analyzing, designing, and
controlling the mobility subsystem. Improved mechanical designs and mobility control systems
will enable the application of mobile robot to perform the task with smooth movement during
navigation. Kinematic methodology is the first step towards achieving these goals. The
objective is thus to model the kinematics of mobile robot. Modeling mobile robots with
differential drive wheels as control systems may be addressed with a differential geometric
point of view by considering only the classical hypothesis of "rolling without slipping". Such a
modeling provides directly kinematic models of the robots. Kinematics is the study of the
geometry of motion. In the context of mobile robot, this chapter provides to determining the
motion of the robot from the geometry of the constraints imposed by the motion of the wheels.
In recent years, much attention has been paid to the motion control of mobile robots [206].
However, practically they need to take into account the specific dynamics that can produce the
input velocity using wheel torque provided by the mobile robot. Broadly, the mobile guidance
robots can be classified into active and passive types. An active mobility assist robot can be
controlled using DC motor or servo motors while the user is guided within the environment. A
passive mobility assist robot need not have actuators on the wheels but only brakes or the
actuators may only steer the wheels. The active robot can perform complicated motions and
enhance the overall maneuverability. However, the user’s safety needs to be considered in the
development of such mobile assistive robots [207]. Hence, from the safety point of view,
passive robots are better than the active robots as the users can exercise their own discretion
during motion.
32
3.2 Type of Wheels used in Mobile Robot
The choice of wheel types for a mobile robot is strongly linked to the choice of wheel
arrangement, or wheel geometry. The mobile robot designer must consider these two issues
simultaneously when designing the locomotion mechanism of a wheeled robot. The wheel type
and wheel geometry require three fundamental characteristics of a robot maneuverability,
controllability, and stability. Minimum two numbers of wheels required for static stability.
Two-wheel differential-drive robot can achieve static stability if the center of mass is below the
wheel axle. Dynamics can also cause a two-wheeled robot to strike the floor with a third point
of contact, for instance, with sufficiently high motor torques from standstill. Conventionally,
static stability requires a minimum of three wheels, with the additional caveat that the center of
gravity must be contained within the triangle formed by the ground contact points of the
wheels. Stability can be further improved by adding more wheels, although once the number of
contact points exceeds three, the hyper static nature of the geometry will require some form of
flexible suspension on uneven terrain.
The most popular robot in research community is the two-wheel differential-drive robot
where the two wheels rotate around the center point of the robot and two diametrically opposed
wheels (i.e., two parallel conventional wheels, one on each side of the robot). One or two
additional ground contact points may be used for stability, based on the application. Mobile
robots employing conventional wheels are significantly simpler and more reliable. When it is
necessary for a mobile robot to perform operations along a specific path, its ability to
accurately track a reference path is a critical performance feature. In general, there are only two
independent posture variables during a path tracking process. Therefore, to reach high control
performance, the tracking control algorithm must be consistent with the kinematics of the
mobile robot [208]. The conventional wheels are the most widely used among wheel mobile
robots with wheeled locomotion. These wheels are simple to construct, require less
maintenance, provide smooth motion, offer high load carrying capacity and are cheap.
Conventional wheels have two degree of freedom. The axis of rolling is orthogonal to the
steering axis and the centre of the wheel is at the intersection of these two axes. It allows travel
along a surface in the direction of the wheel orientation, and rotation about the point-of-contact
between the wheel and the floor shown in Fig. 3.1(a). The rotational degree of freedom is
33
slippage, since the point-of-contact is not stationary with respect to the floor surface. Even
though we define the rotational slip as a degree of freedom, we do not consider slip transverse
to the wheel orientation a degree of freedom, because the magnitude of force required for the
transverse motion is much larger than that for rotational slip. The conventional wheel is by far
the most widely used wheel; automobiles, roller skates and bicycles utilise this wheel. Mobile
robot built with conventional wheels can be classified into four main groups, (i) based on the
way they are driven and steered, namely, (i) differential drives (ii) synchronous drives (iii)
tricycle drives and (iv) car-like drives.
The most maneuverable wheel is a ball which possesses three degree of freedom without
slip as shown in Fig. 3.1(b). Schemes have been devised for actuating and sensing ball wheels,
but generally unaware of any existing implementations. The ball wheels, have the advantages
of full mobility, maneuvers from an arbitrary position at non-zero velocity in all directions are
possible. They all possess three degree of freedom in the plane with no singularities. One
major difficulty concerning robots built around this type of wheel lies in mounting the ball onto
the robot chassis while the ball to roll freely in any direction on the floor. Furthermore, dirt and
friction also hamper the performance of this type of wheels.
Z
Y
V = ω. r
ω
X
r
(a)
(b)
Figure 3.1.(a) Schematic view of conventional wheel and (b) Ball wheel used in mobile robots.
34
3.3 Analysis of Wheel Kinematic Constraints
The first step to a kinematic model of the robot is to express constraints on the motions of
individual wheels. The first constraint enforces the concept of rolling contact that the wheel
must roll when motion takes place in the appropriate direction. The second constraint enforces
the concept of no lateral slippage, that the wheel must not slide orthogonal to the wheel plane.
The fixed standard wheel has no vertical axis of rotation for steering. Its angle to the chassis is
thus fixed, and it is limited to motion back and forth along the wheel plane and rotation around
its contact point with the ground plane. Fig. 3.2 depicts a fixed standard wheel and indicates its
position pose relative to the robot’s local reference frame x , y . The position of P is
expressed in polar coordinates by distance l and angle . The angle of the wheel plane relative
to the chassis is denoted by , which is fixed since the fixed standard wheel is not steerable.
The wheel, which has radius r, can spin over time, and so its rotational position around its
horizontal axle is a function of time t: ω and t.
The rolling constraint for this wheel enforces that all motion along the direction of the
wheel plane must be accompanied by the appropriate amount of wheel spin so that there is pure
rolling at the contact point,
sin α
β
cos α
β
l cos β R θ . q
ωr
(3.1)
Yp
Yp
P
P
l
l
V
α
O
V
α
Xp
(a)
O
Xp
(b)
Figure 3.2. Kinematic parameters of (a) Standard wheel (b) Ball wheel.
35
Where R (θ) is rotation matrix
cosθ sinθ 0
sinθ cosθ 0
0
0
1
R θ
(3.2)
And
q
xyθ
T
f , r, θ, ω , ω
(3.3)
The first term of Eq. 3.1, the sum denotes the total motion along the wheel plane. These
three elements of the vector on the left represent mappings from each of x, y, θ, to their
contributions for motion along the wheel plane.
Note that the R θ q term is used to transform the motion parameters Eq. (3.2) q that are
in the global reference frame [X, Y] into motion parameters Eq. (3.2) in the local reference
frame x y . This is necessary because all other parameters in the equation α, β, , are in terms
of the robot’s local reference frame. This motion along the wheel plane must be equal,
according to this constraint, to the motion accomplished by spinning the wheel, r. ω.
The sliding constraint for this wheel enforces that the component of the wheel’s motion
orthogonal to the wheel plane must be zero,
cos α
β sin α
β l sin β R θ . q
0
(3.4)
The ball or spherical wheel, places no direct constraints on motion (Fig. 3.3(b)). Such a
mechanism has no principal axis of rotation, and therefore no appropriate rolling or sliding
constraints exist. Therefore, Eq. (3.1) simply describes the roll rate of the ball in the direction
of motion of point of the robot.
However, the interpretation of Eq. (3.4) is different. The omnidirectional spherical wheel
can have any arbitrary direction of movement, where the motion direction given by is a free
variable deduced from Eq. (3.4). Consider the case that the robot is in pure translation in the
direction of y . Then Eq. (3.4) reduces to, sin θ
for this special case.
36
α
0, thus, α = - θ, which makes sense
3.4 Motion Control
A common task in mobile robotics is to drive the robot to a certain position and orientation
as fast as possible given the limits of the static and dynamic properties of the robot setup.
Kinematic models and motion-control algorithms for a differential drive has been discussed in
this section. A partially compliant frame provides roll and yaw degrees of freedom between the
axles. Motion control of nanholonomic mobile robot can sub divided in two methods one is
open loop control and another one is close loop control method which have been exhibited in
next section.
3.4.1 Open Loop Control
The objective of a kinematic controller is to follow a trajectory described by its position or
velocity profile as a function of time. This is often done by dividing the trajectory (path) in
motion segments of clearly defined shape, for example, straight lines and segments of a circle.
The control problem is thus to pre-compute a smooth trajectory based on line and a circle
segment which drives the robot from the initial position to the final position (Fig.3.3 (a)). This
approach can be regarded as open-loop motion control, because the measured robot position is
not fed back for velocity or position control. It has several disadvantages:
¾
It is not at all an easy task to pre-compute a feasible trajectory if all limitations and
constraints of the robot’s velocities and accelerations have to be considered.
¾
The robot will not automatically adapt or correct the trajectory if dynamic changes of the
environment occur.
¾
The resulting trajectories are usually not smooth, because the transitions from one
trajectory segment to another are not smooth (for most of the commonly used segments).
This means there is a discontinuity in the robot’s acceleration.
3.4.2 Feedback Control
A more appropriate approach in motion control of a mobile robot is to use a real-state
feedback controller. With such a controller the robot’s path-planning task is reduced to setting
intermediate positions (sub goals) lying on the requested path.
37
Y
Y
xc
Vt
yc
O
X
a
θ
O
X
b
Figure 3.3. Kinematic control of a mobile robot, (a) Open-loop control based on straight lines
and circular trajectory segments, (b) Typical situation for feedback control of a mobile robot.
3.5 Problem Statement
Consider the situation shown in Fig. 3.3(b), with an arbitrary position and orientation of
the robot and a predefined goal position and orientation. The actual pose error vector given in
the robot reference frame {xc yc θ} is e=
R
x y θ
T
with X, Y and θ being goal coordinate.
The task of the controller layout is to find a control matrix K, if it exists
K
k
k
k
k
k
k
with k
k t, e
(3.5)
Such that the control of V(t) and ω(t)
V t
ω t
=K. e= K.
R
x
y
θ
T
(3.6)
Drives the error ‘e’ toward zero.
lim
e t
0
(3.7)
38
3.6 Kinematic Analysis of Mobile Robot
The kinematics analysis of mobile robot which has been used for experimental validation
is analyzed in this section. The driving wheels are independently driven by two actuators
(motor 0 and motor 1) to achieve the motion and orientation. All wheels have the same
diameter denoted by ‘2r’ as shown in Fig. 3.4. The left and right driving wheels are separated
by distance ‘W’. The center of gravity (COG) of the mobile robot is located at point ‘C’. The
point ‘P’ is located in the intersection of a straight line passing through the middle of the
vehicle and a line passing through the axis of the two centre wheels. The distance between
points P and C is‘d’.
The kinematics of the differential drive mobile robot is based on the assumption of pure
rolling and there is no slip between the wheel and surface.
V
v
v
(3.8)
Y
yt=Y
Target
yg
xt=X
yc
y
vl
p
xc
C
vr
w
d
2r
x
O
Figure 3.4. Kinematic analysis of mobile robot
39
X
ω
v
W
v
v
rω And
(3.9)
v
rω
(3.10)
Where
V = linear velocity and
ω = angular velocity of the mobile robot.
Suffix r, l and t stand for right, left wheel and tangential (with respect to its center of
gravity point ‘C’ measured in a right wheel) respectively.
The position of the robot in the global coordinate frame (O X Y) is represented by the
vector notation as,
q
x y θ
T
(3.11)
Where x and y are the coordinates of the point C in the global coordinate frame (Fig.
3.4). The variable θ is the orientation of the local coordination of the local coordinate
frame C x
y
attached on the robot platform measured from the horizontal axis. Three
generalized coordinates can describe the configuration of the robot as Eq. (3.11).
The mobile robot system considered here is a rigid body and the wheels are pure rolling
and no slippage. This states that the robot can only move in the direction normal to the axis of
the driving wheels. Therefore, the component of the velocity of the contact point with the
ground, orthogonal to the plane of the wheel is zero, i.e.
y cos θ
x Sin θ
dθ
0
(3.12)
Let consider all kinematics constraints are independent of time, and can be expressed as,
A q q
0
(3.13)
Where, A q is the input transformation matrix associated with the constraints, and,
40
C T q AT q
0
(3.14)
Where C q is the full rank matrix formed by a set of smooth and linearly independent
vector fields spanning the null space of AT q .
From Eq. (3.13) and Eq. (3.14) it is possible to find an auxiliary vector time function V (t)
for all time ‘t’.
q
C q .V t
(3.15)
The constraint matrix in Eq. (3.13) for a mobile robot is given by
A q
sin θ
cos θ
d
(3.16)
It is easy to verify equations of motion Eq. (3.12) in terms of linear and angular velocity [24].
The matrix C (q) is given by
cos θ
sin θ
0
C q
d sin θ
d cos θ
1
(3.17)
And
v
V t
ω
T
(3.18)
Where ‘v’ is the maximum linear velocity |v|
velocity |ω|
ω
V
and ω is the maximum angular
at the point ‘p’ along the robot axis.
Therefore, the kinematics Eq. in (3.15) can be described as
x
q
y
θ
cos θ
sin θ
0
d sin θ
d cos θ
1
v
ω
(3.19)
Eq. (3.19) is called the steering system of the vehicle. The control problem is to find a
suitable control law so that the system can track desired reference trajectories. The control laws
41
are designed to produce suitable left and right wheel velocities for driving the mobile robot to
follow required path trajectories. The steering angle (SA) can be computed as,
V
SA
V
(3.20)
W
Where V and V are left and right wheel velocities and w is the wheel base. If V
steering angle is in clockwise direction and if V
V the
V the steering angle is in counterclockwise
direction. The control problem is to find a suitable control law so that the robot can follow
desired trajectory.
3.7 Dynamic Analysis of Mobile Robot
The simplified version of the dynamic model used in for differential driven mobile robot.
In this simplified model, the mass and the moment of inertia of the two wheels are considered
to be negligible compared to those of the robot platform. The Euler–Lagrange equations of
motion are used to derive the dynamics of the mobile robot [24]. The dynamical equations of
the mobile robot can be expressed as;
M q q
N q, q q
F q
G q
E q τ
AT q λ
(3.21)
Where;
R3nx3n is a symmetric, positive definite inertia matrix assembled from the individual
M(q)
axle module inertia matrices.
m
0
md sin θ
M q
0
m
md cos θ
md sin θ
md cos θ
I
(3.22)
Here, ‘m’ is the mass and ‘I’ is the moment of inertia of the platform.
N q, q
R3nx3n is the centripetal and coriolis forces,
N q, q
0 0 mdθ cos θ
0 0 mdθ sin θ
0 0
0
(3.23)
42
R3nx1 denotes the surface friction,
F q
F q
0
(3.24)
R3nx1 is the gravitational vector, which is zero, because the trajectory of the mobile base
G q
is constrained to horizontal plane,
G q
0
(3.25)
Rnx1 is the input transformation matrix,
E q
cos θ
sin θ
w/2
E q
cos θ
sin θ
w/2
(3.26)
Here, ‘r’ is radius of the wheel and ‘w’ is distance between the two wheels.
τ
R2nx1is the input torques,
τ
τ
τ
(3.27)
Here, τ and τ represent right and left wheel torques, respectively.
Rnx3n is the global matrix associated with the nonholonomic constraints from Eq. (16),
A q
AT q
And, λ
λ
sin θ
cos θ
d
(3.28)
R2nx1is the vector of Lagrange multipliers associated with the constraint,
m x cos θ
y sin θ θ
(3.29)
By differentiating Eq. (3.15), one gets,
q
C q V t
C q V t
(3.30)
43
Substituting all value, using Eq. (3.15), multiplying both side of C T in Eq. (3.21) and using
the property of equation, the robot dynamics Eq. (3.21) can be transformed into a more
appropriate representation for control purposes.
Mv
Nv
Eτ
(3.31)
C T MC, N
Where, M
C T MC
NC , and E
C T E.
By neglecting the Eq. (3.21) and Eq. (3.31) it is assumed that there is "perfect velocity
tracking" than the Eq. (3.19) is applicable for velocity command. However, it is necessary for
perfect velocity tracking using the computed torque control as exhibited Eq. in (3.21). One can
obtain the necessary control ‘τ’ for Eq. (3.31) which guarantees perfect velocity tracking using
the computed torque control as given in Eq. (3.21). To implement Eq. (3.21) or Eq. (3.31)
explanation of mathematics involved for analysis the robot dynamics is necessary for perfect
velocity tracking of mobile robot.
3.8 Motion Control of Mobile Robot
In Fig. 3.4, let
with the robot
position
denote the angle between the
axis of the robot’s reference frame fixed
and the vector connecting the centre of the axel of the wheels with the final
. When I
,
,
I .
(3.32)
In polar coordinates (see Fig. 3.4) the error is now [209],
ρ
β
∆y
∆x
θ
tan
θ
α
(3.33)
∆
(3.34)
∆
(3.35)
This yields a system description, in the new polar coordinates, using a matrix equation
44
ρ
cos α
0
α =
1
β
0
v
ω
(3.36)
Where ρ = distance between the center of the robot’s wheel axel and the target position. On
other hand, when I
π, π/2
π/2, π ,
I .
Refining the forward direction of the robot by setting v
(3.37)
v, the system described by a
matrix equation will be:
ρ
cos α
0
α =
1
β
0
v
ω
(3.38)
The coordinates transformation is not defined at x = y = 0, as such a point the determinant
of the Jacobian matrix of the transformation is not defined, that is unbounded. For α
forward direction of the robot points towards the target. For α
I
I
it is the reverse direction.
By properly defining the forward direction of the robot at its initial configuration, it is always
possible to have α
I
at t
0 . However, this does not mean that α remains in I for all
time t. Hence, to avoid that the robot changes direction during approaching the target, it is
necessary to determine, if possible, the controller in such a way that α
whenever α 0
I
for all t,
I . The same applies for the reverse direction.
The control problem is to find a suitable control law so that the system can track desired
reference trajectories. The control laws are designed to produce suitable left and right wheel
velocities for driving the mobile robot to follow required trajectory path.
3.8.1 The control Law
The control signals v and ω must now be designed to drive the robot from its actual
configuration, Say ρ
discontinuity at ρ
α
β
to the target position. It is obvious that Eq. (3.36) presents a
0, and it does not obstruct smooth stability [209].
45
If we consider now the linear control law
v
k ρ
ω
k α
(3.39)
k β
(3.40)
We get with Eq. (3.36) a closed-loop system described by
ρ
k ρcos α
α
k sin α
β
k α
k β
(3.41)
k sin α
The system does not have any singularity at ρ
at ρ, α, β
0 and has a unique equilibrium point
0, 0, 0 . Thus it will drive the robot to this point, which is the target position.
In the Cartesian coordinate system the control law Eq. (3.40), leads to equations which are not
defined at x
y
0. The angles are expressed in the range
π, π . The control signal v has
always a constant sign, that is, it is positive whenever α 0
I and it is always negative
otherwise. This implies that the robot performs its parking maneuver always in a single
direction and without reversing its motion.
Figure 3.5. Resulting paths of the robot at initially on the unit circle in X-Y plane.
46
Fig. 3.5 shows the resulting paths when the robot is initially on a circular path in the X, Y
plane. All movements are smooth trajectories toward the target in the center. The control
parameters for this simulation are set to
k
k
k
k
= (3, 8, -1.5)
(3.42)
3.8.2 Local Stability Issue
It can further be shown, that the closed-loop control system Eq. (3.41) is locally
exponentially stable [209] if
k
0, k
0, k
k
0
(3.43)
By linearising around the equilibrium cos α
1, sin α
α
position, Eq. (3.41) can be
written as,
ρ
k
0
0
α
β
0
k
0
k
0
k
k
ρ
α
β
(3.44)
Hence, locally exponentially stable if the Eigen values of the matrix have a negative real
part. The characteristic polynomial of the matrix A is
A
λ
0
k
0
0
k
k
0
k
0
k
k
λ
λ k
k
k k
(3.45)
=0
(3.46)
Eq. 3.46 has all roots with negative real part if it holds the following condition
k
0,
k
0, k
k
0
(3.47)
This Eq. (3.47) gives the stability condition. The condition given in the above expression
provides the local stability.
47
The following conditions ensure that the robot does not change the direction during its
approach to the target along with the stability condition [209].
k
0, k
0,
This implies that α
α 0
k
k
k
0
I for all t, whenever α 0
(3.48)
I and α
I
for all t, whenever
I respectively. This strong stability condition has also been verified in applications.
3.9 Summary
In this chapter the problem of exponential stabilization of the kinematic and dynamic model
of a differential drive mobile robot has been developed. The proposed dynamic controller can
track the desired velocity, which is generated by kinematic controller, without exact knowledge
about the dynamic model of a mobile robot. With the help of developed methodology, the
robot can achieve path following as well as velocity tracking, considering both kinematic
model and dynamic model of the mobile robot. The details of kinematics and dynamics of
mobile robot is addressed and solved using a discontinuous, bounded, time invariant, state
feedback control law. The exact knowledge about the parameter values required to track the
desired velocity, which is generated by kinematic controller. It has been seen using the above
stability condition the robot exponentially converges to the goal position. Moreover, the
derivation of a stabilizing controller for the dynamic model allows a direct implementation of
the proposed control law on real systems. Numerical results were presented and the stability of
the system was verified. Simulation results verify the theoretical conjecture and expose the
flaws in ignoring the dynamics of the mobile robots.
™ Publications
1. “Navigational path analysis of mobile robots using ANFIS controller in dynamic
environment”, Journal of Mechanical Engineering Science part C, IMechE, 2009,
(Accepted).
2. “Heuristic rule base hybrid neural network for navigation of mobile robot”, Journal of
Engineering Manufacture part B, IMechE, 2009, (Accepted).
3. Path optimisation of mobile robot using artificial neural network (ANN) controller,
International Journal of System Science, Taylor & Francis, 2009, (Accepted).
48
4
Analysis of Fuzzy Logic Controller for Mobile Robot
An autonomous mobile robot is a machine that operates in an unknown and unpredictable
environment. A key issue in the research of an autonomous mobile robot is the design and
development of a control technique that enables the robot to navigate in a real world
environment, avoiding structured and unstructured obstacles especially in crowded and
unpredictably changing environment. This chapter presents the development in the area of
intelligent controller for mobile robot in various (known and unknown) environments. Action
coordination of the behaviours will be addressed using fuzzy logic in the present research. The
inputs to the proposed fuzzy control scheme consist of a target angle between a robot and a
specified target and the distances between the robot and the obstacles to the left, front, and right
to its locations, being acquired by an array of sensors. In this chapter an intelligent controller
has been proposed for mobile robot navigation algorithm employing fuzzy theory in a complex
cluttered environment.
4.1 Introduction
It is observed that the human beings do not need precise, numerical information input to
make a decision, but they are able to perform highly adaptive control. Humans have a
remarkable capability to perform a wide variety of physical and mental tasks without any
explicit measurements or computations. Examples of everyday tasks are parking a car, driving
in city traffic, playing golf, and summarizing a story. In performing such familiar tasks, humans
use perceptions of time, distance, speed, shape, and other attributes of physical and mental
objects [210]. Fuzzy logic is a problem-solving control system methodology that lends itself for
implementation in systems ranging from simple, small, embedded micro-controllers to large,
networked, workstation-based data acquisition and control systems. The theory of fuzzy logic
systems is inspired by the remarkable human capability to operate on and reason with
perception-based information. The rule-based fuzzy logic provides a scientific formalism for
reasoning and decision making with uncertain and imprecise information. It can be
implemented in hardware, software, or a combination of both. Fuzzy logic approach to control
problems mimics how a person would make decisions. The main advantages of a fuzzy
49
navigation strategy lie in the ability to extract heuristic rules from human experience, and to
obviate the need for an analytical model of the process [67, 81].
The development of techniques for autonomous navigation in real-world environments
constitutes one of the major trends in the current research on robotics. An important problem in
autonomous navigation is the need to cope with the large amount of uncertainty that is inherent
of natural environments. Fuzzy logic has features that make it an adequate tool to address this
problem. Navigation of mobile robots in presence of static and moving obstacles using fuzzy
technique is presented in this work. At first, a set of navigation rules are extracted from the data
base. The rules are used to control the navigation of mobile robots. The use of fuzzy logic
techniques for controlling wheel-based mobile robots has been effectively proposed by many
authors in the last decade [6, 67, 86, 154]. This chapter proposes an on-line path analysis and
planning approach that embeds a fuzzy strategy to drive a mobile robot. A new intelligent fuzzy
interface system has been developed in this current investigation. In this approach, the fuzzy
logic system is used to control the robot taking inputs from various sensors. Sensor signals are
fed to the fuzzy logic system, and the output provides motor control commands (e.g., turn right
or left). The fuzzy logic system learns the full dynamics of the mobile robot online. Fuzzy
controller for mobile robot has four inputs and two outputs. Both inputs and output have three
membership functions. Each membership function consists of trapezoidal and triangular
membership functions. In this methodology 81 rules have been used to design the fuzzy
controller. This
research focuses a fuzzy logic framework to be implemented in the mobile
robot for behaviour design and coordination. The proposed method has been compared with
other methods [6, 86, 154, 211] which show the effectiveness of the developed method. It is
also concluded that the current method can be successfully employed for navigation of mobile
robot. This fuzzy controller of mobile robot for path analysis and planning has been
authenticated by experimental verification.
This chapter organized into five sections following the introduction, the entire behaviour of
mobile robot is described in section 4.2. The simulation results are discussed in section 4.3. In
section 4.4, experimental results are verified with simulation to demonstrate the superiority of
the proposed methodology and comparison has been made with other methods [6, 86, 154,
211]. Finally summary is discussed in section 4.5.
50
4.2 Fuzzy Logic Behaviour for Control Technique
The first and most common application of fuzzy logic techniques in the domain of an
autonomous mobile robot is the use of fuzzy control to implement individual behaviour units.
Fuzzy logic controllers incorporate heuristic control knowledge in the form of if-then rules and
are a convenient choice when a precise linear model of the system to be controlled cannot be
easily obtained. Fuzzy logic has features that are particularly attractive in light of the problems
posed by autonomous robot navigation. Fuzzy logic allows the modeling of different types of
uncertainty and imprecision, building robust controllers starting from heuristic and qualitative
models, and integrating symbolic reasoning and numeric computation in a natural framework
[2]. Fuzzy controller helps autonomous mobile robot in navigating to a desired location.
Fuzzy logic behaviour control architecture is implemented using fuzzy rule-base and
inference engine. Depending on the type of action, from a set of inputs different fuzzy rule
bases are activated and hence the corresponding outputs. The output parameters from the fuzzy
rule-bases for all actions are same i.e. the velocities of the left and right wheels of the robot,
which drive the robot to a desired posture. The fuzzy rules control the steering of the robot
according to whether there are obstacles or targets around it and how far they are from it.
Because this information is usually not known precisely, fuzzy logic is an appropriate
technique for handling it [6]. An Intelligent Fuzzy controller for mobile robot enables the robot
to avoid the obstacle and improve target seeking ability. The inputs to the proposed fuzzy
control scheme consist of a target angle between a robot and a specified target and the distances
between the robot and the obstacles to the left, front, and right locations, acquired by an array
of sensors. The outputs from the control scheme are commands for the speed control unit of
two side wheels of the mobile robot. The input signals of fuzzy controller are the distances
between the robot and obstacles to the left, front, and right locations as well as the target angle
between the robot and a specified target, as shown in Fig. 4.1(a) and Fig. 4.1(b). As the robot
perceives the target from the image sensor, it computes the difference in angle with respect to
global coordinate system between its current position and the target. And get the angle between
the robot current moving direction and the target [212]. When the target is located at the left
sides of the mobile robot, target angles (tar-ang) are negative and if the target is located to the
right side of the mobile robot, the target angles (tar-ang) is defined as positive.
51
Target
INPUTS
Front-obs
FUZZY
CONTROLLER
OUTPUT
Left-obs
Path
Tar-ang
Tar-ang
Left-v
Front-obs
Right-obs
Left-obs
Right-obs
Mobile robot
Right-v
Fuzzy Sets &
Fuzzy rule
(b)
(a)
Figure 4.1. Simulation resulting paths of mobile robot.
According to acquired range information by sensors, reactive behaviours are weighted by
the fuzzy logic algorithm to control the velocities of the two driving wheels of robot. The basic
configuration of a fuzzy system consists of four principal elements: fuzzifier, fuzzy rule base,
fuzzy inference engine, and defuzzifier. The fuzzifier is a mapping from the observed crisp
input space to the fuzzy sets defined in, the fuzzy set defined is characterized by a membership
function and is labeled by the linguistic variables near, medium and far and these are chosen to
fuzzify left obstacle distance (left-obs), right obstacle distance (right-obs) and front obstacle
distance (front-obs). The linguistic variables positive (P), zero (Z) and negative (N) are used to
fuzzify tar-ang and the linguistic variables slow, med. (medium) and fast (Table 4.1). These are
used to fuzzify the velocities of the left wheel (left-v) and right wheel (right-v), respectively
[86].
Table 4.1. Parameter for variables
Left obstacle distance(left-obs)
Right obstacle distance(right-obs)
Near(meter)
Medium(meter)
Far (Meter)
0.0 to 0.6
0.3 to 0.9
0.6 to 1.2
Negative
Zero
Positive
-600 to 00
-300 to + 300
00 to 600
Slow (m/s)
Medium (m/s)
Fast (m/s)
0 to 2
1 to 3
2 to 4
Front obstacle distance(front-obs)
Target angle (tar-ang)
Left wheel velocity(Left-v)
Right wheel velocity(Right-v)
52
The fuzzy rule base is a set of linguistic rules in the form of “if a set of conditions are
satisfied, then a set of consequences are inferred.” For four inputs two outputs fuzzy system,
the general fuzzy rule base may consist of the following.
If “matching degree of
degree of
is
and matching degree of
is
and matching degree of
and matching degree of
is
is
and matching
is
” Then “matching degree of
is
”.
The matching degree of final output is computed by the following formula.
,
,
Where, i = (1, 2, 3,……n),
,
,
,
,
(4.1)
are the sensor inputs of left, right, front obstacle
,
distance and target angle respectively,
,
,
degree of corresponding sensor inputs, and
are the matching
are the inferred inputs matching
degree of corresponding left and right wheel velocity.
When the matching degree is one the inferred conclusion is identical to the rule’s
consequence and if it is zero no conclusions can be inferred from the rule.
Finally the output firing area of the left wheel velocity and right wheel velocity value can
be computed by following formula.
,
,
,
(4.2)
The final output (crisp value) of the fuzzy logic controller of left wheel velocity and right
wheel velocity can be calculated by
,
Where,
,
∑
(4.3)
∑
is the firing area of left and right wheel velocity for ith rule,
centroid distance of the area, n is the total number of parameter, and
and right wheel respectively.
53
,
,
is the
Velocity of left
In order to reach a specified target in a complex environment, the mobile robot at least
needs the following reactive behaviours: 1. Obstacle avoidance, 2. Wall following and 3.Target
steer. In this case, a set of fuzzy logic rules is used to describe the reactive behaviours
mentioned above. Now, the last part of fuzzy rules from the rule base is to explain, in
principle, how these reactive behaviours are realized.
4.3 Behavioural Architecture
One of the major sensor based approaches to mobile robot control is the behaviour
architecture. The term behaviour comes from biology and refers to the reaction of an agent to a
given situation. Therefore, a behaviour in a mobile robot navigation system usually represents a
concern of the robot such as follow the path or avoid obstacle. Behaviour-based architecture
helps to decompose control systems into subsystems with task achieving behaviours. A
nonholonomic mobile robot (Appendix-C.1) has been designed according to the behaviourbased approach. Kinematics constraint in two dimensional work spaces is discussed in section
3.5. Each robot has four wheels. Two front supported ball wheels which are free and two side
middle wheels are powered by separate DC gear servo motors. Each robot has an image and an
array of infrared sensors for measuring the distances of obstacles around it, and the bearing of
the target and a radio system for communicating with other robots. The information’s being
sent among the robots are (a) their positions, (b) how far they are from the target, and (c)
whether reached the target or not. According to the information acquired by the robots using
their sensors, some of the fuzzy control rules are activated accordingly. The outputs of the
activated rules are combined and defuzzyfied to get the velocities of the driving wheels of the
robots. For the velocities of the left wheel and right wheel of each robot the abbreviations such
as left-v and right-v are used respectively. The above membership functions consist of
trapezoidal and triangular. The parameters defining the function are listed as shown in Fig. 4.2.
These parameters can be used to generate different fuzzy rules, for example.
Rule: If (left-obs is far and right-obs is medium and front-obs is near and tar-ang is N) Then
(left-v is slow and right-v is medium).
By fuzzy reasoning and the centroid defuzzification method, Rule related to the obstacle
avoidance wall-following and target seeking behaviours, is weighted to determine an
54
appropriate control action, i.e., the velocities, left-v and right-v, of the robot's side wheels as
shown in Fig. 4.3, the values of the parameters are decided empirically.
4.3.1
Obstacle Avoidance
When the acquired information from the sensors shows that there exist obstacles nearby
robot, it must reduce its speed to avoid obstacles. When a robot is close to an obstacle, it must
change its speed and steering angle to avoid the obstacle. Mobile robot is able to avoid static as
well as dynamic obstacle. If more than one robot is present in the environment, then a robot
treats other robots as dynamic obstacles, simulation result shown in Fig. 4.5(a). The fuzzy rules
used for obstacle avoidance and motion control by the robots are listed in Table 4.2 as rules 1–
27. All the rules in the table are obtained heuristically. Figure 4.3 shows a typical fuzzy
controller scenario for obstacle avoidance. The surface view has been shown in Fig. 4.4.
When the robot sense obstacle near to it or the robot moves at curved and narrow roads, it
must reduce its speed to avoid collision with obstacles. In this case, its main reactive behaviour
is decelerating for obstacle avoidance. This gives the first and second of fuzzy logic rules for
realizing this behaviour as follows.
µ
µ
Near
Medium
0
0.3
0.6
0.9 1.2
Far
Near
0.3
0.6
X0
0.9 1.2
Z
-30
0
P
30
1
60
Target angle (degree)
A
0
0.3
0.6
0.9 1.2
X
µ
µ
N
Far
Front obstacle in meter
Right obstacle in meter
µ
Medium
1
X0
Left obstacle in meter
-60
Medium
1
1
1
µ
Near
Far
Slow
3
Med
6
Slow
Fast
9
12
Med
Fast
1
V
Left wheel velocity m/s
0
V
Right wheel velocity m/s
3
6
9
12
Figure 4.2. Fuzzy membership functions used to design fuzzy logic controller.
55
Table 4.2. List of rules for obstacle avoidance
RuleNo. Action Left-obs
Right-obs
Front-obs
Tar-ang
Left-v
Right-v
1.
AO
Near
Near
Near
Any
Slow
Fast
2.
AO
Near
Near
Medium
Any
Slow
Slow
3.
AO
Near
Near
Far
Any
Med
Med
4.
AO
Near
Medium
Near
Any
Med
Slow
5.
AO
Near
Medium
Medium
Any
Med
Slow
6.
AO
Near
Medium
Far
Any
Fast
Med
7.
AO
Near
Far
Near
Any
Fast
Slow
8.
AO
Near
Far
Medium
Any
Med
Slow
9.
AO
Near
Far
Far
Any
Fast
Med
10.
AO
Medium
Medium
Near
Any
Slow
Fast
11.
AO
Medium
Medium
Medium
Any
Slow
Slow
12.
AO
Medium
Medium
Far
Any
Fast
Fast
13.
AO
Medium
Near
Near
Any
Slow
Fast
14.
AO
Medium
Near
Medium
Any
Slow
Med
15.
AO
Medium
Near
Far
Any
Slow
Med
16.
AO
Medium
Far
Near
Any
Med
Slow
17.
AO
Medium
Far
Medium
Any
Med
Fast
18.
AO
Medium
Far
Far
Any
Fast
Med
19.
AO
Far
Near
Near
Any
Slow
Med
20.
AO
Far
Near
Medium
Any
Med
Fast
21.
AO
Far
Near
Far
Any
Med
Fast
22.
AO
Far
Medium
Near
Any
Slow
Fast
23.
AO
Far
Medium
Medium
Any
Slow
Med
24.
AO
Far
Medium
Far
Any
Med
Fast
25.
AO
Far
Far
Near
Any
Slow
Fast
26.
AO
Far
Far
Medium
Any
Fast
Med
27.
AO
Far
Far
Far
Any
Fast
Fast
56
µ
Near
Medium
µ
Far
1
0
Near
Medium
µ
Far
1
0.3
x1
0.6
0.9 1.2
X0
µ
N
Z
µ
P
1
0.3
0.6
0.9
1.2
-30
x4
0
30
Tar-angle
60
X0
A
0
0.3
0.6
Front-obs
Far
0.9
1.2
X
x4
µ
Slow
Med
Fast
1
1
-60
Medium
1
Right-obs x2
Left-obs
Near
3
6
9
12
Slow
Vl 0
3
Med
6
Fast
9
12
Right-v
Left-v
Left-v
Figure 4.3. Schematic diagram of the fuzzy logic for navigation of mobile robots.
Right-obs
Left-obs
Figure 4.4. The surface view of the fuzzy logic for navigation of mobile robots.
57
Vr
Path followed
by robot 1
Target
Mobile robot
Path followed
by robot 2
Obstacles
Target
Obstacles
Path
Robot 1 at initial
Robot 2 at initial
Start
(b)
(a)
Figure 4.5. (a) Static as well as dynamic obstacle avoidance (b) Obstacle avoidance and motion
control behaviour.
If (left-obs is near and right- obs is near and front-obs is near and tar-ang is any) Then
(left-v is slow and right-v is fast).
If (left-obs is near and right- obs is near and front-obs is medium and tar-ang is any) Then
(left-v is slow and right-v is slow).
Such fuzzy rules represent that the robot only pays attention to obstacle avoidance and
moves accordingly to the listed rule in Table 4.2 when it is close to obstacles or at curved and
narrow roads. The Simulation result of static as well dynamic obstacle avoidance has been
exhibited in Fig. 4.5(a) and Fig. 4.5(b).
4.3.2 Wall Following Behaviour
The wall following behaviour mode will be adopted when the mobile robot detects an
obstacle in the front while it is moving towards target along the left or right side of the wall, the
mobile robot may turn left or right because presence of obstacle in the front. When the robot
moves through a large U-shaped obstacle, at the initial stage, it runs directly towards the target,
since the obstacles sensed are far away from it. Then, it makes a left turn, to avoid the obstacles
58
situated at the direct front. As the target is located at the right side of the robot, the behaviour of
the approaching target tries to make it turn to the right. As a result, it moves into the right, and
the target orientation increases gradually. When the robot reaches the right side it tries to avoid
obstacles (the right wall) and approach the target, so it turns to the left. On the basis of the
preceding analysis, it will return to the left side. Consequently, the robot travels along the
indefinite loop in this concave trap as shown in Fig. 4.6 (a).
To avoid this loop, the robot must have the wall-following behaviour as shown in Fig. 4.6
(b). When the robot is moving to a specified target through a narrow channel, or escaping from
a U shaped wall or dead end obstacle specific fuzzy rules for wall following behaviour (Table
4.3) are activated. In the absence of wall following behaviour, the robot is incapable of
reaching the goal position when its encounters U shaped or dead end obstacles on their path. In
the absence of the wall-following behaviour, the robot is incapable of reaching the goal
position.
The simulation result of wall following has been shown in Fig. 4.6 (b) and escaping from
dead end obstacle has been shown in Fig. 4.7 (a). For rules 28 and 29 the antecedent and
consequent will be.
If (left-obs is far and right- obs is far and front-obs is near and tar-ang is any) Then (left-v
is med and right-v is slow).
If (left-obs is far and right-obs is medium and front-obs is near and tar-ang is any) Then
(left-v is slow and right-v is med).
Table 4.3. List of rules for wall following behaviour
RuleNo.
Action
Left-obs
Right-obs
Front-obs
Tar-ang
Left-v
Right-v
28
FE
Far
Far
Near
Any
Med
Slow
29.
FE
Far
Medium
Near
Any
Slow
Med
30.
FE
Medium
Far
Near
Any
Fast
Med
31.
FE
Near
Far
Medium
Any
Fast
Med
32.
FE
Near
Far
Near
Any
Fast
Med
33.
FE
Near
Medium
Far
Any
Med
Slow
59
Target
Left wall
Robot sensor
i l
Target
Mobile robot
Path
Wall
Right wall
U shape wall
(Obstacle)
Mobile robot in loop
Loop path
Start
(b)
(a)
Figure 4.6. (a) Robot in indefinite loop in concave trap (b) Wall following behaviour.
These fuzzy rules show that the robot shall follow wall or an edge of an obstacle when the
obstacle is very close to the right or left of the robot, and the target also is located to the right or
left. The wall following behaviour depends on a target angle between the robot and a specified
target. Wall following behaviour helps the robot to move in one room to another room as well
as to escape dead end or find door of typical room, the simulation result shown in Fig. 4.6(b).
4.3.3
Target seeking Behaviour
When the acquired information from the sensors shows that there are no obstacles around
robot, its main reactive behaviour is target steering. The simulation results for target steer and
map localization is shown in Fig. 4.7 (b), by following the rule from Table 4.4 (i.e. rules 34, 35
and 36).
If (left-obs is far and right-obs is far and front-obs is far and tar-ang is P) Then (left-v is
fast and right-v is med).
If (left-obs is far and right-obs is far and front-obs is medium and tar-ang is N) Then (left-v
is med and right-v is fast).
If (left-obs is far and right-obs is far and front-obs is far and tar-ang is Z) Then (left-v is
fast and right-v is fast).
60
Table 4.4. List of rules for target seeking and map localisation
RuleNo. Action
Left-obs
Right-obs
Front-obs
Tar-ang
Left-v
Right-v
34
TS
Far
Far
Far
P
Fast
Med
35
TS
Far
Far
Med
N
Med
Fast
36
TS
Far
Far
Far
Z
Fast
Fast
37
TS
Far
Far
Med
P
Slow
Med
38
TS
Far
Med
Far
N
Med
Fast
40
TS
Med
Far
Far
Z
Fast
Fast
These fuzzy logic rules show that the robot mainly adjusts its motion direction and moves
towards the target. Generally, the weights of the behaviours, obstacle avoidance, and target
steer depend largely on the distances between the robot and the obstacles to the left, front, and
right locations. When the robot reaches the local target, it stops and waits for the other robot to
reach the target for further coordinated action at their end. The position of the robots is
communicated between each other in the perception model through radio modems. By this
communication, each robot knows the position of other robots present in that environment.
When the robot gets lost, it tries to make contact with other robots and those robots try to locate
the lost robot by a coordinated action. If a robot is lost, it tries to undo its movement until it is
within the preview of other robots present in that environmental scenario.
Path
Mobile robot
Target
Start
Obstacle
Start
Target
(a)
(b)
Figure 4.7. (a) Escape from dead ends and find the target (b) Target seeking behaviour.
61
4.4 Simulation Results and Discussion
The series simulation tests have been conducted with the ROBNAV software (AppendixA). To demonstrate the effectiveness and the robustness of the proposed method, simulation
results on mobile robot navigation are exhibited in various environments. In the proposed
control strategy, reactive behaviours are formulated by fuzzy sets and fuzzy rules, and these
fuzzy rules are integrated in one rule base. In most of the literatures, the simulation study is
carried out for path-tracking [86], goal-finding, and avoid-static obstacle only.
In this chapter, a new intelligent controller has been proposed for mobile robot navigation
using fuzzy logic. It is more efficient than the other traditional reactive behaviour control and
also easier to design and implement. The navigation algorithm has better reliability and realtime response because perception, localization, cognition, and motion-control decision units are
integrated in one module and are directly oriented to a dynamic environment. The simulation
results show that the proposed method, using information acquired by infrared sensors, can
perform robot navigation in complex and uncertain environments. The results from the
proposed fuzzy controller for mobile robot have been compared with the result from adaptive
controller by Das et al. [86] for path tracking shown in Fig. 4.8. In addition, a comparison has
been done between the results obtained using the controller developed by Zhu et al. [154] and
results from the current developed controller. The comparisons show a good agreement (shown
in Fig. 4.9).
Robot
Path followed
by robot
(b)
(a)
Figure 4.8. (a) Mobile robot reference trajectories by Das et al. [86] (b) Mobile robot reference
trajectories by proposed controller.
62
(a)
(b)
Figure 4.9. (a) Mobile robot trajectories with different number by Zhu et al. [154] (b) Mobile
robot trajectories with different number by purposed method.
63
4.5 Experimental results
In order to exhibit the effectiveness of the proposed fuzzy controller for mobile robot, the
simulation results are verified with experimental results, comparison is also done between the
results from Adaptive fuzzy logic-based controller by Das et al. [86] and neuro-fuzzy based
approach by Zhu et al. [154]. The comparison of controllers with the current developed
controller, demonstrate the feasibility of the current approach (discussed in section 4.4.). It is
found that the developed fuzzy controller can negotiate the obstacles efficiently. Moreover, the
developed controller can be used for several mobile robots.
The experimental results have been conducted by loading the software into the developed
mobile robot in the robotics laboratory. The assumptions about the mechanical structure and
motion of a mobile robot, to which the proposed method is applied, are as follows.
1.
The mobile robot consists of rigid base fitted with DC gear servomotor and wheels are
connected to motor shaft.
2.
The mobile robot moves on a plane surface (on lab specified floor area).
3.
The wheel of a mobile robot rolls on the floor without any translational slip.
4.
The wheel of a mobile robot makes rotational slip at the contact point between each wheel
and the floor.
The experimental paths followed by mobile robots to reach the target are obtained as
shown in Fig. 4.10(a), Fig. 4.10(b), and Fig. 4.10(c). From the fuzzy controller (inputs: left,
front, right obstacle distances, and target angle) after defuzzification, robots get the left and
right wheel velocities, which subsequently give the new steering angles. The paths traced by
the robots are marked on the floor by a pen (fixed to the front of the robots) as they move (Fig.
4.10 (c)). The experimentally obtained paths follow closely those traced by the robots during
simulation (shown in Fig. 4.11). From these figures, it can be seen that the robots can indeed
avoid obstacles and reach the targets. Table 4.5 shows the times taken by the robots in
simulations and in the experimental tests to find the targets. The figures given are the averages
of 12 experiments on each environmental scenario being conducted in the laboratory. These
robotics behaviours have been verified in simulation and experimental modes.
64
Image sensor
(b)
Target
Obstacles
Robot
(c)
(a)
Path followed
by robot
(d)
(e)
Figure 4.10. Experimental results of mobile robot to reach the target successfully.
65
Table 4.5. Time taken by robots in simulation and experiment to reach targets
S.
Average of 12 experiments in
Time during
Time during
Percentage
No.
each environment
simulation(sec.)
01.
For 1st environment scenario
17.37
19.5
12.26 %
02.
For 2nd environment scenario
17.37
19.7
13.41 %
03
For 3rd environment scenario
17.37
19.5
12.26 %
experiment(sec.) of error (%)
Simulation path
Experimental path
Figure 4.11. Experimental results validation with simulation mode.
It is observed that the robots are able to reach the targets efficiently during simulation and
experiment, which demonstrate the feasibility of this approach.
4.6 Summary
From the above theoretical, analytical, simulation and experimental results, the following
conclusions are drawn for the present investigation.
66
1.
The robots are able to navigate successfully in a cluttered environment using the developed
fuzzy controller.
2.
With the help of the developed fuzzy inference technique, the robots are able to recognise
the environment and reach the target successfully. This has been demonstrated in
simulation and experimental results.
3.
The fuzzy rules outlined give a navigational control strategy, which indirectly address the
question of determining the sequence of action to achieve the goal.
4.
To verify the theoretical analysis a simulated environment has been developed by
embedding the fuzzy controller.
5.
The experimental results obtained during the navigation of real mobile robots are
compared with the simulation results. A good agreement has been seen during comparison.
This shows the authentication of the developed intelligent fuzzy controller.
6.
This navigation strategy can be used in a mobile robot working in hazardous conditions,
for cooperative task, unmanned space missions.
7.
Various navigational control strategies (e.g. obstacle avoidance, wall-following action, and
target seeking) have been addressed in the current developed controller. These behaviours
are shown in different simulation and experimental scenarios.
™ Publications
1. “Intelligent fuzzy interface technique for controller of mobile robot”, Journal of
Mechanical Engineering Science part C, IMechE, 222 (1), 2008, 2281-2292.
2. “Fuzzy controller for path analysis and planning of mobile robot” International Journal of
Robotics and Automation, ACTA, conditionally accepted for publication. Revised version
submitted.
3. “Intelligent controller for autonomous mobile robot” International conference on ICMAG08, December, 6-12, 2008, Goa (IIT Mumbai), India.
4. “Design of Fuzzy controller for path analysis and planning of autonomous mobile robot”
International conference of ICSCIS-07, December 27-29, 2007, JEC Jabalpur, India.
5. “Fuzzy logic controller for autonomous mobile robot” International conference on RTIME07, October 5-6, 2007, UCE Ujjain, India.
6. “Path Analysis of Mobile Robot using Fuzzy logic”, National Conference on TSDPS-07,
January 6-7, 2007, IT GGDU Bilaspur, India.
7. Navigation of mobile robot: Fuzzy logic Approach”, 22nd National Convention of
Production Engineers & National Conference, Jun2-3 2007, Institution of Engineers(India),
Jabalpur, India.
8. “Navigation of mobile robot using fuzzy logic” Geominetech symposium on ENTMS-07,
May 11-12, 2007, Bhubneshwar, India.
67
5
Analysis of Neural Controller for Mobile Robot
This chapter provides a novel approach for design of an intelligent controller for autonomous
mobile robot using multilayer feed forward neural network which enables the robot to navigate
in a real world dynamic environment. The inputs to the proposed neural controller consist of
left, right, and front obstacle distance with respect to its position and target angle. The output of
the neural network is steering angle. A four layer neural networks has been designed to solve
the path and time optimisation problem of mobile robots that deals with the cognitive tasks
such as learning, adaptation, generalisation and optimisation. Back propagation algorithm is
used to train the network. The simulation results are compared with experimental results, which
are satisfactory and show a very good agreement. The training of the neural nets and the control
performances analysis of the neural network has been done in a real experimental setup.
5.1 Introduction
A lot of research is going on around the globe to find a suitable intelligent control to be
used for navigation of mobile robot without human interaction. One of the most important
issues in the design and development of intelligent controller for mobile robot is the navigation
problem, i.e. the sequences of actions required during goal achieving without collision with
static as well as dynamic obstacle. This consists of the abilities of a mobile robot to plan and
execute collision free motions within its environment. However, this environment may be
imprecise, vast, dynamical and either partially or non-structured. Bio-inspired robotics, in this
context, tries to give an answer to the issues like mimicking, the behaviours and the structure of
living creatures in the controller of the mobile robot. The bio-inspired neural controller is based
on the working principal of nervous system of simple animals, like arthropods or invertebrates
and can be used to control mobile robot. This chapter proposed a biologically inspired neural
network approach for real-time collision-free motion planning of mobile robots in real world
dynamic environment. The necessary requirements of the mobile robot is tracking and reaching
the given target by avoiding static as well as dynamic obstacles. This is the main research area
being addressed in this chapter. The path and time optimisation of mobile robot depends on the
intelligence of the controller. Many researchers used various methods to optimise the path and
time. Their proposed methods are complicated and they may good for local path planning but
68
not for global path planning. The developed method is simple and obtained results depicts that
the method is efficient and effective for navigation of mobile robot in dynamic cluttered
environment. Four layer perceptron neural networks have been used to design an intelligent
controller. The first layer is used as input layer, which directly read signals from the arrays of
sensors. The input of the network is front obstacle distance, right obstacle distance, left obstacle
distance and target angle. The neural network is consisting of two hidden layer, which adjust
the weight of neurons. The output layer provides steering angle of the robot. Back propagation
algorithm is used to minimise the error and optimise the path and time of mobile robot to reach
the target.
The outline of this chapter is as follows, following the introduction, the neural network
architecture for navigation of mobile robot is presented in section 5.2. The simulation results
are discussed and to prove feasibility of the developed methodology a comparison has been
made with other methods [194, 213, 214] in section 5.3. In section, 5.4 experimental results are
verified with simulation to demonstrate the superiority of the proposed methodology. Finally,
summary has been discussed in the last section 5.5.
5.2 Analysis of Neural Network for Navigation
Artificial neural networks consist of a set of simple, densely interconnected processing
units. These units transform signals in a non-linear way. Neural networks are non-parametric
estimators, which can fit smooth functions based on input-output examples. The neural network
used is a four-layer perceptron [215]. The numbers of layers are found empirically to facilitate
training. The input layer has four neurons, three for receiving the values of the distances from
obstacles in front and to the left and right of the robot and one for the target bearing. If no
target is detected, the input to the fourth neuron is set to zero. The output layer has a single
neuron, which produces the steering angle to control the direction of movement of the robot.
The numbers of neurons are found based on the number of training patterns and the
convergence of error during training to a minimum threshold error. Two hidden layers are used,
as with one hidden layer there is difficult in training the neural network within a specified error
limit. The training error is the difference between desired output and actual output. The first
hidden layer has ten neurons and the second hidden layer has three neurons. These numbers of
hidden neurons were also found empirically.
69
Fig. 5.1 depicts the neural network with its input and output signals. The neural network
trained to navigate by presenting it with 200 patterns representing typical scenarios, some of
which are depicted in Fig. 5.2. For example, Fig. 5.2 (b) shows a robot is advancing towards an
obstacle, another obstacle being on its right hand side. There are no obstacles to the left of the
robot and no target within sight. The neural network is trained to output a command from the
robot to steer towards its left. Table 5.1 shows the list of empirical training patterns based on
Fig. 5.2.
During training and during normal operation, the input patterns fed to the neural network
comprise the following components:
y
Left obstacle distance from the robot
(5.1a)
y
Front obstacle distance from the robot
(5.1b)
y
Right obstacle distance from the robot
(5.1c)
y
Target bearing of the robot
(5.1d)
These input values are distributed to the hidden neurons that generate outputs given by
y
f V
(5.2)
Where
V
∑W
.y
(5.3)
lay = layer number (2 or 3)
j = label for jth neuron in hidden layer ‘lay’
i = label for ith neuron in hidden layer ‘lay-1’
W
= weight of the connection from neuron i in layer ‘lay-1’ to neuron j in layer ‘lay’.
70
First Hidden Layer
Second
Hidden
Layer
Input Layer
Left-obs
Output
Front-obs
Steering
Angle
Right-obs
Tar-ang
Figure 5.1. Four-layer neural network for robot navigation.
Figure 5.2. Example of training patterns.
71
Table 5.1. Some of the training pattern of neural controller
Position
Figure
5.2
Inputs of the network
Right
Left
obstacle
obstacle
distance(cm) distance(cm)
15
20
Target
angle
(degree)
0
Output
Steering
angle
(degree)
-180
Front obstacle
distance (cm)
(a)
20
(b)
20
15
100
0
-90
(c)
20
100
15
0
90
(d)
100
15
100
0
0
(e)
100
100
20
0
0
(f)
20
100
100
0
90
(g)
100
20
20
0
0
(h)
30
10
10
0
-20
(i)
30
100
100
35
30
(j)
30
15
10
45
10
(k)
30
10
10
0
5
(l)
100
30
15
0
0
(m)
100
15
30
-45
-40
(n)
100
100
10
-50
0
(o)
100
15
100
30
0
(p)
100
100
100
-20
-20
(0, +1.0)
f(x)
(0, 0)
X
(0, -1.0)
Figure 5.3. Hyperbolic tangent function used for activation function.
72
f(.) = activation function, chosen in this work as the hyperbolic tangent function shown in
Fig. 5.3.
f x
(5.4)
During training, the network output θ
may differ from the desired output θ
as
specified in the training pattern presented to the network. A measure of the performance of the
network is the instantaneous sum-squared difference between θ
and θ
for the set of
presented training patterns.
∑
E
θ
θ
(5.5)
The error back propagation method is employed to train the network [215]. This method
requires the computation of local error gradients in order to determine appropriate weight
corrections to reduce Error. For the output layer, the error gradient δ
δ
f V
θ
is
θ
(5.6)
The local gradient for neurons in hidden layer {lay} is given by
δ
f
∑ δ
V
W
(5.7)
The synaptic weights are updated according to the following expressions
W t
1
W t
∆W t
1
(5.8)
And
∆W t
1
α∆W t
∆ηδ
y
(5.9)
Where
73
α = momentum coefficient (chosen empirically as 0.2 in this work)
η = learning rate (chosen empirically as 0.35 in this work)
t = iteration number, each iteration consisting of the presentation of a training pattern and
correction of the weights.
Table 5.2. Reactive behaviours adopted by mobile robot during navigation
Types of
Description of the behaviours
Behaviour
Obstacle
(i)Mobile robot detects (by
avoidance
Implementations
sensory The robot reduces the speed and
information) any obstacle in front, left or set
the
steering
angle
right side. This behaviour required to avoid accordingly.
collision with obstacle (Fig. 5.4).
The robot stopped and takes
(ii)When the acquired information from the counter clockwise rotation both
sensors shows the presence of obstacles to left and right wheel in same
the front, left and right side of the robot. speed (i.e. reverse direction).
The robot reverses its movement (Fig. 5.4).
Target
When the acquired information from the The robot mainly adjusts its
seeking
sensors shows that there are no obstacles motion direction and quickly
around
the
robot,
its
main
reactive moves towards the target.
behaviour is to seek the target. This
behaviour requires to locate the target (Fig.
5.4).
Wall
Mobile robot detects an obstacle in the The robot adjust the speed and
following
front while it is moving towards target and set the heading angle 90° with
also having wall to the left or right side. wall so that it align with wall
The robot has to follow the wall to reach and moves along the wall. The
the target (Fig. 5.5).
robot automatically makes turns
to align itself along the wall and
move parallels with the wall to
reach the target.
74
The final output from the neural network is
θ
f V
(5.10)
Where
V
∑W
y
(5.11)
It should be noted learning can take place continuously even during normal target seeking
behaviour. This enables the controller to adopt the changes in the robot’s path while moving
towards target. Mainly three behaviours (obstacle avoidance, wall following and target seeking)
are required to train and to design an intelligent controller for mobile robot being used to
navigate in a cluttered environment. Table 5.2 depicts the used behaviour being trained by
network.
5.3 Simulation Results and Discussions
Existing approaches for learning to control a mobile robot rely on supervised methods,
where correct behaviour is explicitly given. The simulation results present the effectiveness of
novel approach that evolves neural network controller. The series of simulations test have been
conducted with the ROBNAV software (Appendix–A). To demonstrate the effectiveness and
the robustness of the proposed method, simulation results on mobile robot navigation in various
environments are exhibited.
For visual guidance of behaviour, in navigation the perception of motion plays a prominent
role. An important part of robot behaviour is avoidance of obstacles. Examples of static
obstacles include walls, poles, fences, trees etc. as well as other moving obstacle like vehicles,
people, animals etc. Encountering such objects can cause avoidance behaviour, which consists
of any combination of slowing down, turning, and stopping (Fig. 5.4). The wall following
behaviour is required to move from one room to another room. The wall following behaviour
mode will be adopted when the mobile robot detects an obstacle in the front while it is moving
towards target, the mobile robot may turn left or right because presence of obstacle in the
front. In this case, the robot tries to maintain perpendicular to the wall. The simulation result of
wall following behaviour is shown in Fig. 5.5.
75
Target
tracker
robot
Target
Static obstacles
Other robot
as dynamic
obstacles
Robots at initial
Position
Path
followed by
target
(b)
(a)
Figure 5.4. Static as well as dynamic obstacle avoidance behaviour (a) At initial position before
simulation (b) Navigational path during simulation.
Mobile
Robot
Target
Target
Path
Wall
shaped
obstacle
Wall shaped obstacle
Rectangle
obstacle
Path
(b)
(a)
Figure 5.5. Robot with wall following behaviour (b) Robot escaping from dead end obstacles.
Target searching algorithms assume that the goal state is fixed and does not change during
navigation of mobile robot. For example, in the problem of moving from the current location to
a desired goal location along a network of paths, it is assumed that the target location is fixed
and does not change during the navigation. Neural controller mainly adjusts robots motion
direction and quickly moves it towards the target if there are no obstacles around the robot as
shown in Fig. 5.4. In the proposed control strategy, reactive behaviours are formulated and
trained by neural network.
76
(a)
Target
Target
Path
Path
Start
Obstacles
Start
Obstacles
Target
Obstacles
Obstacles
Target
Path
Path
Start
Start
(b)
Figure 5.6. (a) Navigation of a mobile robot in unknown environment by Ray et al. [216] (b)
Navigation of a mobile robot in unknown environment using a developed controller.
77
(a)
Wall
shaped
obstacle
Wall shaped
obstacle
Rectangle
obstacle
Path
Path
Rectangle
obstacle
Initial configuration
Final configuration
Wall
shaped
obstacle
Rectangle
obstacle
Final configuration
Wall shaped obstacle
Path
Rectangle obstacle
Path
Initial configuration
(b)
Figure 5.7. (a) Experimental result of planned path by Hamel et al. [194] (b) Navigation of
mobile robot using developed controller.
78
(a)
(b)
Figure 5.8. (a) Static and dynamic experimental result by Sanchis et al. [214] (b) Static and
dynamic simulation result by developed neural controller.
79
In order to exhibit the effectiveness of the proposed neural controller of mobile robot, the
results obtained by Ray et al. [216] for navigation of a mobile robot in an unknown
environment (Fig. 5.6(a)) are compared with obtained the results from the current developed
controller (Fig. 5.6(b)). They show a very good agreement. The results obtained using feedback
control law by Hamel et al. [194] have been compared with the results obtained from proposed
neural controller of mobile robot (Fig. 5.7). In addition, a comparison has been done between
the static and dynamic result using classifier systems described by Sanchis et al. [214] and
results obtained from the current developed controller (Fig. 5.8). The comparisons show a good
agreement.
5.4 Experimental results
The navigation method has been tested in a series of experiments to exhibit its
effectiveness. All experimental result carried out using C++ executable code loaded on
Khepera-III (Appendix-C.2) mobile robot. The position of wheels and sensors of Khepera-III
mobile robot has been depicted in Fig. 5.9. The assumptions about the mechanical structure and
the motion of the mobile robot moves on a plane surface and wheels are pure rolling.
Figure 5.9. The chassis of the KHEPERA-III robot.
80
Table 5.3 Time taken by robots in simulation and experiment to reach targets
Average of 9 experiments in
S.
No. each environment
Path length
Time during
Time during
(in pixel)
simulation(sec.) experiment(sec.)
01.
For 1st environment scenario 221
Fig. 5.10-i and Fig.5.11(a)
23
26
02.
For 2nd environment scenario 206
Fig. 5.10-ii and Fig.5.11(b)
22
25
03
For 3rd environment scenario 175
18
21
25
27
Fig. 5.10-iii and Fig.5.11(c)
04
For 4th environment scenario 234
Fig. 5.10-iv and Fig.5.11(d)
From the neural controller (inputs: left, front, right obstacle distances and heading angle)
after learning and training, robots get the left and right wheel velocities which subsequently
give the new steering angles. During experiment, it has been found that the experimental path
lengths and time taken are more than the simulation path lengths and time taken. This is due to
presence of various errors (e.g. signal transmission error in data-cable, obstacle/ target tracking
error, presence of friction in rotating elements, slippage between floor and wheels, friction
between supported point and floor etc.). Table 5.3 shows the times taken by the robots in
simulations and in the experimental tests during finding the targets.
The experiment has been conducted in the laboratory for different environmental scenarios.
The figures given are the averages of three experiments on each environmental scenario
conducted in the laboratory. All mention above robotics behaviours are verified in simulation
and experimental mode (Fig. 5.10 and Fig.5.11). The fuzzy logic controller proposed by
Pradhan et al. [213] has been examined and compared with the proposed neural controller in a
similar navigational environment. It has been found that the neural controller gives a more
optimised path than the fuzzy controller (the total path length using a fuzzy controller by
Pradhan et al. [213] is 13.7m and the time taken is 14.67 s to reach the target, whereas the total
path length using a proposed neural controller is 12.0m and the time taken is 12.84 s). In
addition, a neural controller requires less computing time and computing memory than a fuzzy
controller.
81
(i-a)
(i-b)
(ii-a)
(ii-b)
(iii-a)
(iii-b)
(iv-a)
(iv-b)
Figure 5.10. Experimental results during target seeking by the mobile robot in various
environments
82
Simulation path
Experimental path
(a)
(b)
(c)
(d)
Figure 5.11. Comparison of experimental results with simulation results.
It has been observed that the robot controlled through neural control has better
performance than the fuzzy controller in terms of positioning accuracy and collision avoidance
and it provides optimise path to reach the goal.
Table 5.4. Simulation results comparison between the fuzzy controllers developed by Pradhan
et al. [213] and the current developed neural controller
S.
Navigation with
Fuzzy controller
Neural controller
Percentage
No.
different method
01.
Length of path (in meter)
13.8
12.2
11.58 %
02.
Time taken (seconds)
14.67
12.97
11.59 %
of deviation
83
5.5 Summary
The conclusion drawn based on the theoretical; simulations and experimental analysis are
depicted below.
Both in simulation and experimental modes the developed controller worked efficiently.
The simulation results are also compared with the results obtained from the other investigations
and they show a very good agreement. Back-propagation neural network is used to design the
controller. The developed neural controller has got the following salient feature:
1.
Mobile robots are able to avoid any static and dynamic obstacles on their path. In dynamic
environment, the proposed neural controller can be efficiently applied.
2.
During navigation using the sensors information robots are able to map the surrounding.
3.
On comparison with three various approaches (i.e. feedback control law, classifier systems
and fuzzy controller) it is found that the developed controller is simple but efficient for
navigation of mobile robot in dynamic environment.
4.
Training patterns of each network can be generated by simulation rather than by
experiment, saving considerable time and effort.
5.
behaviours such as obstacle avoidance, wall following, and target seeking are integrated in
the current controller to obtain an efficient navigational controller.
Some features of the intelligent controller cannot be added by using a single technique like
fuzzy logic or neural network technique. Certainly, these two fields can be integrated into a
new emerging technology called adaptive neuro-fuzzy system, which combines the benefits of
each field (i.e. perception, cognition, and motion control). Next chapter, describes a hybrid
controller for more efficient navigation of the mobile robots.
™ Publications
1. “Real time navigational control of mobile robots using artificial neural network” Journal of
Mechanical Engineering Science part C, I MechE, 223(7), 2009, 1713-1725.
2. “Path optimisation of mobile robot using artificial neural network (ANN) controller”,
International Journal of System Science, Taylor & Francis, 2009, (Accepted).
3. “Intelligent Neuro-controller for Navigation of Mobile Robot” International conference on
ICAC3’09, January 23–24, 2009, Mumbai, India.
84
6
Adaptive Neuro-Fuzzy Controller for Navigation of Mobile
Robots
This chapter provides about navigation control of multiple mobile robot using adaptive neurofuzzy inference system (ANFIS) in cluttered environment. In the ANFIS controller after the
input layer there is a fuzzy layer and rest of the layers are neural layers. The adaptive neurofuzzy hybrid system combines the advantages of fuzzy logic system, which deal with explicit
knowledge that can be explained and understood, and neural networks, which deal with implicit
knowledge, which can be acquired by learning. The merger of neural networks and fuzzy logic
led to the creation of neuro-fuzzy controllers which are currently one of the most popular
research fields. The inputs to fuzzy logic layer are front obstacle distance, left obstacle
distance, right obstacle distance and target steering. A learning algorithm based on neural
network technique has been developed to tune the parameters of fuzzy membership functions,
which smooth the trajectory generated by the fuzzy logic system. Using the developed ANFIS
controller, the mobile robots are able to avoid static and dynamic obstacles, and reach the target
successfully in cluttered environments. The experimental results agree well with the simulation
results, proves the authenticity of the theory developed.
6.1 Introduction
Researchers strive to develop new concepts and strategies to improve existing ones in the
area related to mobile robot navigation. To do this, criteria for optimal performance and ways
to optimise design, structure and control of robots must be developed and implemented. The
current robot navigation systems require controllers able to solve complex problems under very
uncertain and dynamic environmental situations. Presently, the ANFIS approach is becoming
one of the major areas of interest because it gets the benefits of neural networks as well as of
fuzzy logic systems and it removes the individual disadvantages by combining them on the
common features. The artificial neural network has injected a new driving force into the fuzzy
literature.
Fuzzy systems are able to treat uncertain and imprecise information, they make, use of
knowledge in the form of linguistic rules. Their drawbacks are caused mainly by the difficulty
85
of designing accurate membership functions and lack of a systematic procedure for the
transformation of expert knowledge into the rule base. Neural networks have the ability to learn
but with some neural networks, knowledge representation and extraction are difficult [152]. An
algorithm for mapping using sparse constraint graphs is descried by Thrun et al. [217] which
obtains the map and the robot path. Their methodology optimises the simultaneous localization
and mapping problems. A methodology used to describe the interaction between perception and
action, can be adapted to yield a mobile robot system that is highly sensitive to the currently
perceived world [211]. Reactive control is an approach to robotics that eliminates the use of
intervening representation and reasoning during the execution of a robot’s mission.
In this chapter, ANFIS approach has been proposed for real time navigation of mobile
robot. In the present work, a time-optimal and collision-free path has been developed for
navigation of mobile robot in unknown and cluttered environments. To achieve optimised path
and time, this chapter proposes a path planning approach based on ANFIS which emulates the
human driving behaviour. Fuzzy logic has been used for behaviour design such as obstacle
avoidance, wall following and target seeking which negotiates uncertain and imprecise
information; they make use of knowledge in the form of linguistic rules. The developed ANFIS
is based on a fuzzy system, which is trained by a learning algorithm derived from neural
network theory. Learning allows autonomous robots to acquire knowledge by interacting with
the environment and subsequently adapting their behaviour and solve the problem of
insufficient knowledge for designing the controller rule-base. The ANFIS learns and generates
the required knowledge for achieving desired goals from the mobile robot behaviour and its
environment. Numerical examples are presented to demonstrate the validity of the approach.
The simulation results are compared with the results from other methods [90, 98, 213, 218].
Experimental results are verified with simulation results to demonstrate the effectiveness of the
proposed methodology.
This chapter is organised into five sections following the introduction; the entire ANFIS
architecture has been discussed in section 6.2. The simulation results are presented in section
6.3 and experimental results are analyzed in section 6.4. Finally, the summary is given in
section 6.5.
86
6.2 Analysis of ANFIS
The adaptive neuro fuzzy inference system (ANFIS) is an integrated system of artificial
neural network (ANN) and fuzzy inference system (FIS). The ANFIS analysed here is a first
order Takagi Sugeno Fuzzy Model [150, 156]. In the current analysis there are four inputs
Front obstacle distance x , Right obstacle distance x , Left obstacle distance x
Target angle x
and
and the output is Steering angle. The if-then rules for the ANFIS architecture
are defined [150] as follows;
:
x is A , x is B , x is C and x is D
f
p x
r x
s x
t x
Where;
f
j
p x
1 to q ; k
r x
s x
1 to q ; m
t x
u ; for steering angle
1 to q ; n
1 to q and i
(6.1)
1 to q . q . q . q
A, B, C and D are the fuzzy membership sets defined for the input variables x1, x2, x3 and
x4. q1, q2, q3 and q4, are the number of member ship functions for the fuzzy systems of the inputs
x1, x2, x3 and x4 respectively. fi is the linear consequent functions defined in terms of the inputs
(x1, x2, x3 and x4) . pi, ri, si , ti and ui are the consequent parameters of the ANFIS fuzzy model.
In the ANFIS model, nodes of the same layer have similar functions. The output signals from
the nodes of the previous layer are the input signals for the current layer. The output obtained
with the help of the node function will be the input signals for the subsequent layer (Fig. 6.1).
Layer 1: The input layer receives signal from arrays of sensors x , x , x , x , which defines the
static as well as moving obstacles, and target poisons from the target tracker robot. The target
position measured according to the target coordinates. The coordinates are given to the robots
during navigation. The robot measures its global position according to its wheel movements
during navigation.
Layer 2: Every node in this layer is an adaptive node (square node) with a particular fuzzy
membership function (node function) specifying the degrees to which the inputs satisfy the
quantifier. For four inputs the outputs from nodes are given as follows;
87
Figure 6.1. Six-layers ANFIS architecture for robot navigation.
µA
1.0
bg/2ag
0.5
0
cg
(cg-ag)
(cg+ag)
X
Figure 6.2. Bell shaped membership function used for fuzzy inference system.
88
L
,
µA x for g
1, … , q
L
,
µB x for g
q
1, … , q
L
,
µC x for g
q
q
L
,
µD x for g
(For input x1)
(For input x2)
1, … , q
q
q
q
q
q
q
1, … , q
q
(For input x3)
q
q
(For input x4)
Here the membership function for A, B, C and D considered are the bell shaped function
and are defined as follows;
µA x
; g
"1" to "q "
µB x
; g
"q
1" to "q
µC x
; g
"q
q
1" to "q
µD x
; g
"q
q
q
(6.2)
q "
(6.3)
q
1" to "q
q "
q
(6.4)
q
q " (6.5)
Where a b and c are the parameters for the fuzzy membership function. The ballshaped function (Fig. 6.2) changes its pattern as per the change of the parameters. This change
will give the various contour of bell shaped function as needed in accord with the data set for
the problem considered.
Layer 3: Every node in this layer is a fixed node (circular) labeled as “ ”. The output denoted
by L
,
L
for i
the output is the product of all incoming signal.
,
W
µA x , µB x , µC x , µD x ;
1, … , q , q , q , q and g
1, … … , q
(6.6)
q
89
q
q
The output of each node of the second layer represents the firing strength (degree of
fulfillment) of the associated rule. The T-norm operator algebraic product {Tap (a,b) = ab}, has
been used to obtain the firing strength W .
Layer 4: Every node in this layer is a fixed node (circular) labeled as “N”. The output of the ith
node is calculated by taking the ratio of firing strength of ith rule W
to the sum of all rules’
firing strength.
L
W
,
.
∑
W
.
.
(6.7)
W
This output gives a normalized firing strength.
Layer 5: Every node in this layer is an adaptive node (square node) with a node function.
L
,
W f
W px
rx
sx
tx
u
(6.8)
Where W is a normalized firing strength form (output) from layer 3 and {p , r , s , t , u } is
the parameter set for steering angle. Parameters in this layer are referred to as consequent
parameters.
Layer 6: The single node in this layer is a fixed node (circular) labeled as “Σ”, which computes
the overall output as the summation of all incoming signals.
,
∑
.
.
.
∑
∑
.
.
.
.
.
(6.9)
.
In the current developed ANFIS structure there are six dimensional space partitions and
has “q
q
q
q ” regions. Each region is governed by a fuzzy if then rule. The first
layer is the input layer. The second layer (consists of premise or antecedent parameters) of the
ANFIS and is dedicated to fuzzy sub space. The third and fourth layer is fixed node (circular)
labeled as π and N. The parameters of the fifth layer are referred as consequent parameters and
are used to optimise the network. The first order Takagi-Sugeno model is used for
difuzzyfication in fifth and sixth layer. During the forward pass of the hybrid learning
algorithm node outputs go forward till layer five and the consequent parameters are identified
90
by least square method. In the backward pass, error signals propagate backwards and the
premise parameters are updated by a gradient descent method.
6.3 Simulation Results
The simulations results are obtained by using ROBNAV software (Appendix-A). To
demonstrate the effectiveness and the robustness of the proposed method, simulation results on
mobile robot navigation in various environments are exhibited.
The obstacle avoidance behaviour is activated when the readings from any sensors are less
than the minimum threshold values (50 mm). This is how the robot determines if an object is
close enough for a collision. When an object is detected too close to the robot, it avoids a
collision by moving away from it in the opposite direction. Collision avoidance has the highest
priority and therefore, it can override other behaviours, in this case, its main reactive behaviour
is decelerating for static as well as dynamic obstacle avoidance as shown in Fig. 6.3 (a). When
the acquired information from the sensors shows that there are no obstacles around robot, its
main reactive behaviour is target steer. ANFIS mainly adjusts robots motion direction and
quickly moves it towards the target if there are no obstacles around the robot as shown in Fig.
6.3 (b). In the proposed control strategy, reactive behaviours are formulated and trained by
ANFIS.
Other robot (OR)
as dynamic
Target
Target
tracker
robot
(TTR)
Start
Static
obstacle
Path followed by TTR
(a)
(b)
Figure 6.3. (a) Static as well as dynamic obstacle avoidance behaviour (b) Target seeking
behaviour of mobile robot.
91
Another special condition appears as the mobile robot detects an obstacle in the front while
the target tracking control mode is on operation. In this case, the fixed wall following
behaviour should be performed first, that is, the mobile robot must rotate clockwise or
counterclockwise such that it can align and move along the wall. When the robot is moving to a
specified target through a narrow channel, dead end or escaping from a U shaped obstacle, in
such a situation the robot should keep on heading towards the goal position. But when it moves
towards the goal position, the robot also comes across the obstacles. Any obstacle-avoidance
behaviour except wall following behaviour would make the robot divert from its goal position.
The navigation path of mobile robot by purposed ANFIS methodology and escaping from dead
end has been shown in Fig 6.4 (a) and Fig. 6.4 (b).
The results obtained from the proposed ANFIS approach for real time navigation of mobile
robot during vehicle controlled motion with a cluttered obstacle environment from two
different goal and starting points have been compared with the result from Abdessemed et al.
[90] during vehicle controlled motion with a cluttered obstacle environment from two different
starting points (shown in Fig. 6.5). Apart from comparison between fuzzy and neural technique
a comparison has also been made between the current developed controller and the potential
field method proposed by Arkin [211] during navigation of robot, shown Fig 6.6.
(b)
(a)
Figure 6.4. (a) Navigation path of mobile robot by purposed ANFIS (b) Escaping from dead
end by purposed ANFIS methodology.
92
(a)
(b)
Figure 6.5. (a) Results of Abdessemed et al. [90] during vehicle controlled motion with a
cluttered obstacle environment from two different starting points. (b) Results of proposed
ANFIS approach during vehicle controlled motion with a cluttered obstacle environment from
two different goal and starting points.
(a)
(b)
Figure 6.6. (a) Path traced by the robot embedded with Arkin’s[211] controller, (b) Path traced
by the robot embedded with proposed ANFIS controller.
93
A comparison has also been done between the results obtained by Camilo et al. [221] for
navigation of mobile robot in a double U shaped environment and large and recursive U shaped
environment and the results from the developed ANFIS method shown in Fig. 6.7 (a) and Fig.
6.7 (b). They show a very good agreement.
(i)
(a)
(ii)
(iii)
(b)
(iv)
Figure 6.7. Comparison results of Camilo et al. [221] proposed approach (i) in a double U shape
environment (ii) in a large and recursive U-shape environment (b) Results of proposed ANFIS
approach (i) in a double U shape environment (ii) in a large and recursive U-shape
environment.
94
6.4 Experimental Results
Experimental results are found out using Khepera-III mobile robot (Appendix-C.3) loaded
simulation ROBNAV software (Appendix-A). The assumptions about the mechanical structure
and the motion of a mobile robot are, the mobile robot moves on lab specified floor area and
the wheel of a mobile robot rolls on the floor without any translational slip.
During experiment the paths followed by mobile robots to reach the target are traced. From
the ANFIS (inputs: left, front, right obstacle distances and target angle) after learning, training
and testing, robots gets the new steering angles. The experimental paths traced by the obstacle
robots (OR) (Khepera-II (Appendix-C.2)) and target tracker robot (TTR) are marked on the
floor by a pen as they move (Fig. 6.8). The OR1, OR2, OR3, OR4 are term as moving obstacle
and TTR (Khepera-III) is terms as the target tracker. The paths followed by OR and TTR have
been shown in Fig. 6.9. The results obtained from experimental setup are more close to results
obtained from simulation mode (Fig. 6.10) which validate the proposed method.
During simulation and experimental result it has been found that the robot efficiently
avoids the obstacles presents in the environment and successfully reach the targets. These
robotics behaviours are verified in simulation and experimental mode (Fig. 6.10). Table 6.1
shows the times taken by the robots in simulations and in the experimental tests scenario during
target finding. It is observed that the robots are able to reach the targets efficiently during
simulation and experiment. It is found that the navigation of mobile robot with purposed
ANFIS method has better performance than the fuzzy as well as neural controller in terms of
positioning accuracy and collision avoidance.
Table 6.1 Time taken by robots in simulation and experiment to reach targets.
S.
Observations
No.
(Fig.14)
Simulation
environment
Experimental
environment
Deviation of results
(simulation Vs. experiment)
01.
Length of path
(in meter)
15.4
16.2
5.19%
02.
Time taken
(seconds)
16.32
18.63
14.15%
95
(a)
(b)
Figure 6.8. Experimental results of purposed ANFIS method.
Y
Target
OR3
TTR
OR4
OR1
OR2
X
Figure 6.9. Paths followed by mobile robots using ANFIS method.
96
Target
Simulation path
Experimental path
Figure 6.10. Experimental results validation in simulation mode.
6.5 Summary
The summary drawn on the basis of theoretical simulation and experimental analysis are
depicted below:
The developed ANFIS controller has been used for navigation control of multiple mobile
robots both in simulation and experimental mode. ROBNAV software has been developed to
the handle the navigation control of mobile robot using ANFIS controller. The proposed
method has got the following salient feature:
1. The proposed ANFIS controller is successfully applied for navigation in dynamic as well as
static environments, mobile robot able to avoid static as well dynamic obstacle in a
cluttered environment.
97
2. The robots are able to move in the surroundings using the embedded infrared sensors. The
robot rapidly maps their surroundings which provide sufficient information for path
optimization during navigation.
3. The proposed method is simple but efficient tool for mobile robot navigation, especially in
a real world dynamic environment. Training patterns of each network can be generated by
simulation rather than by experiment, saving considerable time and effort.
In the next chapter more robust hybrid technique has been discussed for better navigation
control.
™ Publications
1. “Navigational path analysis of mobile robots using ANFIS controller in dynamic
environment”, Journal of Mechanical Engineering Science part C, IMechE, 2009,
(Accepted).
2. “ANFIS approach for navigation of mobile robots”, IEEE International conference on
ARTCom09, October 27–28, 2009, Kerela, India.
3. “Design of intelligent control systems for autonomous mobile robot navigation using soft
computing” GE Global Conference on DREAMS-07, March 11, 2007, Banglore, India.
4. “Design of intelligent controller for mobile robot using soft computing”, National
Conference on NCMSTA'08, November 13-14, 2008, NIT Hamirpur, Himachal Pradesh,
India.
98
7
Heuristic Rule Base Neural Controller for Mobile Robot
This chapter presents a novel technique for mobile robot to navigate in real world dynamic
environment. When an autonomous mobile robot navigates in an unknown environment it
requires to plan a path based on the information gathered from sensors in order to avoid
obstacles and get to a target. This research is related to the idea of perception based heuristic
rule formation for navigation of mobile robots in static as well as dynamic environments. The
proposed method is simple and fast in execution using the concept from distance-transform
path-finding algorithms. The proposed methodology provides a general, robust, safe and
optimised path. The heuristic rule base network (HRBN) consists of a simple algorithm which
makes predefined estimation function very smaller. The estimation function should be
adequately defined for desired movement in the environments. A navigation system using rule
based technique that allows a mobile robot to travel in an environment about, which the robot
has no prior knowledge. This heuristic rule is applied in conjunction with artificial neural net
work (ANN). The ANN is trained by back propagation algorithms (BPA). A HRBN provides
an optimum trajectory which increases the effectiveness of a mobile robot. A Petri Net Model
(PNM) has been used to prevent the inter robot collision during navigation. A series of
simulations and experiments are conducted using the mobile robot to show the effectiveness of
the proposed algorithm.
7.1 Introduction
Autonomous mobile robots have a wide range of applications in industries, hospitals,
offices, and even in the military section, due to their superior and intelligent mobility. They are
also useful in emergencies for fire extinguishing and rescue operations. Combined with
manipulation abilities, their capabilities and efficiency will increase and can be used for
dangerous tasks such as security guard, exposition processing, as well as undersea,
underground and even space exploration [187]. In addition, their capabilities also allow them to
carry out specialized tasks in hazardous or hardly accessible environments for human beings
such as nuclear plants and chemical exposed environments. Motion planning algorithms
construct such a path which deals with the planning of motion of a robot between starting
positions to a target location [191]. This chapter introduces a control system for a mobile robot
99
which provides heuristic learning concretely. Useful heuristic rules are hybridized with the
ANN to build the desired mapping between perception and motion. ANN consisting of four
inputs the left obstacles distances (Left-obs), right obstacles distances (Right-obs), front
obstacles distances (Front-obs) and the interim steering angle and an output of final steering
angle. To estimate the risk of colliding with other robots a petri net model (PNM) is used for
the robot motions. It allows continuous, fast motion of the mobile robot without any need to
stop for obstacles. This proposed approach has been tested in extensive simulation mode and
implemented on Khepera III mobile robot as target tracker mobile robot and Khepera-II
(Appendix-C.2) used as moving obstacle robot. In different experiments the proposed approach
is well suited to control the motions of a team of robots in a typical environment and illustrate
its advantages over other techniques developed so far. The hybrid path is much safer than the
shortest path, but shorter than the safest one.
7.2 Perception Based Heuristic Rule
The heuristic rules are based on human perception (i.e. the working environment provides
a fixed referential frame for the rules). In the current analysis the robot uses this environmental
information to adjust itself according to it. This research goal is to obtain algorithms that,
executed on a man-made visual system, result in the acquisition of perceptual capabilities that
robot could use to perform specific commands [219]. Khepera III (Appendix-C.3) and Koala
silver version (Appendix-C.4) mobile robot has been used for experimental validation. The
Khepera III mobile robot has nine sensors placed around the robot and other two sensors are
placed on the bottom. The sensors positions are numbered as shown in Fig. 7.1 (1to11). These
sensors embed an infra-red light emitter and a receiver. This sensor device allows to measures
the normal ambient light, which is strongly influenced by the robot’s environment. Objects
color, materials and surfaces do have an influence on the sensors response. In its base of the
robot, five sensors are placed around the robot and are positioned and numbered as shown in
Fig. 7.1(U1-U5), in fact five pairs of ultrasonic sensors where each pair is composed of one
transmitter and one receiver. The ultrasonic sensors are powered by a 20 Vdc source. And
Koala mobile robot has sixteen and sensors are placed around the robot. Their position and
number are shown in Fig. 7.2 (L0 to L7 & R0 to R7). These sensors embed an infra-red light
emitter diode and a receiver.
100
5
U3 4
U4
6
U2
10 11
3
Supported
wheel
Right
Left
driving driving
wheel wheel
U5
7
8
U1
2
1
9
Figure 7.1. Position of wheels and sensors in Khepera-III mobile robot, infrared (1-11) and
ultrasonic sensors (U1-U5).
L1
L0
R0
L2
R1
L3
R2
R3
Top view
R4
L4
Positive direction
Motor 0
L5
Negative direction
Motor 1
R5
Sensors left L0 to L7 Sensors right R0 to R7
L6
R7
L7
R6
Figure 7.2. Position of wheels and sensors in koala mobile robot.
101
Based on these sensors a human perception based heuristic rule can be formulated. The
methodology is a general, robust, and safer which provides fast path planning framework for
robotic navigation. If the target is located right side then the robot will steer clockwise direction
i.e. positive steering angle but it the target is located left side then the robot will steer counter
clock direction i.e negative. Human perception based some of the heuristic rules from Table 7.1
are listed below based on the left obstacle and target both are situated in left side of the robot.
Rule 1: If left-obs = 150 mm and right-obs
200 mm and front-obs
200 mm and tar-ang =
200 mm and front-obs
200 mm and tar-ang =
200 mm and front-obs
200 mm and tar-ang =
82˚ Then change in steering angle = 0˚
Rule 2: If left-obs = 150 mm and right-obs
75˚ Then change in steering angle = -15˚
Rule 3: If left-obs = 150 mm and right-obs
54˚ Then change in steering angle = -30˚
Similarly rule can also formulate with reference to the obstacle as well as target are located
in right side of the robot. Some of the heuristic rules from Table 7.2 are listed below.
Rule 7: If left-obs
200 mm and right-obs = 150 mm and front-obs
200 mm and tar-ang =
73˚ Then change in steering angle = 17˚
Rule 8: If left-obs
200 mm and right-obs = 150 mm and front-obs
200 mm and tar-ang =
51˚ Then change in steering angle = 31˚
Table 7.1. Heuristic rule formulation for obstacle and target located in the left side of the robot.
RuleNo.
Left-obs
Right-obs
Front-obs Tar-ang Steering angle
(millimeter) (millimeter) (millimeter) (Degree)
(Degree)
01
150
200
200
82
0
02
150
200
200
75
-15
03
150
200
200
54
-30
04
150
200
200
31
-30
05
150
200
200
37
-37
102
Table 7.2 Heuristic rule formulation for obstacle and target located in the right side of the
robot.
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
06
200
150
200
70
0
07
200
150
200
73
17
08
200
150
200
51
31
09
200
150
200
31
27
10
200
150
200
38
38
Rule 9: If left-obs
200 mm and right-obs = 150 mm and front-obs
200 mm and tar-ang =
31˚ Then change in steering angle = 27˚
Some of the heuristic rules from Table 7.3 are listed below based on the obstacle presents
in the front of the robot and target located in right side of the robot.
Rule 11: If left-obs
100 mm and right-obs
100 mm and front-obs = 1000 mm and tar-ang
= 20˚ Then change in steering angle = 29˚
Rule 12: If left-obs
100 mm and right-obs
100 mm and front-obs = 800 mm and tar-ang =
22˚ Then change in steering angle = 34˚
Table 7.3. Heuristic rule formation for obstacle present front of the robot and target located in
right side of the robot.
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
11
100
100
1000
20
29
12
100
100
800
22
34
13
100
100
600
24
41
14
100
100
400
26
51
15
100
100
200
28
72
103
Target
Path
followed
by robot
Obstacle
Robot
(a)
(b)
Figure 7.3. Perception based rule formation for obstacle avoidance in different environments.
Rule 13: If left-obs
100 mm and right-obs
100 mm and front-obs = 600 mm and tar-ang =
24˚ Then change in steering angle = 41˚
Fig. 7.3(a) depicts the environment to avoid the obstacles and motion control by the robots.
Based on this scenario some formulated heuristic rules are listed in Table 7.4. These parameters
can be used to generate different perception based heuristic rules, for example rule 16, 17 and
18 are given below.
Rule 16: If left-obs = 600 mm and right-obs = 150 mm and front-obs =600 mm and tar-ang =
7˚ Then change in steering angle = 7˚
Table 7.4. Perception based heuristic rule formation for obstacle avoidance Fig. 7.3(a)
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
16
600
150
600
7
7
17
700
150
150
0
-80
18
515
150
550
90
50
19
420
150
440
53
53
104
Table 7.5. Perception based heuristic rule formation for obstacle avoidance (Fig.7.3(b))
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
20
460
1650
1480
0
0
21
430
1100
200
0
110
22
100
810
850
-77
-42
23
70
420
1000
-49
-49
Rule 17: If left-obs = 700 mm and right-obs = 150 mm and front-obs = 150 mm and tar-ang =
0˚ Then change in steering angle = -80˚
Rule 18: If left-obs = 515 mm and right-obs = 150 mm and front-obs = 550 mm and tar-ang =
90˚ Then change in steering angle = 50˚
Similarly Fig. 7.3(b) depicts the different environment to avoid the obstacles and motion
control by the robots. Based on this scenario some formulated heuristic rules are listed in Table
7.5. These parameters can be used to generate different perception based heuristic rules, for
example rule 20, 21 and 22 are given below.
Rule 20: If left-obs = 460 mm and right-obs = 1650 mm and front-obs =1480 mm and tar-ang
= 0˚ Then change in steering angle = 0˚
Rule 21: If left-obs = 430 mm and right-obs = 1100 mm and front-obs = 200 mm and tar-ang =
0˚ Then change in steering angle = 110˚
Rule 22: If left-obs = 100 mm and right-obs = 810 mm and front-obs = 850 mm and tar-ang =
-77˚ Then change in steering angle = -42˚
Based on Fig. 7.4(a) illustrates the environment if the robot enters into U shaped wall, in
such a situation, the robot keep on heading towards the goal position. But when it moves
towards the goal position, it also comes closer to the obstacles. Any obstacle-avoidance
behaviour except wall-following behaviour would make the robot divert from its goal position.
To avoid such situation some of the rules are listed in Table 7.6. These parameters can be used
to formulate heuristic rule for wall following, for example rule 25, 26 and 27 are given below.
105
Path
followed
by robot
Target
Wall shaped
obstacles
Robot
(b)
(a)
Figure 7.4. Perception based rule formation for wall following behaviour in different
environments
Rule 25: If left-obs = 780 mm and right-obs = 835 mm and front-obs = 200 mm and tar-ang =
0˚ Then change in steering angle = 77˚
Rule 26: If left-obs = 80 mm and right-obs = 1510 mm and front-obs = 285 mm and tar-ang =
-112˚ Then change in steering angle = 90˚
Rule 27: If left-obs = 155 mm and right-obs =1490 mm and front-obs=660 mm and tar-ang =
168˚ Then change in steering angle = -90˚
Table 7.6. Human perception based heuristic rule formation for wall following Fig. 7.4(a)
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
24
680
1160
1220
13
13
25
780
835
200
0
77
26
80
1510
285
-112
90
27
155
1490
660
168
-90
28
250
530
1085
-117
90
29
235
515
No obstacle
-54
-54
106
Table 7.7. Perception based heuristic rule formation for wall following (Fig. 7.4 (b))
Rule
No.
Left-obs
(millimeter)
Right-obs
(millimeter)
Front-obs
(millimeter)
Tar-ang
(Degree)
Steering angle
(Degree)
30
1100
1890
2070
13
13
31
780
835
80
0
77
32
80
1630
130
-112
90
33
1000
2000
660
168
-90
34
250
530
1085
-117
90
35
235
515
No obstacle
-54
-54
Similarly Fig. 7.4(b) illustrates the other wall shaped environment. To avoid such situation
some of the rules are listed in Table 7.7. These parameters can be used to formulate heuristic
rule for wall following, for example rule 30, 31 and 32 are given below.
Rule 30: If left-obs = 1100 mm and right-obs = 1890 mm and front-obs = 2070 mm and tarang = 13˚ Then change in steering angle = 13˚
Rule 31: If left-obs = 780 mm and right-obs = 835 mm and front-obs = 80 mm and tar-ang =
0˚ Then change in steering angle = 77˚
Rule 32: If left-obs = 80 mm and right-obs =1630 mm and front-obs=130 mm and tar-ang = 112˚ Then change in steering angle = 90˚
Rule 32: If left-obs = 80 mm and right-obs =1630 mm and front-obs=130 mm and tar-ang = 112˚ Then change in steering angle = 90˚
The rules used for navigation of mobile robots are generated by induction from examples.
Approximately one thousand five hundred rules are fed into the induction program, within the
Clementine data ROBNAV software package. The examples present the situations encountered
by a robot while moving in a multi-robot, highly cluttered environment, and the actions that
each robot has to take to avoid colliding with other robots as well as with static obstacles. The
velocity of the robot motion is decided on the steering angle which in tern is related to the
position of the obstacles around. For higher values of steering angle the turning velocity is
more.
107
7.3 Back Propagation Algorithms (BPA)
A back-propagation algorithm has been used to calculate the gradient of the error of the
network with respect to the network's modifiable weights. This gradient is almost always then
used in a simple stochastic gradient descent algorithm to find weights that minimise the error.
Back-propagation usually allows quick convergence on satisfactory local minima for error in
the kind of networks to which it is suited. The network is trained to navigate by presenting it
with 200 patterns representing typical scenarios, some of which are depicted in Fig. 7.5. These
parameters can be used to formulate heuristic rules for obstacle avoidance, wall following and
target searching behaviours. The number of hidden nodes depends upon the number of training
patterns. For the current analysis two layers of hidden nodes are taken so that the output is
within the error limit and the deviation between desired output and actual output, of the neural
network converges to minimum threshold value during training. The training error is the
difference between desired output and actual output. The “first steering angle” is the “interim
steering angle” and is one of the inputs to neural network in the hybrid controller. Some rules
are listed in section 7.2. The training pattern is similar to depicted in chapter 5 section 5.2.
7.4 Petri Net Model (PNM)
The Petri Net Plans framework (PNPs) allows the representation of high level programs for
robotic behaviour, providing all the action features needed to describe complex plans in
dynamic, partially observable and unpredictable environments (Fig.7.6).The multi-robot
extension of PNPs allows the synchronization of actions among different robots, the
performance of deliberate cooperation and the cooperative handling of local failures in a multirobot system. A multi-robot PNP is automatically divided by each single robot of the system
for the individual execution. The robots perform their actions relying on their individual
knowledge base, and during the plan execution they are able to communicate through a reliable
channel, to attain synchronization and sharing of information. Fig. 7.6 depicts the petri net
model built into each robot to enable it to avoid collision with other robots. The model
comprises 6 states (or Tasks). The location of the token indicates the current state of the robot.
It is assumed that, initially, the robots are in a highly cluttered environment, without any prior
108
knowledge of one another or of the targets and obstacles. This means the robot is in state “Task
1” (“Wait for the start signal”).
First hidden layer
Second
hidden
layer
Rule Layer
Input
Layer
Left-obs
Left-obs
Right-obs
Output
Right-obs
Front-obs
Front-obs
Tar-ang
Interim
Steering
Angle
Final
Steering
Angle
Figure 7.5. Four-layer heuristic rule neural network for robot navigation.
Task 1
Task 6
Task 1
Task 2
Task 3
Task 4
Task 5
Task 6
Task 2
Task 3
Task 5
Task 4
Wait for the start signal
Move, avoid obstacles and search for targets
Detecting conflict
Negotiating
Checking for conflict and executing movements
Waiting
Place
Transition
Token
Arc
Figure 7.6. Petri net model to avoid inter collision among robots during navigation.
109
In Fig. 7.6, (Appendix-B) the token is in place “Task 1”. Once the robots have received a
command to start searching for the targets, they will try to locate targets while avoiding
obstacles and one another. The robot is thus in state “task2” (“Moving, avoiding obstacles and
searching for targets”). During navigation, if another robot obstructs the path of a robot, then a
conflict situation is raised. (State “Task 3”, “Detecting Conflict”). Conflicting robots will
negotiate with each other to decide which one has priority. The lower priority robot will be
treated as a static obstacle and the higher priority robot as a proper mobile robot (state “Task
4”, “Negotiating”). As soon as the conflict situation is resolved, the robots will look for other
conflicts and if there is no other conflict they will execute their movements (state “Task 5”,
“Checking for conflict and executing movements”). If a robot meets two other robots already in
a conflict situation, then its priority will be lowest and it will be treated as a static obstacle
(state “Task 6”, “Waiting”) until the conflict is resolved. When this is done, the robot will reenter state “Task 2”. The dynamic and asynchronous structure of the PNM is ideally suited for
the modeling of multiple mobile robots to provides inter collision avoidance among robots and
also helps to find the target.
7.5 Simulation Results and Discussion
The series of simulations test has been conducted using ROBNAV software (Appendix-A).
To demonstrate the effectiveness and the robustness of the proposed method, simulation results
on mobile robot navigation in various environments are exhibited.
The obstacle avoidance behaviour is activated by using perception base rule introduced
into the software as discussed in section 7.2. When arrays of sensor receive the information of
object (which is too close to the robot), it avoids a collision by moving away from it in the
opposite direction. In this case, the obstacle avoidance behaviour is activated when the readings
from any sensors are less than the minimum threshold values. The simulation result obstacle
avoidance and inter collision avoidance among mobile robot has been shown in Fig. 7.7. The
wall following behaviour is activated by using perception base rule introduced into the software
as discussed in section 7.2. i.e. the mobile robot detects an obstacle in the front while the target
tracking control mode is on operation. In this case, the wall following behaviour is activated i.e.
The mobile robot rotates clockwise or counterclockwise such that it can align and move along
the wall shown in Fig. 7.8.
110
Obstacles
Target 2
Target 1
Initial position of 100 robots
Target 3
Target 4
Figure 7.7. Simulation result of inter robot collision avoidance among robots via petri net
model (a) Initial position of mobile robots (b) After simulation result.
Obstacles
Figure 7.8. Simulation result of wall following behaviour in different environments.
(b)
(a)
Figure 7.9. (a) Simulation result of target searching behaviour of mobile robots (b) target
searching behaviour.
111
When the acquired information from the sensors tracks the target and shows that there are
no obstacles around robot, its main reactive behaviour is target steer. HRBN mainly adjusts
robots motion direction and quickly moves it towards the target if there are no obstacles around
the robot as shown in Fig. 7.9 (a). In the proposed control strategy, human perception based
heuristic rules are formulated and PNM is used to provide inter collision of robot as well as to
find the target which has been trained by ANN using back propagation algorithms. The target
searching behaviour has been demonstrated in Fig. 7.9(b) it has found that it is more reliable in
position accuracy than the other approaches. The results from the proposed method for real
time navigation of mobile robot have been compared with the result from obtained by Ayari et
al. [220] for navigation of mobile robot in collision free goal reaching in learned environment
and the results from the developed HRBN method (Fig. 7.10).
(a)
(b)
Figure 7.10. (a) Simulation results of Ayari et al. [220] collision free goal reaching in learned
environment (b) Simulation results of proposed method collision free goal reaching.
112
(a)
(b)
Figure 7.11. (a) Simulation results comparisons with Yang et al. [88] (b) Simulation results of
proposed method.
113
The proposed methodology has been also compared between the results obtained by Yang
et al. [88] for navigation of mobile robot in collision free goal reaching and the results from the
developed HRBN method (Fig. 7.11). The effectiveness of the developed controller has been
verified both in simulation and real mode and they are in good agreement. The effectiveness of
the developed controller has been verified both in simulation and real mode and they are in
good agreement.
7.6 Experimental Results with Real Mobile Robot
The effectiveness of the proposed method has been verified in a series of practical tests on
Khepera-III and Koala mobile robot. The developed ROBNAV software (Appendix-A) used
for simulation test is loaded into the mobile robot to obtain experimental result. The
assumptions about the mechanical structure and the motion of a mobile robot to which our
proposed method is applied as mobile robot moves on lab specified floor area and the wheel of
a mobile robot rolls on the floor without any translational slip.
7.6.1 Implementation of HRBN Controller on Khepera robot
To exhibit the experimental test of multiple mobile robot the developed software
ROBNAV is loaded into the Khepera-II and Khepera-III mobile robot. The Khepera-III mobile
robot is the main robot which is termed as target tracker robot (TTR) which are able to track the
target where as Khepera-II mobile robot is termed as moving obstacle robot (OR) which is not
suppose to track the target.
From the human perception based HRBN consist of four inputs left, front, right obstacle
distances and interim steering angle after learning, training and testing, robots gets final
steering angles as an output. The paths traced by the obstacle robots (OR) and target tracker
robot (TR) on the floor as they move is shown in Fig. 7.12. The OR1, OR2, OR3, OR4
(Khepera-II), are termed as moving obstacle and TR (Khepera-III), is termed as the target
tracker. The paths followed by OR and TR have been shown in Fig. 7.13. It has been found that
the results obtained from experimental setup are more close to results obtained from simulation
mode which validate the proposed method (Fig. 7.14). From these figures, it has been seen that
the robots can indeed avoid obstacles and reach the targets.
114
Figure 7.12. Experimental validation of simulation result on Khepera robots
Y
R2
Target
TTR
R3
R1
R4
Initial
Position
X
Figure 7.13. Traced paths of mobile robots during experiment
Table 7.8 shows the times taken by the robots in simulations and in the experimental tests
scenario during target finding. It is observed that the robots are able to reach the targets
efficiently during simulation and experiment. This method provides much faster response in an
unknown environment and is less computational effort than other conventional approaches.
This chapter contributes to the efforts of developing practical, modular, and easy-to-implement
robot navigation algorithms that are both cost and computationally effective.
115
Simulation path
Experimental path
Figure 7.14. Path optimization of target tracker robot (TR) avoiding static as well as dynamic
obstacle with experimental validation.
Table 7.8 Total path traveled and time taken by robots during simulation and experimental
environment by proposed method.
S.No.
Observations
(Fig.7.15)
Simulation
environment
Experimental
environment
Deviation of results
(simulation Vs.
experiment)
+01
Length of path
(in mm)
10750
11300
05.12%
02
Time taken
(seconds)
11.40
12.99
13.99%
7.6.2 Implementation of HRBN Controller on Koala robot
To perform the experimental test of mobile robot the developed software ROBNAV
(Appendix-A) is loaded into the Koala robot mobile robot. The sensors position has been
illustrated in Fig. 7.2. To control the functionalities of the Koala robot (motors, sensors etc.), a
set of command are implemented in the control protocol.
116
(a)
(b)
Figure 7.15. (a) Experimental result with Koala mobile robot to start moving towards target and
(b) Finally robot tracks the target following optimal path.
117
From the human perception based HRBN consist of four inputs left, front, right obstacle
distances and first steering angle after learning, training and testing, robots gets final steering
angles as an output. The path traced by the robots on the floor as they move is shown in
Fig.7.15 (a) and Fig.7.15 (b). It has been found that the results obtained from experimental
setup are more close to results obtained from simulation mode which validate the proposed
method (Fig. 7.16). Table 7.9 shows the times taken by the robots in simulations and in the
experimental tests scenario during target finding.
Table 7.9. Total path traveled and time taken by robots during simulation and experimental
environment by proposed method
S.No.
01
02
Observations
(Fig.7.17)
Simulation
environment
Experimental
environment
Length of path
(in mm)
Time taken
(seconds)
21750
23530
Deviation of results
(simulation Vs.
experiment)
08.18%
23.05
25.65
11.27%
Simulation path
Experimental path
Figure 7.16.Experimental result validation with simulation mode.
118
7.7 Summary
This chapter proposed a new human perception based control law for nonholonomic
wheeled mobile robot. From the theoretical, simulations and experimental analyses the
following conclusion can be drawn:
1.
The methodology is a general, robust, and safest which provides fast path planning
framework for robotic navigation using human perception based HRBN. The developed
method is simple and efficient tool for mobile robot navigation, especially in a real world
dynamic environment.
2.
It is successfully applied for navigation in dynamic as well as static environments. The
robot rapidly recognises their surroundings which provide sufficient information for path
optimization during navigation.
3.
The proposed methodology is successfully applied for navigation in dynamic as well as
static environments. The robot rapidly recognises their surroundings which provide
sufficient information for path optimization during navigation. Training patterns of ANN
can be generated by simulation rather than by experiments, saving considerable time and
effort.
4.
Comparison of results between the current developed and with other techniques have
shown good agreement. This validates the authenticity of the proposed technique.
5.
The presented motion planner has demonstrated its effectiveness in planning for multiple
mobile robots within a bounded workspace. It is planned with a high probability of
success, even in cluttered environments involving robots, stationary obstacles and moving
obstacles.
This chapter depicts a methodology to achieve the co-operation navigation in pragmatic
way.
™ Publication
“Heuristic rule base hybrid neural network for navigation of mobile robot”, Journal of
Engineering Manufacture Part B, IMechE, 2009, (Accepted).
119
8
Results and Discussion
This investigation discusses the development of autonomous navigation and obstacle avoidance
systems for differential drive mobile robots operating in unstructured real world dynamic
environments. In this chapter the performance of developed intelligent controllers are
summarised and their results are outlined.
8.1 Kinematics and Dynamic Stability of Mobile Robot
The kinematic design is a basic part of the mobile robot system. Improved mechanical
designs and mobility control systems will enable the mobile robot to navigate in no marked
paths and for autonomous operation. A kinematic methodology is the first step towards
achieving these goals.
In chapter three, the advance kinematic modeling of mobile robot, from the motivation of
the kinematic methodology through its development and applications has been proposed. The
kinematic modeling of the wheels, robot coordinate systems and positions on the robot has
been developed and discussed. The presented kinematic methodology provides valuable
insights into these areas. Just as the mobility characterization tree allows determining the
motion characteristics of an existing mobile robot, this may utilise the tree to design mobile
robots to possess such desired characteristics as two or three degree of freedoms. It is
concluded that a mobile robot having two diametrically opposed driven wheels is ideal for this
application because of the simplicity of its mechanical design and kinematic model. Similarly,
the sensing characterization tree may be applied to design a mobile robot with a robust sensing
structure to minimise the adverse effects of wheel slip on the calculation of the mobile robot
position. It is noted that the set of actuated wheel variables and sensed wheel variables cannot
coincide if both robust actuation and robust sensing are desired for kinematic modeling of
mobile robots is the first step towards, designing feedback control systems. The developed
kinematic calculations of positions, velocities and accelerations can be applied to calculate the
dynamic forces and torques produced by the motion of the robot components. For example, the
recursive Eular langrage dynamics formation applies kinematics to propagate positions,
velocities and accelerations from the robot wheel to the robot base.
120
8.2 Intelligent Controller of Mobile Robots
The intelligent controller plays an important role in path analysis and planning of the
mobile robots. The obstacle avoidance, wall following, target searching and collision free
navigational path depends on intelligence of the controller. The control techniques are a very
important area of research in the field of mobile robot navigation. This thesis presents new
techniques to for intelligent navigational controller.
Before the introduction of learning algorithms into the fuzzy controller the relationships
between the neural controller and the fuzzy controller can be viewed as two extreme endpoints
on a spectrum of designing approaches. At one end fuzzy controller has meaningful
representations fuzzy if then rules and fuzzy reasoning derived from human expertise but it has
no adaptive capability learning from examples to take advantage of a desired input output data
set. At the other end neural controller represents a totally different paradigm with learning
capability that adapts its parameters based on desired input output pairs but neither can it
accommodate a priori knowledge from human experts
nor can we transform network
configurations and connection weights into a meaningful representation to account for
structured knowledge. Conceptually this may say that designing of fuzzy controller is a top
down approach which employs high level knowledge rules to describe a system while neural
controller is a bottom up approach which uses low level knowledge input output pairs to tackle
the same problem. In some cases fuzzy controller has gained an advantage over neural
controller that is the knowledge representation feature that can both speed up learning by
encoding prior knowledge in the form of fuzzy if then rules into parameters and interpret the
parameters after learning by transforming the parameters back to fuzzy if then rules. The basic
learning rule of fuzzy controller is of gradient descent type which is the same as that of neural
controller. In some situation the neural controllers do not rely on the system model, they are
suitable for uncertain and highly nonlinear situations. Moreover, neural controller has strong
parallel processing, adaptive and learning capabilities, thus they are popular in the design of
robot controllers. This fact allows these two modeling approaches to benefit from research
findings and results in both literatures. To get the advantages of both an adaptive neuro fuzzy
controller has been proposed, which integrates the fuzzy logic representation of human
121
knowledge with the learning capability of neural networks, to solve the dynamic control of
mobile robot navigation problems.
In chapter four, a theoretical development of a complete navigation procedure of a mobile
robot in an unknown and cluttered environment has been illustrated. To formalize the imprecise
reasoning processes, a method using a fuzzy logic technique has been presented. Intuitively,
this would result in a more robust and accurate model, which is also easily interpretable. The
model has been fine tuned using behaviour based control. A Mamdani fuzzy system has been
used for design of intelligent controller that is more compatible with the reasoning process of
human behaviours. A new method of obstacle avoidance, wall following as well as target
searching behaviour has been presented in this chapter as part of the navigational procedure.
The behaviour-based mobile robot developed in this study has several levels of competence.
This allows a reactive control, which results in an efficient behaviour towards unforeseeable
situations. The problem of extracting the IF–THEN rule base has been carried out via an
evolutionary programming method. Simulations were carried out on a nonholonomic mobile
robot to test the performances of the proposed fuzzy controller. The theoretical analysis
provides the requirements for the design of a suitable fuzzy rule base, in order to guarantee the
asymptotical stability of the robot system. Simulation and experimental studies on the
developed fuzzy controller of the robot system are conducted to investigate the system
performance. The presented extensive experiments shows that the developed behaviour robot is
capable of achieving the desired turn angle and making the mobile robot follow the target by
avoiding static as well as dynamic obstacle satisfactorily. The proposed methodology has been
compared with previous work presented by many researchers, it is found that the method of
designing fuzzy controller is simple, robust and obtained result are accurate.
In chapter, five a neural controller for mobile robot navigation, in the dynamic
environments using the principle of back propagation algorithm has been discussed. The
algorithm produces the robot’s path positioned within the road boundaries and avoids any fixed
as well as moving obstacles along the path. The algorithm also produced acceptable results
when tested with different kinds of static as well as moving obstacles. The controllers found
suitable control torques, permitting the robot to follow these paths. The significance of this
work is the development of a dynamic system model and controllers for mobile robot
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navigation, rather than robot manipulators, which is a new research area. In addition, the
navigation system can be utilised in numerous applications, including various defenses,
industrial and medical robots. Simulation and experimental results verify the effectiveness of
the developed navigation algorithm and the controllers.
In chapter six, adaptive neuro-fuzzy inference system (ANFIS) approach is analysed for
robot navigation. In adaptive neuro-fuzzy modeling, there is a tendency to sacrifice model
interpretability in pursuit of model accuracy. The main contribution is to overcome this
problem by using takagi-sugano method to evaluate the similarity among fuzzy membership
functions. Similar membership functions are then combined to minimise the number of
linguistic terms. The result shows that it is possible to keep the fuzzy model concise and
interpretable while maintaining a high level of model accuracy. A piece of software has been
developed under windows environment to implement the adaptive neuro fuzzy controller for
robot navigation (Appendix-A). The developed ANFIS controller has been compared with
other approaches the result found to be satisfactory.
In chapter seven, heuristic rule base neural network (HRBN) controller has been
developed. The output from the heuristic rule base is fed as an input (interim steering angle) to
neural network and the final outputs (final steering angle) from the neural controller are used
for motion and turning control of robots. The inputs to the heuristic rule base are obtained from
the robot sensors (such as left, front, right obstacle distances and the target angle). The HRBN
controller is used to avoid various shaped obstacles and to reach target. A Petri-net model has
been developed and is used to take care of inter-robot-collision during multiple mobile robot
navigation. By using the algorithm it has been visualised that, multiple mobile robots can
navigate successfully avoiding static as well dynamic obstacles placed in the environment and
reach the target successfully. Simulation software has been developed to test the proposed
algorithms and loaded into the Khepera-III and Koala mobile robot to perform and validate
experimental test. The developed methodology has been compared with the other approach
proposed by many researchers, which shows a very good agreement.
The proposed research takes holistic approach to address the problem of extending the
application domain. The holistic approach is applied to design the intelligent controller for
mobile robot. Local navigation, by definition, cannot generate an optimal trajectory generally
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because no map information is available. The robot only knows where it is and where the goal
is. Furthermore, the optimality of a global path, obtained by a concatenation of the local paths
to be decided upon at each instant of time, can be only determined after the completion of
navigation. The solution obtained from current research is the navigational path analysis of
mobile robot in various environments. The results obtained from various approaches are given
in Table 8.1. It shows the percentage of deviation of experimental results with respect to
simulation result in various controllers being used for finding the navigational path and time
taken to reach the target by mobile robot.
Table 8.1. Results deviation of travelled path and time taken during simulation and
experimental mode
S.No. Navigational Analysis with various Controller
Percentage of Results deviations
Simulation Vs Experimental mode
Path
Time
1.
Navigation with Fuzzy controller
12.27%
12.26%
2.
Navigation with Neural controller
11.58%
11.59%
3.
Navigation with ANFIS controller
5.19%
14.15%
4.
Navigation with HRBN controller
5.12%
13.99%
A simulation comparison has been done between various techniques i.e. Fuzzy, Neural,
ANFIS and HRBN controller (Fig. 8.1). During the comparison path length of “13.8 meter” and
“8.3 meter”, time taken to reach the target “14.63 second” and “12.93 second” are recorded for
fuzzy and ANFIS controllers respectively (Fig. 8.1(a)).
From Fig. 8.1(b) path length of “12.2 meter” and “6.6 meter”; time taken to reach the
target “12.93 second” and “7.02 second” are observed for neural and ANFIS controllers
respectively. Also during the comparison path length of “15.4 meter” and “9.6 meter”, time
taken to reach the target “16.32 second” and “10.21 second” are recorded for fuzzy and ANFIS
controllers respectively (Fig. 8.1(c)).
Path length of “6.6 meter” and “5.9 meter”; time taken to reach the target “7.02 second”
and “6.25 second” are recorded respectively (Fig. 8.1(d)) for ANFIS and HRBN controllers
during the comparison.
124
(a.i)
(a)
(a.ii)
(b)
(b-ii)
(c-i)
(c)
(c-ii)
(d-i)
(d)
(d-ii)
(b-i)
Figure 8.1. Comparison of results between Fuzzy, Neural, ANFIS and HRBN controller.
125
9
Conclusions and Future Works
The previous chapters have presented the background, approach and results of this research in
detail. This chapter summarises the conclusions of the research and proposes idea for future
work. This investigation expects to make the following contributions to the field of
navigational path analysis of mobile robots in various environments.
9.1 Conclusions
In this research proposal, attempt has been made to solve a problem related to navigational
path analysis of mobile robots in various environments. The above investigation has been
carried out in several stages as follows:
1. Starting from the kinematics analysis a dynamic controller for a mobile robot is developed.
2. A fuzzy and neural network controller for navigating mobile are developed.
3. Further Adaptive Network based Fuzzy Inference System (ANFIS) controller for
controlling multiple mobile robot is developed and finally Heuristic Rule Base Neural network
controller (HRBNC) for mobile robot is developed.
The conclusions drawn from the above investigation are as follows:
1. From the kinematic analysis of mobile robot (chapter-3), left wheel and right wheel
velocities of the mobile robot has been calculated. From the wheel velocities, steering angle for
the robot is calculated. In this thesis, by using robust adaptive control technique, a dynamic
controller for a mobile robot is proposed. The proposed dynamic controller can track the
desired velocity, which is generated by kinematic controller, without exact knowledge about
the dynamic model of a mobile robot.
2. In chapter four, a robust fuzzy controller has been developed for navigation of mobile robot
in the presence of obstacles. The proposed membership function is found best for navigation of
mobile robots in various environments.
3. A neural network controller has been developed for mobile robot navigation in chapter 5. It
is found that the neural controller is better than the fuzzy controller in terms of position
accuracy.
126
4. The neural network technique has been modified to produce an ANFIS controller and is
discussed in chapter 6. A human perception based HRBN controller is analysed in chapter 7.
Both the techniques are used for enhancing the navigational path analysis and planning
performance of the robots.
5. The best performing controllers are based on the ANFIS control technique and the human
perception based HRBN control technique, which has been found to yield equally robust
navigation results. From the demonstrated results of path optamisation and inter collision
avoidance among robots, it is noted that the ANFIS and perception based HRBN controller can
be applied successfully in multi-robot cooperative exercises. The results of all the proposed
techniques have been discussed in Chapter 8.
Validation of theoretical work has been done by simulation and a real world tests. A
ROBNAV simulation software has been developed. Several mobile robots have been used in
the tests: NITR, Khepera-II, Khepera-III and Koala.
9.2 Future Works
This work provides a foundation for future expansion of integrated designing approaches
of intelligent controller based on artificial intelligence technique. Regardless of all research that
has been conducted, autonomous navigation in various environments is still an open area of
research. There are a number of interesting directions to pursue as future work. The suggestions
with several crucial and promising researches for future investigation are as follow.
In the current research work, the techniques developed for navigational path analysis of
mobile robot enable the robots to avoid collision among each other and with static obstacles.
However, further development of the techniques may be required for the avoidance of moving
obstacles other than the robots. This will make the algorithm more effective in dealing with
unpredictable real life situations. The navigational techniques developed in this research work
are capable of detecting and reaching the static targets. Further modifications in these
navigational techniques may be carried out so that the robots can not only detect dynamic
targets but also reach them using an optimum path. Further research is required for cooperative
behaviour coordination between the robots for task and handling a particular object by avoiding
static as well as moving obstacles.
127
Appendix-A
ROBNAV Software used for Navigation of Mobile Robot
The typical screen of ‘ROBNAV’ software has been developed using C++ shown in Fig.
A.1. The software runs on operating under WINDOWS NT/95/ 98/2000/XP/Vista. The menus
incorporated in the software are:
A.1. Obstacle Menu: The Obstacle Menu allows the user to draw different types of obstacles
in the robots’ environment. The shape of the obstacle has been shown in Fig. A.2.
A.2. Number of Robot Menu: Using this menu, a user can draw any number of robots
(<=1000) as required to be placed in the environment. The number of robot has been shown in
Fig. A.3(i).
R ob ots
Ob stacles
Figure A.1. The Typical Screen of ROBNAV Software used for Navigation of Mobile Robots.
128
Rectangle
Hexagon
Parallelogram
Line
U shaped
Triangle
Boundary
Figure A.2. The obstacles into the software.
Targets
30 Robots
Figure A.3. (i) The number of robot into the software (ii) The target into the software.
A.3. Run Menu: With this menu, the user can choose to run the software in simulation mode
or control the navigation of real mobile robots.
A.4. Techniques Menu: This menu enables the user to select the techniques to control the
navigation of the robots.
A.5. Target Menu: This menu is for placing targets in the environment. The target has been
shown in Fig. A.3 (ii).
A.6. Parameter Menu: This menu enables the user to start again a process, refresh the screen,
robot behaviour to select a particular robot and control its movements manually, and drag any
of the obstacles to any place in the environment, and obstacle delete from the environment.
129
Appendix-B
Petri Net Model (PNM)
The theory of Petri Nets was developed from the work of Carl Adam Petri in Germany in 1962.
He developed a new model for information flow in a communication system [222]. Petri Net
model is used as a visual communication aid to model the system behaviour. It is based on
strong mathematical foundation. Petri Net is a graphical paradigm for the formal description of
the logical interactions among parts or of the flow of activities in complex systems. Petri Net is
particularly suited to model:
–Concurrency and conflict,
–Sequencing, conditional branching and looping,
–Synchronization,
–Sharing of limited resources and
–Mutual exclusion.
B.1. Basic Definitions of Petri Net Model
Petri net model (PNM) has been developed by Petri as a means of representing the behaviour of
a dynamical system. The purpose of PNM is to specify the integration of the individual efforts
on avoiding inter collision and to achieve co-operation between multiple robots.
Place
Transition
Before Firing
Token
Arc
After Firing
Figure B.1. A Simple Petri Net Model.
130
PNM can be used as a motion scheduler and it is capable of representing concurrent
activities and the responsibility of decisions in the coordination level of the intelligent mobile
robot navigation system. A Petri net is a bipartite directed graph consisting of two kinds of
nodes: places and transitions [222] (Figure B.1).
¾ Places typically represent conditions within the system being modeled.
¾ Transitions represent events occurring in the system that may cause change in the condition
of the system.
¾ Arcs connect places to transitions and transitions to places but never an arc from a place to
a place or from a transition to a transition. In addition to the basic elements of petri nets i.e.,
places, transitions and direct arcs, tokens are included to model the systems. In petri net theory,
places represent status such as operation process, conditions or availability of resources e.g., a
robot is ready to move in an environment. Transitions are used to model events i.e., the start
and termination of operations. Places contain tokens (denoted by circles) and the distribution of
tokens in the place of petri net is called its marking. The execution of a Petri net is controlled
by the position and movement of these tokens.
In a petri net model, petri net structure (PN) can be defined as a five tuple. The
mathematical analysis of the PNM is defined by Eq. (b.1).
, , ,
,
(b.1)
Where:
P
P ,P ,P ……..P
T
t ,t ,t ……..t
F
P
T
T
is a finite set of places.
is a finite set of transitions.
P is a set of curve.
W: F= {1, 2, 3..}is a weight function and w (ns, nd) denotes the weight of the edge from ns to nd.
M : P = {0, 1, 2, 3 . . .} is the initial marking.
131
P
T ≠ 0 and P
T =0, Petri nets are used to model complex systems that can be described in
terms of states and their changes.
Input arcs are directed arcs drawn from places to transitions, representing the conditions
that need to be satisfied for the event to be activated as shown in Fig. B.2(i). Output arcs are
directed arcs drawn from transitions to places, representing the conditions resulting from the
occurrence of the event as shown in Fig. B.2(ii).
(i) Input arcs
(ii) Output arcs
Figure B.2. The Input and Output arcs.
Input places of a transition are the set of places that are connected to the transition through
input arcs where as the output places of a transition are the set of places to which output arcs
exist from the transition as depicts in Fig.B.3.
n
Before Firing
Firing Initiate
After Firing
Figure B.3. Firing of Petri Net Model.
Tokens are dots (or integers) associated with places; A place containing tokens indicates
that the corresponding condition holds. Marking of a petri net is a vector listing the number of
tokens in each place of the net (n1, n2, n3,......np), P = of places. When input places of a transition
have the required number of tokens, the transition is enabled. An enabled transition may fire
132
(event happens) taking a specified number of tokens from each input place and depositing a
specified number of tokens in each of its output place as shown in Fig.B.3.
Role of a place
¾ A type of communication medium, like a telephone line, a middleman, or a communication
network.
¾ A buffer: for example, a depot, a queue or a post bins.
¾ A geographical location, like a place in a warehouse, office or hospital.
¾ A possible state or state condition: for example, the floor where an elevator is, or the
condition that a specialist is available.
Role of a transition
¾ An event: for example, starting an operation, the death of a patient, a change seasons or the
switching of a traffic light from red to green.
¾ A transformation of an object, like adapting a product, updating a database, or updating a
document.
¾ A transport of an object: for example, transporting goods, or sending a file.
Role of a token
¾ A physical object, for example a product, a part, a drug, a person.
¾ An information object, for example a message, a signal, a report.
¾ A collection of objects, for example a truck with products, a warehouse with parts, or an
address file.
¾ An indicator of a state, for example the indicator of the state in which a process is, or the
state of an object.
¾ An indicator of a condition: the presence of a token indicates whether a certain condition is
fulfilled.
133
Appendix-C
Robots Hardware used for Experimental Verification
C.1
NITR Mobile Robot
The NITR mobile robot developed in the robotics laboratory has been shown in Fig. C.1 used
for experimental results. It has two differentials drive standard wheels and two supported ball
wheels front and rear of the robot used for stability. The standard driving wheels have a radius
of 35mm and are mounted on an axle of length 180 mm. The chassis of the robot measures 160
× 180 × 150 mm (L × W × H) and contains two DC gear servo motors for driving the wheels. Five
pairs of infrared sensors are connected for obstacle detection. The radio modem used for radio
frequency transmission, and 12-V battery is used for power supply. The wheels are driven by
motors having rated torque 12 Kg-cm at 30 rpm and at 12 rated voltage.
(a)
(b)
Figure C.1. (a) Chassis of the robot (b) Working model of NITR Mobile Robot.
134
C.2
Khepera-II Mobile Robot
The Khepera-II mobile robot has been illustrated in Fig. C.2. The active control mode is set
according to the kind of command received. If the controller receives a speed control
command, it switches to the speed mode. Different control parameters can be set for each of the
two control modes. This sensor device allows two measures: The normal ambient light. This
measure is made using only the receiver part of the device, without emitting light with the
emitter. A new measurement is made every 20 ms. During the 20 ms, the sensors are read in a
sequential way every 2.5 ms. The value returned at a given time is the result of the last
measurement made. The output of each measurement is an analogue value converted to a 10 bit
digital value. The Khepera is equipped with four Nickel Metal Hydride batteries providing
250mAh each. The serial communication protocol is designed to control all Khepera's functions
using a RS232 serial line. The control protocol is used to send control messages to the robot.
The Khepera robot is equipped with two DC motors and incremental encoders. An easy and
efficient way to control DC motors is to use a Pulse Width Modulation signal. The Khepera's
API provides two controllers, one for position control and the other for speed control.
Figure C.2. KHEPERA-II mobile robot.
135
C.3
Khepera-III Mobile Robot
The Khepera-III mobile robot has two driving wheels and a point supporter for stability. Each
wheel is moved by a DC motor coupled with the wheel through a 43.2:1 reduction. The motor
has its own embedded incremental encoder, placed on the motor axis, gives 16 pulses per
revolution of the motor. Each motor is driven by its own motor controller implemented in a
PIC18F4431. The motor controller can be used in two control modes, the speed or position
mode. The active control mode is set according to the kind of command received. It has nine
sensors placed around the robot and two placed on the bottom. The later allow experiments like
line following. These sensors embed an infra-red light emitter and a receiver. In its base set,
five sensors are placed around the robot and are positioned and numbered as shown in Fig. C.3.
Five sensors are in fact five pairs of ultrasonic devices where each pair is composed of one
transmitter and one receiver. The ultrasonic sensors are powered by a 20 Vdc source. When the
upper body is mounted, there’s some noise because of inside rebound echo, which are deleted
in software. It has equipped with a battery pack composed of two Li-Ion Polymer elements.
This provides a 7.4V volt battery with a 1400 mAH capacity. The communication interface
module used a standard RS232 line, while the interface module converts RS232 signal into a
TTL level signal to communicate with the robot.
Figure C.3. KHEPERA-III mobile robot.
136
C.4
Koala Mobile Robot
The Koala robot is a robotic platform for real world experiments and is more powerful, and
capable of carrying larger accessories than Khepera shown in Fig. C.4. It rides on six wheels
having 320
320
200 mm (L W H), and sports stylish bodywork for attractive
demonstrations. Every wheel is moved by a DC motor coupled with the wheel through an 84:1
reduction gear. An incremental encoder is placed on the motor axis and gives 100 pulses per
revolution of the motor. This allows a resolution of 8400 pulses per revolution of the wheel that
corresponds to 32.5 pulses per millimeter of forward displacement of the robot. Its weight is
4.0kg with battery and 3.6 kg without battery. The Koala main processor has the direct control
on the motor power supply and can read the pulses of the incremental encoder using a special
unit called UPP (Universal Pulse Processor). It can also read the current used by each motor,
which are proportional to the torque on the wheels. The processor installed in the koala robot is
Motorola 68331 @ 22MHz, RAM is 1Mbyte and ROM is 1Mbyte. The sensors mounted on the
robot are sixteen Infrared proximity and ambient light sensors, four optional triangulation
longerrange IR sensors and six optional ultrasonic sonar sensors. The maximum payload the
robot can take is 3 kg. It has been designed for easy to use, easy to transport, and able to deal
with a standard office environment as well as a rough indoor terrain. It is also fully software
compatible with Khepera.
Figure C.4. Koala mobile robot.
137
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Published and Accepted Papers
Paper Published / Accepted in International Journal
1. Parhi, D.R., Singh, M.K., “Intelligent fuzzy interface technique for controller of mobile
robot”, Journal of Mechanical Engineering Science Part C, IMechE, 222(11), 2008, 22812292.
2. Parhi, D.R., Singh, M.K., “Various strategies of navigation of mobile robot: A review”
International Journal of Automation and Control, Inderscience, 3(2/3), 2009, 114-134.
3. Parhi, D.R., Singh, M.K., “Real time navigational control of mobile robots using artificial
neural network” Journal of Mechanical Engineering Science Part C, IMechE, 223(7),
2009, 1713-1725.
4. Singh, M.K., Parhi, D.R., Path optimisation of mobile robot using artificial neural network
(ANN) controller, International Journal of System Science, 2009, Taylor & Francis,
accepted for publication.
5. Parhi, D.R., Singh, M.K., Navigational path analysis of mobile robots using ANFIS
controller in dynamic environment, Journal of Mechanical Engineering Science Part C,
IMechE, 2009, accepted for publication.
6. Parhi, D.R., Singh, M.K., Heuristic rule base hybrid neural network for navigation of
mobile robot, Journal of Engineering Manufacture Part B, IMechE, 2009, accepted for
publication.
7. Singh, M.K., Parhi, D.R., “fuzzy controller for path analysis and planning of mobile robot”
International Journal of Robotics and Automation, ACTA, 2009, provisionally accepted for
publication. Revised version submitted.
Paper Published / Presented in International Conferences
1. Singh M.K., Parhi D.R., Pothal J. K., ANFIS approach for navigation of mobile robots,
IEEE International Conference on ARTCom2009, October 27–28, 2009, Kerela, India.
2. Singh M.K., Parhi D.R., “Intelligent neuro-controller for navigation of mobile robot”
International Conference on ICAC3’09, January 23–24, 2009, Mumbai, India.
156
3. Singh M.K., Kasyap S.K., Parhi D.R., Singh B.K., “Optimisation of mine support
parameter using neural network approach”, International Conference on ICMAG-08,
December 6-12,2008, Goa (IIT Mumbai), India.
4. Singh M.K., Bhowmik S., Parhi D.R., Kasyap S.K., “Intelligent controller for autonomous
mobile robot” International Conference on ICMAG-08, December 6-12, 2008, Goa (IIT
Mumbai), India.
5. Singh M.K, Bhowmik S., Parhi D.R., Subudhi B.D., “Formation Control of multiple mobile
robots using fuzzy logic approach” International Conference on ICSCIS-07, December 2729, 2007, JEC Jabalpur, India.
6. Singh M.K., Parhi D.R., Bhowmik,S., Singh P.K.; “Swarming of multiple mobile robots for
searching operation using ACO” International Conference on ICSCIS-07, December 27-29,
2007, JEC Jabalpur, India.
7. Singh M.K., Parhi D.R., Bhowmik,S., Singh P.K.; “Design of fuzzy controller for path
analysis and planning of autonomous mobile robot” International Conference on ICSCIS07, December 27-29, 2007, JEC Jabalpur, India.
8. Singh M.K., Parhi D.R., Bhowmik,S., Kasyap S.K.; “Fuzzy logic controller for autonomous
mobile robot” International Conference on RTIME-07, October 5-6, 2007, UCE Ujjain,
India.
9. Singh M.K., Bhowmik S., “Design of Intelligent Control Systems for Autonomous Mobile
Robot navigation using soft computing” GE Global Conference on DREAMS-07, March 11,
2007, Banglore, India.
10. Singh M.K., Bhowmik S., Parhi D.R., Subudhi B.; “Design of intelligent controllers for
mobile robot navigation: A Review” International Conference on ETEE07, January12-14,
2007, Science City Kolkata, India.
Paper Published / Presented in National Conferences
1. Singh M.K., Kumar S., Mahto A.L., Evolution of CIM architecture for small to medium
enterprises: A review, National Conference on NCMSTA'08, November 13-14, 2008, NIT
Hamirpur, Himachal Pradesh, India.
157
2. Singh M.K., Parhi D.R., “Design of intelligent controller for mobile robot using soft
computing,” National Conference on NCMSTA'08, November 13-14, 2008, NIT, Hamirpur,
Himachal Pradesh, India.
3. Singh M.K., Parhi D.R.K., Bhowmik S. Kasyap S.K.; “Navigation of mobile robot: Fuzzy
logic approach”,
22nd National Convention of Production Engineers & National
Conference on RTMMR-07, Jun 2-3, 2007, Institution of Engineers(India), Jabalpur, India.
4. Singh M.K., Parhi D.R., Bhowmik S., Kasyap S.K.; “Navigation of mobile robot using
fuzzy logic” Geominetech symposium on ENTMS-07, May 11-12, 2007, Bhubneshwar,
India.
5. Singh M.K., Parhi D.R., Bhowmik S.; “Navigational path analysis of mobile robot in
various environments: A survey”, National Conference on ATENM-07, January 23-24,
2007, BIT Mesra, India.
6. Singh M.K.,Parhi D.R., Bhowmik S.;“Path analysis of mobile robot using fuzzy logic”,
National Conference on TSDPS-07, January 6-7, 2007, IT GGDU Bilaspur, India.
Bibliography
Mr. Mukesh Kumar Singh is a faculty member in the Department
of Mechanical Engineering, Government Engineering College
Bilaspur-09, Chhattisgarh, India. He has 14 years of research and
teaching experience in his field. He did M.Tech. in CAD/CAM.
This dissertation is submitting for fulfillment of the Ph.D. degree.
The contact address is:
Mukesh Kumar Singh
Department of Mechanical Engineering
Government Engineering College Bilaspur.
Phone: 07752-260526 (o) Fax: 07752-260339(o).
C/3, Government Engineering College Campus
Koni, Bilaspur, Chhattisgarh, India- 495009. +919479171019(cell).
E-mail: [email protected], [email protected]
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