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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
SAJJAD SAMIEE, Ph.D.
(Corresponding author)
E-mail: [email protected]
Graz University of Technology
Institute of Automotive Engineering
Inffeldgasse 11, Graz 8010, Austria
SHAHRAM AZADI, Ph.D.
E-mail: [email protected]
REZA KAZEMI, Ph.D.
E-mail: [email protected]
K. N. Toosi University of Technology
Faculty of Mechanical Engineering
Tehran 19991-43344, Iran
ARNO EICHBERGER, Ph.D.
E-mail: [email protected]
Graz University of Technology
Institute of Automotive Engineering
Inffeldgasse 11, Graz 8010, Austria
Intelligent Transport Systems (ITS)
Original Scientific Paper
Submitted: Apr. 4, 2015
Accepted: Dec. 1, 2015
TOWARDS A DECISION-MAKING ALGORITHM FOR
AUTOMATIC LANE CHANGE MANOEUVRE CONSIDERING
TRAFFIC DYNAMICS
ABSTRACT
This paper proposes a novel algorithm for decision-making on autonomous lane change manoeuvre in vehicles. The
proposed approach defines a number of constraints, based
on the vehicle’s dynamics and environmental conditions,
which must be satisfied for a safe and comfortable lane
change manoeuvre. Inclusion of the lateral position of other
vehicles on the road and the tyre-road friction are the main
advantages of the proposed algorithm. To develop the lane
change manoeuvre decision-making algorithm, first, the
equations for the lateral movement of the vehicle in terms
of manoeuvre time are produced. Then, the critical manoeuvring time is calculated on the basis of the constraints. Finally, the decision is made on the feasibility of carrying out
the manoeuvre by comparing the critical times. Numerous
simulations, taking into account the tyre-road friction and
vehicles’ inertia and velocity, are conducted to compute the
critical times and a model named TUG-LCA is presented
based on the corresponding results.
KEY WORDS
autonomous driving; lane change manoeuvre; decision making; Drive Assistance System;
1.INTRODUCTION
Lane change manoeuvres are an important part
of microscopic traffic simulations, and significantly
affect the results produced by these simulations [1].
Lane changes contribute to a significant percentage
of the collisions due to wrong estimation of distances
between the vehicles by the drivers [2]. Wang et al.
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
report that 20% of the highway collisions occur due to
the inappropriate lane changes [3].
Studies on lane change have been conducted for
around three decades, e.g. [4]. In [5] a group of 16
drivers was gathered to investigate the characteristics
of lane change. The characteristics examined included
lane change duration and required distance as well as
the initial position of the vehicle. This study showed
that the driver’s age and the direction of lane change
do not influence the aforementioned characteristics.
Another research based on the use of a driving simulator for steering wheel data recording during lane
change showed that the type of the front vehicle does
not affect the manoeuvre duration and maximum angle of the steering wheel, while the velocity of the front
vehicle influences the aforementioned characteristics
[6]. In [7], a model was developed for vehicle lane
change based on the cellular automaton (CA) which
mainly focused on some of the vehicle’s constraints
such as maximum acceleration and deceleration. The
rules used in [7] were later used in another study for
traffic simulation in double- and triple-lane highways in
[8] and it was demonstrated that the developed model
allows realistic simulations.
A Multi-input Multi-output adaptive neuro-fuzzy
system was used in [9] to model the driver behaviour
during the lane change based on realistic data. The
developed model exhibited satisfactory performance
even in the presence of operation delay. In the research conducted by Song et al. [10] for the design of
emergency lane change path (automated lane change
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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
due to driver inability to control the vehicle), a model was proposed based on the artificial potential approach and the elastic band theory, which can be used
in different circumstances such as driving on straight
and curved paths as well as lane change manoeuvres.
In this study, yaw rate and lateral vehicle acceleration
were used to evaluate the generated path. In another study, an algorithm was proposed which is able to
identify the boundaries of the path, store the obtained
information and design the desirable driving path using a vectorial approach [11]. In [12] the driving task
was interpreted as a model predictive control which is
able to control and stabilize the double-lane change
manoeuvre using fuzzy logic in accordance with the
ISO standard. The aforementioned approach was also
employed in another study [13] to control vehicle velocity in addition to the lane change manoeuvring. The
experiments conducted on a one-way two-lane road
demonstrated suitable longitudinal and lateral control
action of the vehicle consistent with the traffic condition of the road.
In research carried out by Zhang et al. [14], the process of path design was adapted to the driving condition. In this approach, first the optimal steering angle
is computed by forming a trade-off between vehicle
performance and passenger comfort and then a lane
change path is suggested based on the calculated
angle and in accordance to the dynamic constraints
of the vehicle. Finally, if no collision occurs between
the vehicles on the suggested path, it would be se-
Data
lected as the final path. In [15], some models were
proposed for passenger cars and heavy vehicles using
accurate camera information and analysis of experimental recorded data. By inclusion of car-following behaviour and taking dynamic constraints into account,
a new model was developed which allowed for velocity
change during vehicle manoeuvring [16]. This model
was simple and more consistent with the real lane
change behaviour of the drivers. During a research on
parameters affecting the vehicle lane change process,
it was revealed that the shape and duration of a manoeuvre do not depend on the leading vehicle and are
only influenced by the starting point of the manoeuvre
[17]. Moreover, in this study a simple mathematical
model was developed based on the optimization of the
consumed fuel during the manoeuvre.
In all aforementioned studies, decision-making
unit considers only the initial condition of traffic vehicles and assumes there will be no changes in their
behaviour during the lane change manoeuvre. Hence,
in case of any changes in traffic movement, the system
will not be able to correct its primary decision. The innovation of the proposed algorithm is the integration of
process dynamics which enables the system to modify
the manoeuvre if any environmental change appears
in the middle of the lane change. The inclusion of the
effect of lateral displacement of all vehicles, taking
tyre-road friction into account, respecting vehicle dynamics, and providing real-time performance are the
other advantages of the proposed system.
Lane Change Collision Avoidance System
Sensors & cameras
Parallel Systems
Decision Making
Collision
Avoidance
Lane Keeping Assist
(LKA)
Path Planning
Continuity
Vehicle Dynamics
Comfort
Adaptive Cruise Control
(ACC)
Vehicle Control
Stability
Performance
Robustness
Anti-lock Braking System
(ABS)
Multi-Layer Controller
Constraints
Figure 1 – Schematic structure of multi-layer lane change controller
92
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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
2. AUTOMATIC LANE CHANGE SYSTEM
In general, a lane change control system consists
of three layers. Figure 1 shows an illustration of different layers of this system and the one-way top-down
format of signal flow between these layers. This figure
also presents the system interface to other driver assistance systems.
The first layer embraces the decision-making system which investigates the possibility of a lane change
by using sensor data and comparing the ego (lane
changer) vehicle’s position to other vehicles. In the
second layer, the vehicle’s trajectory is generated.
The generated trajectory must fulfil the dynamic constraints of the vehicle and can be optimized based on
different measures such as safety, passenger comfort
or fuel consumption. Finally, the third layer carries out
the steering of the vehicle on the designed trajectory.
In this study, the conventional format of one-way
top-down signal flow between the layers of automatic
lane change algorithm (see Figure 1) has been modified. In the proposed algorithm, as demonstrated in
Figure 2, the Decision Making (DM) unit gathers all
required information from the sensors and decides
if the lane change is possible. Then, it transfers the
corresponding data to Path Planning (PP) unit where
the initial path is designed. If the traffic behaviour and
road condition do not change during the manoeuvre,
the Vehicle Control (VC) unit guides the vehicle to follow the initial designed path for a safe lane change.
If any changes appear in the middle of the manoeuvre so that the initial path is not safe anymore, then
the DM is able to correct its primary decision to avoid
any collision. It delivers all the updated data to Path
Decision Making
Path Planning
Path Re-planning
Vehicle Control
Multi-Layer Controller Algorithm
Figure 2 – The configuration of the developed automatic
lane change algorithm
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
Re-planning (PR) unit for redesigning a safe path. This
task can be repeated several times during the lane
change manoeuvre based on environment traffic behaviour. The design of PP, PR, and VC units are not
discussed here and this study mainly focuses on the
development of the DM Unit.
It is clear that like the conventional lane change
system, the proposed algorithm has to satisfy constraints such as vehicle dynamics, stability, continuity,
and robustness. In addition, it should be able to operate in cooperation with Advanced Driver Assistance
Systems (ADAS) such as LKA and ACC.
3. PROBLEM DEFINITION AND PROPOSED
APPROACH
In this study it is assumed that the vehicle is being driven on a straight, level highway without any
intersections. Due to some reasons, such as driver’s
drowsiness or heart attack, the vehicle is intended to
be steered toward the right side of the road to avoid
collision with other vehicles. This manoeuvre needs to
be done in presence of other vehicles in a dynamic
traffic environment.
During this manoeuvre, the longitudinal velocity of
the vehicle is assumed to be constant. These assumptions are usually valid during lane change in normal
condition. Hence, the trajectory equation can be derived by expressing the lateral displacement of the vehicle in terms of time,
y (t) = at 5 + bt 4 + ct 3 + dt 2 + et + f (1)
where y is lateral displacement of the vehicle, t represents time, and a to f are factors of the polynomial
which needs to be defined for the definition of the lane
change path. The displacement and lateral velocity of
the vehicle at the beginning and end of the manoeuvre are zero. In addition, based on the assumption in
[20], and considering the vehicle constant longitudinal
velocity during the lane change, lateral acceleration at
the beginning and end of the manoeuvre can be set to
zero. The mathematical representations of the aforementioned assumptions are
y
y
t=0
t = tm
= 0, y
:
= -h, y
:
t=0
t = tm
= 0,
= 0,
r
y
r
y
t=0
t = tm
=0
= 0
(2)
In this research, x axis of the ground based coordinate directed toward the highway and vehicles movement direction. Besides, y axis is selected such that z
axis is upward and perpendicular to the road surface.
The selected coordinate is illustrated in Figure 3-a. In
equation (2), the maximum value of h equals the maximum lateral displacement of the vehicle at the end
of the manoeuvre. The negative sign indicates lane
change to the right side of the road. Moreover, tm represents the manoeuvre time. By applying conditions of
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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
(2) to equation (1) the trajectory equation is obtained,
which is the basis for this research
-6h
15h
-10h
y (t) = c t 5 m t 5 + c t 4 m t 4 + c t 3 m t 3, m
m
m
(3)
As mentioned earlier, the decision on the lane
change must be made in the presence of other vehicles and in a dynamic environment. It is assumed that,
in the worst-case scenario there are three other surrounding vehicles during the manoeuvre, as shown in
Figure 3. Vehicle E represents the ego (lane changer)
vehicle, vehicle A represents the leading vehicle at the
same lane, and vehicles B and D are leading and rear
vehicles on the target lane, respectively. Possible rear
vehicle on the same lane is considered not to affect
the manoeuvre and therefore neglected. Moreover,
the dashed-line vehicle in Figure 3 indicates vehicle E
during the manoeuvre. Next it will be shown that if the
four conditions below are satisfied, the lane change
manoeuvre will be possible:
1) During the manoeuvre, the lateral distance between the right front corner of vehicle E and
right rear corner of vehicle B must be at least C1
(Figure 3-a);
E
y
a)
C1
x
D
y
b)
y
E
2
3
E
E
1
A
B
C2
A
B
x
D
E
c)
A
E
x
D
C4
E
B
Figure 3 – Definition of constraints in lane change
manoeuvre
Then, the decision on lane change possibility is
made by comparing the computed lane change durations. Further, the methodology of calculating critical
trajectories based on each of the aforementioned constraints will be described.
2) After the manoeuvre and movement of vehicle E to
the target lane, its distance from vehicle B must be
C2 (Figure 3-b);
3.1 Case 1: A vehicle in front on the same lane
3) During the manoeuvre, the lateral distance from
the right rear corner of vehicle E to the left front corner of vehicle D must be at least C3. Moreover, after
the manoeuvre, the longitudinal distance between
these vehicles must be at least C4 (Figure 3-c);
Considering Figure 3-a, during the lane change the
left front corner of vehicle E (point P) will touch the
right rear corner of vehicle A (point M) if C1 is zero.
A magnified illustration of this situation is shown in
Figure 4.
4) The generated lateral acceleration of E during the
manoeuvre must be achievable, considering the
prevailing friction potential between the road and
the tyre.
The proposed decision-making algorithm investigates the possibility of designing a trajectory, considering all the abovementioned constraints. If a trajectory
is feasible, the algorithm allows the manoeuvre within
the suggested time; otherwise, the ego vehicle is kept
on the current lane until appropriate manoeuvre conditions are available.
The decision-making algorithm focuses on time
as the main decision-making parameter. First, the
lane change duration for the most critical trajectory in
terms of each constraint is derived.
94
ΘA
ΘM
A
M
C1
ΘP
ΘE
E
P
1
Figure 4 – Illustration of lateral constraint between ego
vehicle and vehicle in front on the same lane
Considering the safe distance of C1 between the vehicles when their longitudinal coordinates coincide, one
will obtain:
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
y A (t) - y E (t) = C 1 + O A M sin (i M - i A (t)) +
(4)
+ O E P sin (i P - i E (t))
where yA (t) and yE (t) indicate the lateral position of
the centre of gravity of vehicles A and E, respectively,
while O E P is the length of the imaginary line connecting vehicle E’s centre of gravity to point P and can be
computed using,
OE P =
1
( 2 w E) 2 + (l Ef ) 2 (5)
where lEf indicates the longitudinal distance from vehicle E’s centre of gravity to the vehicle’s front and wE is
the width of vehicle E. On the other hand, in equation
(4), θP is the angle between O E P and longitudinal axis
of the vehicle, hence:
w
i p = tan -1 a 2l E k Ef
(6)
Similarly, parameter O A M in equation (4) indicates
the length of the imaginary line between vehicle A’s
center of gravity and point M and θM is the angle between OAM and longitudinal axis of the vehicle. Therefore,
a 1 w A k + ^ l Ar h2
2
(7)
w
i M = tan -1 a 2l A k
Ar
where lAr indicates the longitudinal distance from vehicle A’s centre of gravity to the vehicle’s rear and w_A is
the width of vehicle A. In addition, in equation (4), parameter θ_A (t) is the angle between the vehicle’s longitudinal axis and the horizon while θ_E (t) represents
the angle between the longitudinal axis of vehicle E
and the horizon at any moment. These parameters
can be computed by,
OA M =
2
2y E (t) v yE(t)
(8)
tan (i E (t)) = 2x (t) = v xE E
where vxE and vyE are the longitudinal and lateral velocity of the ego vehicle in the global coordinate system.
Based on equation (8), the following is obtained,
v yE (t)
(9)
(v xE) 2 + (v yE (t)) 2
v xE
cos (i E (t)) =
(10)
(v xE) 2 + (v yE (t)) 2
The condition for longitudinal coincidence of points P
and M can be stated by
sin (i E (t)) =
x A - O A M cos (i M - i A (t)) = x E + O E P cos (i P - i E (t)) (11)
By substituting (5)-(8) and (10-11) into (4) and using the numerical technique presented in [21], one can
solve (4) and obtain the manoeuvre duration tm such
that constraint C1 is satisfied. This time is labelled as
t1. Obviously, this constraint designates all trajectories
in which the lateral distance between M and P is greater than C1, as a candidate for a safe trajectory. The
value of C1 itself can be a function of environmental
conditions and the desirable safety factor.
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
3.2 Case 2: Another vehicle in front and on the
target lane
Various studies have addressed the issue of the
minimum safe longitudinal distance between two vehicles and several formulations have been developed for
this distance, e.g. [22, 23]. In this study, the method
proposed by Juala et al. [24] is employed. In this conservative method, it is assumed that the velocity of the
front vehicle suddenly becomes zero in case of collision with an obstacle. In this circumstance, the safety
distance is obtained as,
v2
C 2 = s 0 + v xE t d + 2axE (12)
Eb
In (12), s0 is the safe stopping distance, while aEb is
the maximum acceleration of vehicle E. In addition, td
is the reaction time of the driver which depends on various factors such as physical and mental condition of
the driver as well as road conditions and usually varies
between 0.67 and 1.11 [25]. In case when automatic
braking systems are used, such as emergency braking
system (EBS), td is reduced. Moreover, the maximum
deceleration is determined based on different conditions such as the actual value of tyre-road friction. Finally, by substituting all required parameters in (12),
C2 and hence the manoeuvre time, labelled t2, can be
obtained. Hence, at the specified time instant, the longitudinal and lateral positions of two vehicle are governed by (13) and (14),
v2
x B - x E = s 0 + v xE t d + 2axE + l Ef + l Br Eb
(13)
yB = yE (14)
where xB and yB indicate the longitudinal and lateral
positions of the centre of gravity of vehicle B, respectively, and lBr indicates the longitudinal distance from
vehicle B’s centre of gravity to the vehicle’s rear. Obviously, this constraint designates all trajectories in
which the longitudinal distance between centres of
gravity of vehicles E and B at the end of the manoeuvre is greater than the value obtained in (13), as a candidate for a safe trajectory.
3.3 Case 3: A vehicle behind and on the target
lane
This case is a combination of the first two cases. To
obtain the lane change duration, firstly the appropriate
manoeuvre time is computed based on the safe lateral distance using (15). Then, the suitable manoeuvre
time is obtained using the safe longitudinal distance at
the end of the manoeuvre using (16). As the behaviour
of vehicle D is controlled by the automatic system, the
possibility of sudden velocity change is almost negligible and hence a two-second law [26] is used instead
of the conservative method in case two. Finally, the
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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
higher value among the two obtained values is introduced as t3. The aforementioned equations are
y E (t) - y D (t) = C 3 + O D N sin (i N - i D (t) +
+ 0 E Q sin (i E (t))
(15)
x E - X D = 2v xD + l Er + l Df (16)
Q
C3
In equations (15-16), xD(t) and yD(t) represent the longitudinal and lateral position of vehicle D’s centre of
gravity. Moreover, vxD and lDf indicate the longitudinal
velocity of vehicle D and the longitudinal distance
from vehicle D’s centre of gravity to the vehicle’s rear,
respectively. O E Q is the length of the imaginary line
between vehicle E’s centre of gravity and right rear corner of the vehicle, i.e. point Q, and is calculated by,
OE Q =
a 1 w E k + (l Er) 2 2
2
D
To date, various studies have been carried out
based on the real driving data or driving simulation
data to calculate lane change manoeuvre duration
preferred by human drivers [27-31]. Table 1 presents a
summary of the obtained results.
(18)
a 1 w D k 2 + ^ l Df h2 2
N
In this case, there is no vehicle around the ego vehicle. Hence, it is sufficient to calculate a certain time
duration tm for the lane change manoeuvre. The only
necessary constraint is the prevailing tyre-road friction
potential.
Based on Table 1, the average time of 4.3 s has
been taken for lane change manoeuvre. This time has
been obtained on highways when there is no pressure
on the driver, and hence, is suitable for this study. Setting tm=4.3 (s) and lateral displacement to the width of
the highway trajectory, i.e. h=3.75 (m), the trajectory
equation for this case, generally presented in (3), can
be obtained as,
Similarly, O D N in (15) shows the length of the imaginary line from the gravity centre of vehicle D and its
left front corner (Point N). Moreover, θN indicates the
angle between this line and longitudinal axis of the vehicle and read
OD N =
3
3.4 Case 4: No vehicle on the lane
where lEr is the longitudinal distance between vehicle
E’s centre of gravity and its rear. Moreover, θQ in (15)
indicates the angle between OEQ and longitudinal axis
of the vehicle. Now, one can state
Er
ΘN
ΘD
Figure 5 – Illustration of lateral constraint between ego
vehicle and vehicle behind on the target lane
(17)
w
i Q = tan -1 a 2l E k E
Θ
ΘEQ
(19)
y (t) = -0.015t 5 + 0.165t 4 - 0.472t 3 w
i N = tan -1 a 2l D k Df
(20)
(21)
The lateral displacement, velocity and acceleration of
the trajectory in terms of time are shown in Figure 6. As
seen in this figure, the maximum lateral acceleration
on this trajectory is about 1.2 m/s2, which maintains
passenger comfort.
In equations (19-20), wD indicates vehicle D’s width. A
larger illustration of the vehicles condition in this case
is shown in Figure 5.
Table 1 – A summary of different studies on lane change time duration
96
Source
Year
Salvucci
Lee
Lane change duration (s)
Min
Max
Avg.
S. D.
2002
-
2006
-
-
5.14
0.86
-
6.28
2
Toeldo
2007
1
13.3
4.6
2.3
Thiemann
2008
-
-
4.01
2.31
Gurupackiam
2012
2.6
6
4.19
0.81
Cao
2013
1
6.8
2.54
1.29
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
By substituting h = 3.75 (m) into (24), the maximum lateral acceleration at the following time instants
can be obtained,
Lateral Position, Velocity, and Acceleration
1
t m _ 1 ! 1/3 i
(25)
2
After substituting (25) into (24), the maximum lateral acceleration can be computed as follows,
0
t=
-1
^ a y hmax = 21.265 -2
-3
Lateral Position [m]
Lateral Velocity [m/s]
Lateral Acceleration [m/s2]
-4
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 6 – Lateral displacement, velocity and acceleration
during a lane change based on case four
3.5 Case 5: The most aggressive lane change
The designed trajectory for the vehicle must be feasible with respect to vehicle dynamics. In other words,
in addition to continuity and differentiability of the trajectory, the dynamic constraints of the vehicle must be
satisfied. In particular, in case of the lane change, it
must be ensured that the generated lateral acceleration during the manoeuvre is attainable, considering
maximum tyre-road friction coefficient, and that vehicle stability can be maintained.
To ensure this, the duration of the most severe
lane-change manoeuvre must be computed and then
the trajectory designed which allows a manoeuvre
time duration greater than the duration of the most
severe lane-change manoeuvre. In this case, the dynamic equation of the vehicle at the lateral axis can
be stated by,
(22)
where p is the roll rate, r indicates the yaw rate, ay represents the lateral acceleration of the vehicle, vx and
vz are longitudinal and perpendicular velocity of the
vehicle, m is vehicle’s weight and Fy is the lateral force
applied to the vehicle and obtained by,
Fy = | ^ Fxi sin (d i) + Fyi cos (d i) h 4
i=1
(23)
where Fxi, Fyi and δi are longitudinal force, lateral force
and steering angle of i-th wheel, respectively. If the
vehicle travels through the path which was obtained
from equation (3), lateral acceleration can be calculated using,
y=b
::
-120h l 3 b 180h l 2 b -60h l
t +
t +
t
t 5m
t 4m
t 3m
21.65
(27)
max ^ m1 Fy - rv x + pv z h
Hence, the influence of the vehicle dynamics
and prevailing road conditions on the minimum lane
change time is taken into account. The lateral force
produced beneath each tyre, Fyi, depends on the lateral slip angle and can be computed using (28) based on
the Fialla model [32],
(t m) min =
Time [s]
m ^ a y + rv x - pv z h = Fy (26)
tm
Obviously, the lateral acceleration increase is proportional to the square of manoeuvre time duration
and to achieve higher acceleration, manoeuvre time
must be decreased. By substituting (22) into (26),
(tm)min is obtained.
(24)
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
a i = d i - tan -1 d
^ v y + r $ l xi h
n
^ v x - r $ l yi h
(28)
where αi and δi are lateral slip angle and steering angle associated with wheel i. Besides, lxi and lyi are the
longitudinal and lateral distance between each tyre
and the vehicle’s centre of gravity, while vy represents
lateral velocity of the vehicle. On the other hand, when
the respective tyre is facing longitudinal and lateral
slip, the longitudinal and lateral forces are interrelated
based on the elliptic friction model [33] which reads,
2
2
F
b Fxi l + b yi l = 1 (29)
n xi Fzi
n yi Fzi
where Fzi, μxi and μyi are perpendicular force, longitudinal friction coefficient and lateral friction coefficient
of tyre i, respectively. According to (23) and (27)-(29),
it is inferred that the shortest lane change duration,
(tm)min depends on different parameters such as vehicle acceleration, tyre performance, road conditions
and some characteristics of the vehicle, e.g. weight
and the distance from front and rear axles to the gravity centre.
Next, the minimum lane change time is derived as
a function of three variables, including the longitudinal
velocity, weight and friction. These factors, apart from
the level of influence, take time-varying values. In a
specific vehicle, the weight may change depending on
the number of passengers or loading volume. Similarly,
the maximum tyre-road friction coefficient depends on
the road condition as well as the tyre characteristics.
Finally, lane change manoeuvre may be carried out at
different velocities. The vehicle’s weight and velocity
can be easily measured instantaneously and there
are different methods to estimate maximum tyre-road
97
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
IPG CarMaker is a platform to simulate vehicle
dynamics and control units [35]. This tool provides
a comprehensive setting for implementing driving
scenarios and can be used for offline and real-time
simulations for hardware-in-the-loop systems [36].
The models in IPG CarMaker are parametric, hence
allowing generation of a variety of models. The development of comprehensive vehicle systems such as
power train, steering, braking and tyre system can be
realized [37]. Moreover, C-language codes can be added to the program and communication with MATLAB/
SIMUINK adds to the enhanced flexibility of the tool
[38]. The results obtained from the pre-set models in
this tool have been used and verified in various studies
[39, 40]. A general view of the IPG CarMaker GUI is
illustrated in Figure 7.
Steering Wheel
Angle
3.5.1 Applied Dynamic Simulation Software
equals road width, i.e. 3.75 m. After calculating θ, manoeuvre time tm, is reduced by 0.05-second steps until
vehicle hits instability boundary. The obtained time is
the minimum attainable time for the lane change, recorded as (tm)min, considering environment and vehicle
conditions. This scenario is repeated for velocities between 60 to 120 km/h with the increment 20 km/h.
For each specific velocity, maximum tyre-road friction
coefficient from 0.1 to 1.2 with increment 0.1 are
considered. All the experiments are executed for the
loaded and unloaded vehicle, conveying passengers.
In total, 96 simulations are conducted.
Time
500 ms
Yaw rate
friction coefficient in real time, as stated in [34]. In this
study, other parameters such as the distance between
front and rear axles of the vehicle are assumed to be
constant. The dynamic vehicle simulation tool, IPG
CarMaker, is used in this paper for analysis.
Time
rpeak
tmtm+1
tm+1.75
Figure 8 – Steering input and estimation of stability based
on the corresponding yaw rate [41]
Figure 7 – A view of the IPG CarMake GUI
3.5.2 Methodology and criterion for minimum
acceptable time
For this study, the vehicle is moving on a triple lane
highway at constant speed. At a certain moment of
time, an input shown in Figure 8 (top) is applied to the
vehicle. The maximum value of steering angle, shown
by θ in this figure, is determined based on the lateral
position of the vehicle at the end of the manoeuvre. In
other words, θ is determined such that the lateral displacement of the vehicle at the end of the manoeuvre
Vehicle stability is analyzed based on ESC system
standard [41]. Based on this standard, the performance of the ESC system is acceptable if, in case of
a change in the steering wheel (Figure 8, top), the yaw
rate does not exceed 35% and 25% of rpeak (Figure 8,
bottom) after 1 and 1.7 s from the end of the manoeuvre, respectively. In Figure 8, rpeak indicates the maximum change in the yaw rate during the manoeuvre.
Important vehicle parameters are presented in Table 2.
As an example, the time history of lateral acceleration and yaw rate in two different cases are shown in
Figure 9. In this scenario, the vehicle is moving at the
constant velocity of 80 km/h. The sine dwell input on
the steering wheel with a frequency of 0.33 Hz and
value of 90 degrees is applied to the steering system
after 1 s. The tyre-road friction potential in the first
Table 2 – Important parameters of the vehicle
98
Vehicle’s CG distance from front axle
1.268
Coefficient of rear spring
30,000 N/m
Vehicle’s CG distance from rear axle
1.62 m
Coefficient of front damper (Push)
2,500 Ns/m
Distance between front wheels
1.558 m
Coefficient of front damper (Pull)
5,000 Ns/m
Distance between rear wheels
1.582 m
Coefficient of rear damper (Push)
3,000 Ns/m
Mass of vehicle
2,064 kg
Coefficient of rear damper (Pull)
6,000 Ns/m
Coefficient of front spring
25,000 N/m
Rack travel to Steering pinion angle
100 rad/m
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S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
scenario (solid line) is 0.9 and in the second scenario
(dashed line) is 0.2. Based on the result of Figure 9
and according to the evaluation criterion of [41], the
vehicle is unstable in the second manoeuvre. Hence,
the lane change time is not acceptable and needs to
be increased.
Lateral Acceleration [m/s2]
4
Mue=0.9
Mue=0.3
2
-2
1
2
3
4
4) The minimum acceptable time is highly dependent
on maximum tyre-road friction coefficient potential.
5
Time [s]
Yaw Rate [deg/s]
10
Mue=0.9
Mue=0.3
5
0
-5
-10
-15
0
1
2
3
Time [s]
4
2) Vehicle mass increase does not affect manoeuvre
time monotonically. In other words, mass increase
may lead to a larger manoeuvre time in some conditions, but in other condition manoeuvre time may
be reduced.
3) Velocity change has more influence on manoeuvre
time increase in the presence of small friction rather than large friction.
0
-4
0
1) Decrease in friction and vehicle mass and increase
in speed, produces a smaller minimum acceptable
time for the manoeuvre.
5
Figure 9 – Lateral acceleration and yaw rate of the ego
vehicle in response to sin dwell input to the steering wheel
3.5.3 Simulation results
The analysis of the simulation results, illustrated in
Figure 10, leads to the following,
For a better analysis of the produced curves, the
influence of the mass on manoeuvre the minimum
time (tm)min is applied in a different manner. For this
purpose, two available curves shown in Figure (8), are
integrated together. In the integration procedure, for
each specific velocity and mass, the larger time value
is selected. For instance, at 120 km/h (solid line) with
the friction of 0.1, the values of time in both curves are
compared. This time is 6 s for the unloaded vehicle,
and 5.15 s for the loaded vehicle with passengers. By
choosing the larger time, it is guaranteed that the computed manoeuvre time is acceptable for any condition
in between.
Figure 11 shows the 3-D diagram of the manoeuvre time in terms of mass, velocity and tyre-road friction. The illustrated surface divides the space into two
parts. The volume above the surface indicates acceptable manoeuvre time.
M=2,064 [Kg]
6
V=120 [Km/h]
V=100 [Km/h]
V=80 [Km/h]
V=60 [Km/h]
5.5
5
4.5
4
4
3.5
3
3.5
3
2.5
2.5
2
2
1.5
1.5
1
V=120 [Km/h]
V=100 [Km/h]
V=80 [Km/h]
V=60 [Km/h]
5
Time [s]
Time [s]
4.5
M=2,464 [Kg]
5.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Friction Coefficient
1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Friction Coefficient
Figure 10 – Time duration of lane change manoeuvre based on different velocities, vehicle masses, and road conditions
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
99
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
6
5
Time [s]
4
3
2
1
0
0.2
0.4
0.6
0.8
1
Friction Coefficient
1.2
35
30
25
20
15
Velocity [m/s]
2) The distance between this model and the main
surface is due to a safety factor considered for the
manoeuvre. The safety factor attains the highest
value for high velocities and low frictions. The difference between the main surface and the TUGLCA is shown in Figure 13;
3) The computational burden is low and hence suitable for real-time calculations;
4) The TUG-LCA model has to be computed for any
specific vehicle.
Although the results are only presented for a specific passenger cars with the parameters that are described in Table 2, the same procedure can be applied
to all non-articulated vehicles such as any type of passenger cars, buses, and heavy vehicles.
3.6 Decision-Making Strategy
Figure 11 – 3-D diagram of the manoeuvre time in terms
of different weight, velocity and maximum tyre-road friction
coefficient
The time values below the surface are not acceptable as they do not satisfy the stability criterion as explained earlier. The points on the surface correspond
to the minimum acceptable time. The results of different simulations are approximated by (30), where the
minimum manoeuvre time tm is expressed in terms of
maximum tyre-road friction coefficient μ and vehicle
velocity vx.
n ^ 8 + 0 .5 v x h + 5
t m ^ n, v x h =
(30)
10n
The presented model in (30) is labelled TUG-LCA.
This model can be illustrated in 3-D as shown in
Figure 12. The TUG-LCA model has the following characteristics:
1) It is entirely above the generated surface;
6
4
Value
Par.
Value
C1
1 (m)
wA
1.65 (m)
wE
1.56 (m)
s0
2 (m)
td
0.5 (s)
aEb
0.7g (m/s2)
As an example, the second case in Table 4 is considered. In this case, t1>t2>t3>t4, as shown in Figure 14.
1
0.5
0
-1
0.2
0.4
0.6
0.8
20
1
Friction Coefficient
1.2
35
25
30
Velocity [m/s]
Figure 12 – TUG-LCA lane change time duration model
100
Par.
-0.5
2
0
0
Table 3 – Value of the parameters
Time difference [s]
Time [s]
8
In this paper, the value of the required parameters
to obtain t1, t2 and t3 based on the aforementioned
equations are presented in Table 3.
By calculation and comparison of these times and
settings (tm)min=t4, the decision can be made. Table 4
presents the possible lane change cases along with
the acceptable time or time interval for the manoeuvre.
15
0.2
0.4
30
0.8
25
20
Velocity [m/s]
0.6
1
1.2
Friction Coefficient
Figure 13 – The difference between the main surface
and the TUG-LCA model
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
E
y
A
x
3
D
4
2
1
B
Figure 14 – An example of possible paths based on
different constraints
As presented, a trajectory between paths 1 and 2
cannot be selected, because the constraint of trajectory 2, i.e. C2, is not fulfilled. Moreover, all trajectories between paths 3 and 4, violate constraint C4. Hence, safe
trajectory for lane change manoeuvre in this example
can be any path which is located between trajectories
2 and 4.
The selection of the final suitable path can be made
based on different criteria such as fuel and manoeuvre time minimization or passenger comfort maximization, which is not the focus of this paper. Obviously,
if the comparison of the computed time does not correspond to any of the cases presented in Table 4, the
lane change manoeuvre is not allowed. If any of the
three vehicles A, B and D does not exist on the path,
its corresponding time is eliminated from calculations.
For instance, if vehicle A does not exist, time t1 will be
eliminated and in case vehicle D does not exist, time
t3 is removed. In case of absence of all three vehicles,
the time value tm= 4.3 s in section 4-4 will be used for
the manoeuvre. In this case, it must be checked that
this time value is larger than the minimum acceptable
time produced by the TUG-LCA model; i.e. tm > t4.
4. CONCLUSION
This paper has proposed an automatic lane change
decision-making algorithm for vehicles on a straight
highway. The proposed algorithm considers vehicle
dynamics and environmental conditions for decision
making on lane change. In addition of taking into consideration the lateral position of other vehicles and
maximum tyre-road friction coefficient potential, the
proposed algorithm outputs a suitable time interval
for lane change. For this purpose, firstly the equations
for lateral displacement of the vehicle in terms of manoeuvre time were developed. Then, the critical manoeuvre time was calculated based on the introduced
constraints. Finally, the decision on lane change was
made by comparing the obtained time values and the
suitable manoeuvre time duration was generated using a logical procedure. Various simulations were carried out considering tyre-road friction and vehicle velocity and mass. Then a model called TUG-LCA model
was developed which transferred the results of off-line
simulations into a real-time capable look-up table.
The advantages and innovations of the proposed
algorithm include (1) inclusion of the effect of the lateral displacement of the vehicles and tyre-road friction, (2) respecting vehicle dynamics, and (3) providing
real-time performance. Hence, in case of any environmental change in the middle of the manoeuvre, the
modification of the path is possible. In other words,
the dynamics of the process has been integrated into
the proposed algorithm. Flexibility in decision-making
process is (4) another advantage of the algorithm. In
other words, in case of change in algorithm parameters and hence setting more conservative requirements, the safety of the manoeuvre can be enhanced.
However, there might be a considerable difference
between the generated and optimal path due to the
imposed restrictions. On the other hand, by relaxation
of the boundary conditions and hence lowering safety
factors, the possibility of achieving the optimal path
is increased. The simulations implemented in IPG CarMaker confirmed the effectiveness of the proposed
algorithm.
During development of the proposed algorithm,
some restrictions were imposed, as stated below,
which are the topics for future studies,
–– The vehicle moves along a highway and on a
straight lane, road curvature and slope have been
excluded.
–– The lane changing vehicle has zero longitudinal acceleration and lane change takes place at a con-
Table 4 – Vehicle dynamic specifications of the vehicle used in simulations
Acceptable time
(range)
No.
Case
Acceptable time
(range)
8
t2>t1=t3>t4
t1
t3]
9
t1>t2=t4>t3
t2
t4]
10
t1>t2=t3>t4
t2
t3]
11
t2>t1>t4=t3
[t1
t3]
t4]
12
t1>t2>t4=t3
[t2
t3]
t3]
13
t1=t2=t3>t4
[t1
t3]
14
t1=t2=t4=t3
No.
Case
1
t1>t2>t4>t3
[t2
t4]
2
t1>t2>t3>t4
[t2
3
t2>t1>t4>t3
[t1
4
t2>t1>t3>t4
[t1
5
t1=t2>t4>t3
[t1
6
t1=t2>t3>t4
[t1
7
t2>t1=t4>t3
t1
Promet – Traffic&Transportation, Vol. 28, 2016, No. 2, 91-103
t1
101
S. Samiee, et al.: Towards a Decision-Making Algorithm for Automatic Lane Change Manoeuvre Considering Traffic Dynamics
stant longitudinal velocity. In real world conditions,
velocity change during the manoeuvre is possible.
–– If lane change is not possible, the developed system produces no suggestion for speed increase
or decrease to facilitate lane change manoeuvre.
Only the current lateral position and velocity of the
vehicle is maintained until suitable lane change
condition occurs.
A systematic approach for evaluating the algorithm
performance in infinite possible number of traffic situations is an essential outlook for the study.
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
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