Enhanced Navigation and Tether Management of Inspection Class

Enhanced Navigation and Tether Management of Inspection Class
Enhanced Navigation and Tether Management of Inspection Class
Remotely Operated Vehicles
by
Jonathan Zand
B.A.Sc., University of British Columbia, 2005
A Thesis Submitted in Partial Fulfillment
of the Requirements for the Degree of
MASTER OF APPLIED SCIENCE
in the Department of Mechanical Engineering
 Jonathan Zand, 2009
University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by
photocopy or other means, without the permission of the author.
ii
Enhanced Navigation and Tether Management of Inspection Class
Remotely Operated Vehicles
by
Jonathan Zand
B.A.Sc., University of British Columbia, 2005
Supervisory Committee
Dr. Bradley Buckham, (Department of Mechanical Engineering)
Co-Supervisor
Dr. Daniela Constantinescu, (Department of Mechanical Engineering)
Co-Supervisor
Dr. Afzal Suleman, (Department of Mechanical Engineering)
Departmental Member
iii
Abstract
Supervisory Committee
Dr. Bradley Buckham, (Department of Mechanical Engineering)
Co-Supervisor
Dr. Daniela Constantinescu, (Department of Mechanical Engineering)
Co-Supervisor
Dr. Afzal Suleman, (Department of Mechanical Engineering)
Departmental Member
Remotely Operated Vehicles (ROVs) provide access to underwater environments too
deep and dangerous for commercial divers. A tether connects the ROV to a vessel on the
surface, providing power and communication channels. During extended manoeuvres,
hydrodynamic forces on the tether produce large tensions which hinder ROV
manoeuvrability. The research presented in this thesis focuses on the design of new
tether management strategies that alleviate the tether disturbance problem, and the
implementation of a navigation suite for tracking the ROV position and velocity which
are needed to close the loop on the tether management method.
To improve the
estimation of the ROV state, an Extended Kalman Filter (EKF) is developed.
An inspection class Falcon™ ROV was used for this research. Typical of the ROVs in
its class, the Falcon™ ROV has a neutrally buoyant tether which reacts to hydrodynamic
forces that accumulate over its length when exposed to currents or when the ROV
attempts to move at high speed. Dynamics models of the ROV and the tether were
utilized in numerical simulations of deepwater Falcon™ operations and were also
embedded in the process model of the EKF. The parameters of these Falcon™ dynamic
models, including the propulsive thrusts, hydrodynamic drag forces and added masses,
were identified through a series of shallow water tests. The physical parameters of the
ROV tether were measured in a dry laboratory.
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Transect and transit manoeuvres at 200m depth were investigated through numerical
simulation of the tether and ROV. The position of the ship relative to the ROV was
optimized to minimize steady-state tether disturbance for transect manoeuvres and to
maximize sustained transit speed for transit manoeuvres. Driving the ship to lead the
ROV by 26m was found to be optimal for the transect manoeuvres at 200m depth. At the
0.2m/s transect speed, this optimal configuration produces 25N of tether disturbance,
whereas the conventional method was shown to produce tether disturbances up to 43N.
The fastest sustainable ROV transit speed for operations at 200m depth with the neutrally
buoyant tether was found to be 0.67m/s and was obtained by driving the ship 90m ahead
of the ROV. Beyond this speed, the demanded ROV thrust exceeds capacity during long
transits. However, attaching a depressor mass to the otherwise neutrally buoyant tether
provides more control of the tether profile through ship motion. With use of a depressor,
controlled ship and winch motion further reduce tether disturbance and allowed ROV
transit speeds exceeding 1m/s.
A navigation suite was developed to track ROV position and velocity with the accuracy
and frequency necessary for the proposed tether management strategies. The Falcon™
ROV was instrumented with an acoustic positioning system, a Doppler Velocity Log
(DVL), a depth sensor, a compass, and an Inertial Measurement Unit (IMU).
Asynchronous measurements from the individual devices were processed with an EKF
that used a kinetic model of translational motion to blend the data into a single estimate
of the vehicle state. The EKF performance was tested experimentally with measurements
collected during a shallow water test. The accuracy of the EKF estimate of ROV position
was quantified through comparison with optical motion measurements.
The optical
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motion measurement system accurately tracked ROV position at 100Hz, but needed
optical markers mounted to a mast on the ROV to be above the water surface, restricting
the test domain to shallow water.
ROV operations are typically beyond commercial diver depth, so the shallow water test
results were extended to deepwater operation by applying the EKF to numerically
simulated instrument measurements generated for a 200m deep ROV manoeuvre. The
EKF estimated ROV position at 10Hz with root mean square (RMS) errors less than
3.5m. The ROV velocity was also estimated at 10Hz with RMS errors less than 0.04m/s.
vi
Table of Contents
Supervisory Committee .................................................................................................... ii
Abstract............................................................................................................................. iii
Table of Contents ............................................................................................................. vi
List of Tables .................................................................................................................... ix
List of Figures.................................................................................................................... x
Acronyms ......................................................................................................................... xii
Acknowledgments .......................................................................................................... xiii
Chapter 1. Introduction to Remotely Operated Vehicles.............................................. 1
1.1 Unmanned Underwater Vehicles and Applications.................................................. 1
1.2 Tether Disturbance, ROV Control and Tether Regulation ....................................... 6
1.3 ROV Navigation ....................................................................................................... 7
1.3.1 Acoustic Positioning .......................................................................................... 8
1.3.2 Dead Reckoning and Inertial Navigation......................................................... 11
1.3.3 Extended Kalman Filtering .............................................................................. 12
1.4 Research Objectives................................................................................................ 13
1.5 The ROV Simulation Platform ............................................................................... 15
1.6 The Experimental ROV Platform ........................................................................... 16
1.7 Literature Review.................................................................................................... 19
1.7.1 Tether Management ......................................................................................... 19
1.7.2 Underwater Position Tracking ......................................................................... 20
1.8 Thesis Contributions ............................................................................................... 24
1.9 Thesis Overview ..................................................................................................... 25
Chapter 2. Tether Management .................................................................................... 27
2.1 Numerical Simulation of the ROV System............................................................. 28
2.1.1 Tether Simulation............................................................................................. 28
2.1.2 ROV Simulation............................................................................................... 29
2.1.3 Demonstration Manoeuvres ............................................................................. 30
2.2 Analysis of the Conventional Tether Tending Method........................................... 30
2.2.1 Conventional Tether Management during Transect Manoeuvres.................... 31
2.2.2 Conventional Tether Management during Transit Manoeuvres ...................... 33
2.3 Analysis of the Tether Disturbance......................................................................... 35
2.3.1 Tether Disturbance during Transect Manoeuvres............................................ 35
2.3.2 Tether Disturbance during Transit Manoeuvres .............................................. 36
2.4 Advanced Tether Management ............................................................................... 38
2.4.1 Advanced Tether Management for Transect Manoeuvres............................... 39
2.4.2 Advanced Tether Management for Transit Manoeuvres ................................. 41
2.5 Depressor Effects .................................................................................................... 42
2.5.1 Depressor Tether Management ........................................................................ 43
2.5.2 Demonstration Manoeuvre with Depressor Tether Management.................... 45
2.6 Tether Management Remarks ................................................................................. 48
Chapter 3. Navigation Estimation ................................................................................. 49
3.1 Sensor Installation................................................................................................... 50
3.1.1 Subsea Sensor Pod ........................................................................................... 50
3.1.2 Instrument Placement....................................................................................... 52
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3.1.3 Sensor Telemetry ............................................................................................. 55
3.2 Kalman Filter Fundamentals................................................................................... 59
3.3 The Extended Kalman Filter................................................................................... 63
3.3.1 Linearization about the Current State Estimate ............................................... 64
3.3.2 Measurement Innovation Collection................................................................ 65
3.3.3 Assembly of Measurement Matrices ............................................................... 66
3.4 The EKF for ROV Navigation................................................................................ 68
3.4.1 ROV Kinetics................................................................................................... 69
3.4.2 ROV Kinematics.............................................................................................. 71
3.4.3 Measurement Collection .................................................................................. 73
3.5 The ROV EKF Algorithm....................................................................................... 76
Chapter 4. System Identification ................................................................................... 78
4.1 The Shallow Water Test Facility ............................................................................ 78
4.1.1 Testing Field .................................................................................................... 79
4.1.2 Optical Motion Measurement System Setup ................................................... 80
4.1.3 Processing Optical Motion Measurements ...................................................... 82
4.2 Measurement Modeling .......................................................................................... 85
4.2.1 Acoustic Ranging............................................................................................. 86
4.2.2 Depth Sensors .................................................................................................. 92
4.2.3 Doppler Velocity Log ...................................................................................... 94
4.2.4 Magnetic Compasses ....................................................................................... 95
4.2.5 Inertial Measurement Unit ............................................................................... 98
4.3 System Identification .............................................................................................. 99
4.3.1 Thruster Parameters ......................................................................................... 99
4.3.2 Hydrodynamic Drag Estimation .................................................................... 104
4.3.3 Fluid Inertia Estimation ................................................................................. 107
4.4 Model Uncertainty Characterization..................................................................... 108
4.4.1 Constant Rotation Rate Model Uncertainty................................................... 109
4.4.2 Euler Angle Model Uncertainty..................................................................... 111
4.4.3 Velocity Model Uncertainty .......................................................................... 113
4.4.4 Position Model Uncertainty ........................................................................... 115
4.4.5 Tether Disturbance Model Uncertainty ......................................................... 116
4.5 Parameter Identification Closing Remarks ........................................................... 120
Chapter 5. Near Surface Position Tracking Results.................................................. 121
5.1 The Near Surface Test Manoeuvre ....................................................................... 121
5.2 ROV Position Estimation...................................................................................... 123
5.3 ROV Depth Estimation ......................................................................................... 126
5.4 Tether Disturbance Estimation ............................................................................. 127
5.5 DVL Contribution................................................................................................. 129
5.5.1 ROV Positioning without DVL ..................................................................... 129
5.5.2 Velocity Tracking without DVL.................................................................... 131
5.6 Shallow Water Test Remarks................................................................................ 133
Chapter 6. Simulated Deepwater Position Tracking ................................................. 134
6.1 Deepwater Manoeuvre .......................................................................................... 134
6.2 Simulation Parameters .......................................................................................... 136
6.3 Instrument Simulation........................................................................................... 138
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6.3.1 IMU Measurements ....................................................................................... 138
6.3.2 Compass Measurements................................................................................. 138
6.3.3 Depth Sensor Measurements.......................................................................... 138
6.3.4 DVL Measurements ....................................................................................... 139
6.3.5 SBL Range Measurements............................................................................. 139
6.3.6 SBL Reference Station Positioning ............................................................... 140
6.3.7 Acoustic Position Tracking............................................................................ 141
6.4 EKF Modifications for Deepwater Applications .................................................. 141
6.5 Deepwater Filter Performance Evaluation............................................................ 142
6.5.1 Position Tracking ........................................................................................... 143
6.5.2 Depth Tracking .............................................................................................. 145
6.5.3 ROV Velocity Tracking................................................................................. 146
6.5.4 Tether Disturbance Estimation ...................................................................... 148
6.6 Deepwater Performance Remarks......................................................................... 151
Chapter 7. Conclusions and Recommendations......................................................... 152
7.1 Conclusions........................................................................................................... 152
7.1.1 Falcon™ ROV Parameters Identified. ........................................................... 152
7.1.2 Tether Management Schemes Developed...................................................... 152
7.1.3 The EKF Developed ...................................................................................... 153
7.1.4 Identification of the Tether Disturbance Forces ............................................ 153
7.1.5 Experimental Testing of the Navigation System ........................................... 154
7.2 Future Work .......................................................................................................... 155
7.2.1 Tether Disturbance Mapping ......................................................................... 155
7.2.2 Model Based Ship Dynamic Positioning ....................................................... 156
7.2.3 ROV Collision Detection............................................................................... 156
7.2.4 Enhanced Tether Disturbance Estimation...................................................... 156
Bibliography .................................................................................................................. 157
Appendix A. Parameter Standard Deviations............................................................ 163
Appendix B. Tether Material Properties .................................................................... 165
B.1 Torsional Stiffness................................................................................................ 165
B.2 Bending Stiffness ................................................................................................. 167
B.3 Axial Stiffness ...................................................................................................... 169
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List of Tables
Table 2-1. Falcon™ Tether Properties.............................................................................. 29
Table 2-2. Tether and Hydrodynamic Drag Forces Imparted on the ROV. ..................... 38
Table 2-3. Depressor Properties........................................................................................ 43
Table 3-1. Instrument Locations ....................................................................................... 55
Table 4-1. Visualeyez™ Stationary Marker Locations. ................................................... 82
Table 4-2. Temporary ROV Marker Locations ................................................................ 83
Table 4-3. SBL Reference Station Locations. .................................................................. 87
Table 4-4. Range Measurement Bias Observed with Stationary Tests............................. 88
Table 4-5. SBL Acoustic Ranging Errors ......................................................................... 91
Table 4-6. ROV Depth Measurement Properties.............................................................. 93
Table 4-7. DVL Measurement Error................................................................................. 95
Table 4-8. Compass Measurement Error. ......................................................................... 98
Table 4-9. IMU Measurement Error ................................................................................. 98
Table 4-10. Falcon™ Horizontal Thruster Angles ......................................................... 100
Table 4-11. Falcon™ Hydrodynamic Drag Coefficients................................................ 106
Table 4-12. Falcon™ Inertia........................................................................................... 107
Table 4-13. Constant Rotation Rate Model Errors. ........................................................ 110
Table 4-14. Euler Angle Model Errors. .......................................................................... 113
Table 4-15. Body Fixed Velocity Model Errors. ............................................................ 115
Table 4-16. Position Model Errors.................................................................................. 116
Table 4-17. Tether Disturbance Model Estimated Error Variance. ................................ 120
Table 5-1. RMS Error of Position Estimates during the Near Surface Test Manoeuvre.125
Table 5-2. RMS Error of Falcon™ Depth Sensor and the EKF Estimated Depth ......... 126
Table 5-3. Effect of DVL on Position Estimation Accuracy. ......................................... 131
Table 5-4. Velocity Tracking Accuracies. ...................................................................... 133
Table 6-1. Waypoints for the Simulated Manoeuvre...................................................... 135
Table 6-2. Simulation Parameters................................................................................... 137
Table 6-3. Ship Mounted Reference Station Locations. ................................................. 140
Table 6-4. Ship Position Tracking Error Variance ......................................................... 141
Table 6-5. ROV Position Tracking Accuracy for the Deepwater Manoeuvre................ 143
Table 6-6. Depth Tracking Accuracy during the Deepwater Manoeuvre....................... 146
Table 6-7. Velocity Tracking Accuracy during the Deepwater Manoeuvre................... 146
Table 7-1. Summary of Shallow Water Navigation Accuracy. ...................................... 154
Table 7-2. Summary of the Simulated Deepwater Navigation Accuracy....................... 155
Table A-1. Simulation Parameters.................................................................................. 164
Table B-1. Torsional Deflection Data............................................................................. 166
Table B-2. 3-Point Bending Test Data............................................................................ 168
Table B-3. Bending Stiffness.......................................................................................... 169
Table B-4. Axial Stiffness............................................................................................... 169
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List of Figures
Figure 1-1. Commercial AUV Products. ............................................................................ 4
Figure 1-2. Commercial ROV Products.............................................................................. 5
Figure 1-3. Acoustic Positioning Configurations. ............................................................ 10
Figure 1-4. Seaeye Falcon™ ROV System ...................................................................... 17
Figure 2-1. Conventional Transect. .................................................................................. 32
Figure 2-2. Conventional Transit...................................................................................... 34
Figure 2-3. Tether Disturbance Mapped over Ship Lead for a 0.2m/s Transect. ............. 36
Figure 2-4. Tether Disturbance Mapped over Ship Lead for a 1 m/s Transit................... 37
Figure 2-5. Transect with Advanced Tether Management. .............................................. 40
Figure 2-6. Transit with Advanced Tether Management.................................................. 42
Figure 2-7. Transit with Depressor. .................................................................................. 47
Figure 3-1. Sensor Pod...................................................................................................... 51
Figure 3-2. Falcon™ Instrument Layout. ......................................................................... 54
Figure 3-3. The Sensor Data Flow used by the EKF. ....................................................... 56
Figure 3-4. The Standard KF Process. .............................................................................. 62
Figure 3-5. ROV Nomenclature Diagram......................................................................... 69
Figure 3-6. The Kalman Flowchart for ROV Navigation................................................. 77
Figure 4-1. Boathouse Layout........................................................................................... 80
Figure 4-2. Optical Markers Mounted to the ROV........................................................... 81
Figure 4-3. Optical Motion Measurements of ROV ......................................................... 85
Figure 4-4. Range Measurement Bias Observed during Stationary Testing. ................... 88
Figure 4-5. Dynamic Test of SBL Range Accuracy. ........................................................ 90
Figure 4-6. Depth Sensor Test. ......................................................................................... 93
Figure 4-7. Doppler Velocity Log Transducer Head. ....................................................... 94
Figure 4-8. The Falcon™ Thruster Arrangement. .......................................................... 100
Figure 4-9. Time-series of Commanded and Realized Thrust Forces ............................ 102
Figure 4-10. Scatter plot of Realized Thrust over the Range of Thrust Commands. ..... 102
Figure 4-11. Steady-state Surge Thrust Force Response to Thrust Commands. ............ 103
Figure 4-12. ROV Velocity Response to a Thrust Force Step Input. ............................. 105
Figure 4-13. Drag Force as a Function of Speed. ........................................................... 106
Figure 4-14. Error in Constant Rotation Model.............................................................. 110
Figure 4-15. Error Accumulation of Model Propagated ROV Heading......................... 112
Figure 4-16. Body Fixed Velocity Model Errors............................................................ 114
Figure 4-17. Test of Position Model Uncertainty. .......................................................... 116
Figure 4-18. Manoeuvre for Tether Disturbance Model Error Identification................. 117
Figure 4-19. Influence of ROV Acceleration on Tether Tension. .................................. 119
Figure 5-1. Plan View of the Near Surface Test Manoeuvre.......................................... 122
Figure 5-2. ROV Position during the Shallow Water Test. ............................................ 124
Figure 5-3. Shallow Water Position Error. ..................................................................... 125
Figure 5-4. ROV Depth during the Near Surface Test. ................................................. 127
Figure 5-5. Tracking the Tether Tension. ....................................................................... 128
Figure 5-6. ROV Positioning without DVL.................................................................... 130
Figure 5-7. Position Tracking Errors .............................................................................. 131
Figure 5-8. Surge Velocity Estimated by the EKF Unaided by DVL Measurements .... 132
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Figure 6-1. Plan View of ROV Position during the Deepwater Manoeuvre. ................. 135
Figure 6-2. Tether Profiles During the Simulated Manoeuvre. ...................................... 136
Figure 6-3. Simulated ROV X Position .......................................................................... 144
Figure 6-4. Simulated ROV Y Position .......................................................................... 145
Figure 6-5. EKF Velocity Tracking Performance........................................................... 147
Figure 6-6. Tether Tension Estimation. .......................................................................... 148
Figure 6-7. Tether Bearing Estimation. .......................................................................... 149
Figure 6-8. Tether Inclination Estimation....................................................................... 150
Figure B-1. Cross-section of the Falcon™ ROV’s Tether. ............................................ 165
Figure B-2. Torque-Rotation Test to Identify Tether Torsional Stiffness. ..................... 167
Figure B-3. 3-Point Bending Test to Identify Bending Stiffness.................................... 168
xii
Acronyms
Symbol
Description
AUV
Autonomous Underwater Vehicle
DC
Direct Current, Constant Voltage
DOF
Degree of Freedom
DVL
Doppler Velocity Log
EKF
Extended Kalman Filter
GPS
Global Positioning System
HUGIN
High Precision Untethered Geosurvey and Inspection System
IMU
Inertial Measurement Unit
INS
Inertial Navigation System
KF
Kalman Filter
LBL
Long Baseline Acoustic Positioning System
LED
Light Emitting Diode
MMQ
Miniature MEMs Quartz
MRU
Motion Reference Unit
PID
Proportional Integral Derivative
RK45
Runge Kutte 4th order adaptive integration algorithm
RMS
Root Mean Square
ROPOS
Remotely Operated Platform for Ocean Science
ROV
Remotely Operated Vehicle
ROVM
Remotely Operated Vehicle Manipulator
RPM
Rotations Per Minute
RS485
Recommended Standard 485
SBL
Short Baseline Acoustic Positioning System
USBL
Ultra Short Baseline Acoustic Positioning System
UUV
Unmanned Underwater Vehicle - Either ROV or AUV
xiii
Acknowledgments
The efforts, suggestions, and companionship of many others contributed to the success
of this work. I would like to thank Dr. Brad Buckham for his immense support and
thoughtful guidance throughout the project. Dr. Daniela Constantinescu also provided
support and guidance for which I am very grateful. I wish you both continued success in
your research careers.
Suboceanic Sciences Canada Ltd. generously provided access to their Falcon™ ROV.
Mike Wood, Suboceanic director of operations, imparted an ROV operator’s perspective,
providing a practical foundation for research goals. Hopefully this work can be applied
to your future missions to ease your operations and expand your capabilities.
The team at Dynamic Systems Analysis Ltd. provided software implementation and
technical support for numerical simulations. Dean’s Kalman research provided a starting
point, and his software for multi-threaded measurement collection was tremendously
useful for the project. Ryan’s tireless maintenance and development of the ProteusDS™
software provided a powerful framework for numerical simulations of the ROV and
tether dynamics.
I also thank friends and fellow researchers who provided a helping hand. Some, such
as Serdar, Kerem, and Bonnie, spent many late evenings with me in a cold and dark
boathouse doing ‘just one more’ set of wet tests. Off topic discussions with my office
mates, Scott and Clayton, on renewable energy viability and day to day ordeals provoked
many creative thoughts. May we all find some warm sunny days to go for a sail.
Chapter 1. Introduction to Remotely Operated Vehicles
1.1 Unmanned Underwater Vehicles and Applications
Marine environments cover most of the earth’s surface and contain an abundance of
fascinating biological, geophysical and manmade components.
At great depths,
hydrothermal vents and ocean crust formations continue to intrigue scientists in a range
of disciplines. Unfamiliar species living in the deep ocean and their abilities to survive in
such an extreme environment are the focus of many biologists. Industrial projects, from
underwater mining to trans-continental communication lines have provided abundant
resources and advanced technological capabilities.
Modern industrial projects and
scientific research demand interaction with the deep sea.
Much underwater research and development is conducted in the shallower coastal
regions. The regulation of commercial and recreational fisheries is challenged by the
difficulty of surveying aquatic life over sustained time periods. With the emergence of
aquaculture farms and other floating commercial operations comes a need for monitoring
the environmental impacts on nearby habitats. The assessment of seafloor terrain for
mooring design and cable and pipe routing requires detailed geographic surveys.
Maintenance, repairs, and non-destructive testing of floating installations and their
moorings often requires accessing and observing submerged equipment.
2
Employing commercial divers remains the most adept approach for performing the
complex installation, surveillance and maintenance of costal infrastructure. However, the
pressure encountered, even in a coastal domain, pushes the human body to its functional
limit. Commercial divers with surface supplied air are limited to 60m safe working
depths.
Deeper dives can be performed with the use of mixed gas and lengthy
decompression periods, but add considerable cost in equipment and risk. Obviously, an
(Unmanned) Underwater Vehicle (UUV) that can perform the required task is a much
safer alternative in shallower waters and is a required alternative for deeper waters. Even
within shallow waters, the operation of a mobile and navigable UUV is free of the fatigue
constraints faced by a human diver.
The electromagnetic waves which work so well for above surface communication are
highly attenuated in water. Acoustic waves can be efficiently transmitted, but multi-path
reflections, ambient noise, the slower translational speed, and the limited bandwidth of
acoustic telemetry systems combine to hinder the effectiveness of acoustic
communication. Acoustic modems are capable of sending simple UUV command signals
[1], but suffer from considerable transmission delay and are not able to provide the realtime video feedback a human pilot requires to make control decisions.
Some submerged data collection tasks can be completed with Autonomous Underwater
Vehicles (AUVs) like the ones shown in Figure 1-1. These vehicles are usually a
streamlined torpedo shaped, with a single thruster for surge propulsion. Their motion is
predominantly in surge, with yaw and pitch controlled with actuated fins.
Their
autonomous nature makes them well suited for long missions of simple predetermined
tasks, but their reliance on an onboard power supply with limited capacity necessitates
3
efficiency. Ocean gliders [2] reduce energy consumption for low speed missions by
using buoyancy control and pitch control to generate lift that provides horizontal motion
with the use of the vertical buoyancy force. Currently, low level controllers [3, 4, 5] and
high level mission planners, otherwise referred to as autonomous agents [6, 7, 8], can be
combined to execute generic surveying missions with AUVs. However, more complex
tasks requiring human pilot involvement must be performed with another class of
unmanned underwater vehicle - submerged Remotely Operated Vehicles (ROVs).
4
Figure 1-1. Commercial AUV Products.
Top: the HUGINTM AUV manufactured by
Kongsberg Maritime uses a single transom mounted thruster for surge propulsion and four
individually controlled rudder blades for heading, pitch, and roll control. Bottom: the
SeagliderTM manufactured by iRobot varies its buoyancy to glide through the water column
over month long missions. Images courtesy of http://auvac.org/resources/configuration.
Submerged ROVs use a tether to physically connect the ROV to the pilot’s surface
station. The tether provides power and high-bandwidth telemetry for the ROV. Cameras
provide video feedback to the pilot, who controls the motion of the ROV through
actuation of several onboard propeller type thrusters. ROVs are also fitted with lights to
illuminate their surroundings viewed by the video camera. Manipulators, navigation
sensors, and scientific instruments can also be fitted to ROVs to achieve specific tasks.
5
The collective power and telemetry requirements of these devices reinforce the necessity
of the tether. Several commercially available ROV products are shown in Figure 1-2.
b) Falcon™ inspection class ROV
(http://www.cdis.ae/marine_02p.html)
a)ROPOS™ HYSUB™ 40 work-class ROV
(http://www.ROPOS.com)
c)VideoRay™ inspection class ROV
(http://www.videoray.com)
Figure 1-2. Commercial ROV Products.
ROVs are designed for unsteady, omni-directional motion, with actuation, stability and
functionality constraints requiring a more bluff and open frame shape than the
streamlined AUVs. These remotely piloted vehicles range in size from small hand-held
inspection class to the multi-ton work class ROVs. Inspection class ROVs are primarily
used for visual observations of submerged objects. They typically have a 1cm diameter
neutrally buoyant tether and operate at depths up to 300m. Work class ROVs are capable
of full ocean depth operations and are fitted with multiple tools including manipulators to
interact with the underwater environment. These large ROVs required large and costly
surface equipment to support them. The large power budget of a work class ROV is met
by high voltage transmission through kilometre scale tethers with diameters exceeding
2cm. These tethers are negatively buoyant, and are often used in conjunction with a
6
depressor or submerged tether management system to mitigate the tether’s influence on
the ROV dynamics.
The portability and lower operating costs of inspection class ROVs make them more
desirable to employ than work class ROVs. However, work class ROVs are more adept
at manoeuvring in large currents and are fitted with sophisticated navigation sensors for
ROV position tracking.
Improving the manoeuvrability and position tracking of
inspection class ROVs will expand the tasks which they can fulfill, and reduce the cost of
conducting the coastal operations mentioned earlier.
1.2 Tether Disturbance, ROV Control and Tether Regulation
The tether, which is essential in providing the remote human control of the ROV for
complex tasks, has some drawbacks. It can tangle or snag on submerged objects. During
ROV operations, hydrodynamic forces accumulate on the tether, either due to currents or
motion of the ROV, that limit ROV manoeuvrability and, in extreme cases, overpower
the ROV thrusters. Even during normal operation, tether disturbance significantly affects
the ROV dynamics.
To compensate the tether disturbance, sophisticated adaptive
controllers [9, 10] or high feedback gains [11] have been employed. In most cases, the
ROV pilot’s experience and intuition are relied on to maintain a tolerable ROV tether
configuration.
Proper tether management is necessary to mitigate the tether disturbance and ensure
controllability of the vehicle. Unfortunately, without significant alteration to the typical
tethered ROV system, the only means to shape the tether profile, and thus reduce the
tension at the ROV connection, is positioning of the surface ship and active control of the
tether winch on the surface vehicle. As such, complete control of the tether is impossible
7
and the intelligent use of the ship and winch can only seek to regulate the tether profile to
reduce the tether disturbance. Work class ROVs have the infrastructure, thrust capacity,
and negatively buoyant tethers to operate without being exceedingly hindered by tether
disturbance. On the other hand, inspection class ROVs have lower thrust capacity and
neutrally buoyant tethers, and often deal with relatively larger drag forces due to the
search manoeuvres they conduct and the tidal flows they encounter in coastal waters. By
using the surface ship and winch to regulate tether disturbance on inspection class ROVs,
one could increase the maximum transit speed of a small ROV and improve low speed
manoeuvrability in the face of high ambient current.
1.3 ROV Navigation
Accurate tracking of the ROV position is vital to almost all ROV operations. In survey
and search missions, the location of significant features noted by the human pilot through
the video cameras must be recorded. The first part of submerged object recovery is
locating the object with the ROV. Without accurate ROV position reporting, it is nearly
impossible to locate a submerged object. Poor visibility, marine growths, and sediment
deposits surround the object and hinder sighting the object even if the object’s position is
well known. When the exact location of an object is not known, the ROV must cover
large areas to search for it. Position tracking allows efficient search paths to be traversed
– the ROV operator can avoid significant overlap in the search pattern. Once the ROV
has accurately located the object, it can return to the surface to be fitted with a retrieval
device, such as a carabineer with retrieval line and directly return to the located object.
The ROV position, velocity and orientation provide the necessary feedback for
advanced ROV controllers [9, 10, 11]. Model based ROV controllers rely on parametric
8
approximations to the ROV hydrodynamics and there are several dynamic parameters
that must be estimated. The uncertainty in these parameters, as well as large unknown
disturbances (tether disturbance or forces due to unknown currents) necessitates the use
of accurate navigation information as feedback. Furthermore, navigation feedback for
ROV controllers must be accurate and without delay to avoid unstable oscillations and
overshoots in the ROV motion. Accurate real-time navigation data also improves the
performance of a human pilot during manual operation by providing the pilot with up to
date ROV state estimates that facilitate faster decision making. In the context of tether
management, navigation data allows better tether regulation by providing a real-time
estimate of the relative location of the ROV to the surface ship.
The aquatic environment in which ROVs operate renders many of the land based
navigation techniques ineffective. Underwater navigation systems are discussed in the
next three subsections.
1.3.1 Acoustic Positioning
The same electromagnetic signal attenuation that necessitates the use of a tether also
renders the satellite GPS unusable for underwater position tracking. Acoustic systems
analogous to GPS can be used, but are tedious to deploy, and can contain significant
measurement error.
Acoustic positioning operates on similar principles as GPS, but requires local reference
transducers transmitting acoustic waves instead of satellites emitting electromagnetic
waves. Also, since the reference stations (transducers) are local to the tracking target,
most acoustic positioning systems operate on a repeated ping, while GPS transmits a
continuously varying signal. The range between an ROV mounted transducer and a
9
reference station is calculated from the time for acoustic waves to travel between the two
transducers. The ranges from the ROV transducer to several reference stations are used
to trilaterate ROV position.
Several reference station configurations are common, each with their own merits.
Long Base Line (LBL) configurations consist of stationary reference stations distributed
throughout the survey area, and are perhaps the most accurate, but most tedious to set up.
Short Base Line (SBL) configurations space the reference stations apart on the surface
vessel, where they can be permanently mounted, but accurate surface vessel position and
orientation measurements are needed to make accurate ROV measurements in earth fixed
coordinates. Ultra Short Baseline (USBL) systems contain all the reference transducers
in a single instrument and rely on phase lag to resolve direction to the ROV transducer.
Like SBL systems, accurate tracking of the USBL reference instrument’s position and
orientation is needed for useful ROV position tracking. Reference station locations and
acoustic paths for LBL and SBL configurations are depicted in Figure 1-3.
10
Figure 1-3. Acoustic Positioning Configurations. Top: LBL systems have reference stations
set on the seafloor with large spacing and require re-calibration at each survey site.
Bottom: SBL systems have reference stations mounted to the ship, making the system easy
to move between sites, but reference station spacing is limited by ship size. USBL systems
also have a reference station mounted to the ship.
Regardless of system configuration, acoustic positioning measurements are prone to
errors in reference station locations, sound speed estimation, and multi-path signals.
11
Also, acoustic range measurements can contain considerable delay, due to the travel time
between the reference station and target transducer.
1.3.2 Dead Reckoning and Inertial Navigation
The velocity and acceleration of ROVs can be measured with onboard sensors. With
either of these measurements, the progression of ROV position can be calculated with
kinematics.
The ROV velocity is most readily measured by an onboard sensor that provides speeds
in the surge, sway, and heave directions of the vehicle. Flow sensing meters (such as
paddle wheels and hotwires) measure velocity relative to the ambient water velocity. A
Doppler Velocity Log (DVL) finds the over ground velocities by measuring the
frequency shift of echoes off the seafloor.
Vehicle heading is commonly measured with flux gate magnetometers functioning as a
compass. The three dimensional magnetic field is measured, and the projection on the
horizontal plane reveals the angular offset from magnetic north. The horizontal plane can
be resolved with a tilt sensor. Accelerometers used to resolve the direction of gravity can
also provide the tilt of the vehicle.
In addition to horizontal plane errors, local
environmental magnetic anomalies and magnetic field disturbances from onboard
equipment degrade the accuracy of the compass.
The compass’s measurements of ROV orientation can be used to rotate the ROV
velocity measurements made by the DVL in the body fixed coordinates to rates of change
of the vehicle’s position.
Integration of these values with time produces the dead
reckoning estimate of ROV position. The integration process provides high frequency
12
estimates and smoothes random measurement fluctuations, but accumulates systematic
bias errors of the velocity and heading measurements
Similar to dead reckoning, self contained Inertial Navigation Systems (INS) integrate
measurements of linear acceleration and rotational velocity measured by an Inertial
Measurement Unit (IMU) to calculate ROV position and velocity. However, due to the
double integration with time, INS position calculations are even more sensitive to
measurement bias than dead reckoning estimates. Gravitational acceleration must be
taken out of the IMU acceleration measurements, requiring accurate tracking of the ROV
orientation. As such, INS systems require an IMU with high quality gyroscopes. Ring
laser and fibre-optic gyroscopes are sufficiently accurate for this task, and can detect the
earth’s angular velocity to bound the error on the heading estimate calculated from
integrated yaw rates. Complementary filtering of the ROV rotation rate measurements
and the inertial acceleration measurements is used to estimate the ROV velocity and
orientation. Dead reckoning can be applied to the INS estimates of ROV velocity and
orientation to estimate ROV position. However, external position sensors are required to
reset the error accumulation of the estimated position and translational velocity.
1.3.3 Extended Kalman Filtering
Slow and noisy acoustic positioning measurements can be combined with high
frequency but error accumulating dead reckoning and INS measurements via
complementary filtering to improve navigation estimates. Kalman filtering [12] is a
commonly used complementary filter.
Its blending criteria aim to minimize error
variance in its estimate based on estimates of measurement and process uncertainties.
The Kalman Filter (KF) includes a state transition matrix to evolve the filter’s state with
13
time, and then corrects state errors with available measurements while keeping track of
the state’s uncertainty. For states with nonlinear dynamics, an Extended Kalman Filter
[13] (EKF), can be used to calculate the varying state transition matrix.
1.4 Research Objectives
This work aims to improve the operating capabilities of inspection class ROVs working
in coastal regions. The Falcon™ shown in Figure 1-2(b) is the ROV used in this work.
Access to a Falcon™ was shared with Suboceanic Sciences Canada Ltd, which provides
ROV services to BC’s coast and around the world. The Falcon™ is small enough to be
easily transported and launched while sufficiently powerful to perform light interaction
with submerged objects. These ROVs are currently navigated by dead reckoning from a
buoy line with the use of a compass and depth sensor. More sophisticated sensors,
providing position, speed, and orientation will be fitted to the ROV.
Navigation
performance is enhanced to simplify mission planning, to provide position tracking, and
to generate the feedback required by automatic ROV controllers. Also, a means to
regulate the tether position and mitigate the tether disturbance is addressed to expand the
ROV manoeuvrability and the range of allowable operating sea states. The technical
objectives are as follows:
1. Identify the parameters of a Falcon™ ROV. These parameters are needed to conduct
numerical simulations of the ROV dynamics.
Simulations are necessary for
developing, testing, and refining the other objectives. The navigation system will
include a dynamics model that also requires some of these parameters.
The
parameters will be identified by piloting the Falcon™ ROV through a series of test
14
manoeuvres and recording velocity and acceleration data. This data will be used in a
sequential parameter identification process.
2. Develop tether management schemes. Ship and winch activity which mitigates tether
disturbance during both low speed transects and high speed transits will be developed
through numerical simulation. The relationship between the ship position relative to
the ROV and the steady-state tether disturbance will be mapped to find operating
configurations with minimal tether disturbance. The benefit of using a depressor
mass on the ROV’s neutrally buoyant tether will be investigated.
3. Develop an EKF for sensor fusion. ROV navigation with low noise and high update
rate will be achieved by blending the measurements of an acoustic positioning
system, a DVL, a low cost IMU, a compass, and a depth sensor. A kinetic model of
the ROV will be embedded within an EKF to further reduce navigation uncertainty.
EKF performance will be demonstrated with experimental shallow water testing and
simulation results of full scale deployments.
4. On-line identification of the tether disturbance forces. Tether disturbance will be
included as an EKF state, and its evolution with time will be coarsely modeled within
the ROV kinetic model embedded in the EKF. Since no load-cell is installed on the
ROV to provide tether disturbance measurements, the EKF will refine its estimate
using the mismatch between model dynamics and measured dynamics.
5. Experimental testing of the EKF navigation system on an inspection class ROV. The
ROV will be fitted with an IMU, a DVL, a compass, and an SBL target transducer. A
shallow water test facility will be setup to provide a protected environment in which
to pilot the ROV through a series of test manoeuvres.
An optical motion
15
measurement system will be used at this facility to accurately track the ROV position.
The optical measurements will be used to evaluate the accuracy of the EKF’s estimate
of ROV position during the shallow water tests.
1.5 The ROV Simulation Platform
Given the depth constraints of the test facility being used for the experimental EKF
development, a numerical simulation of the Falcon™ ROV system was used throughout
this research whenever full scale, or deepwater, operation of the ROV was considered.
The tether management scheme will be designed through simulation studies and the
tether management scheme and navigation algorithm will be tested in deepwater
conditions via simulations.
Perhaps the most difficult component of the ROV to simulate is the tether disturbance
force, as it depends on the non-linear dynamics of a highly variable tether shape. In this
research, the ProteusDS™ simulation package, created and maintained by Dynamic
Systems Analysis Ltd., was used to simulate the ROV system during deepwater
operations. In the ProteusDS™ simulations, the tether is modeled as a variable length
cable using a finite cable element unique to the ProteusDS™ code [14, 15]. The ROV is
modeled as a six Degree of Freedom (DOF) rigid body with the five thrusters modeled as
equivalent point loads [16]. The ProteusDS™ simulation package handles the interaction
between these objects and propagates the system through time with an adaptive 4th order
Runge-Kutta integration algorithm (RK45). The state of the surface ship and winch are
specified as kinematic inputs.
Parameters of the Falcon™ system, such as tether stiffness and ROV hydrodynamic
coefficients are measured during parameter estimation tests and passed to the
16
ProteusDS™ simulation as constants.
Though much effort is necessary to accurately
determine and numerically model the dynamics, once in place, they allow the simulation
to predict the detailed behaviour of the ROV system over a large range of operating
scenarios.
1.6 The Experimental ROV Platform
The Falcon™ ROV is an inspection class ROV manufactured by Saab Seaeye. The
system consists of the subsurface vehicle, tether, and surface station as shown in Figure
1-4. Suboceanic Sciences Canada Ltd. typically uses the Falcon™ ROV for marine
surveys and sunken object recoveries. Marine surveys include aquaculture impacts on
nearby marine ecosystems, anchor line inspections, and bathymetry mapping for pipeline
routing. Retrieved objects include sunken boats, nets, scientific instruments, and other
ROVs.
17
Figure 1-4. Seaeye Falcon™ ROV System
The subsurface vehicle has a 300m depth rating, which allows it to access most coastal
seafloors, even those far beyond the reach of commercial divers. The ROV has a mass of
50kg, making it easy to deploy with the help of a davit, or can even be hand launched
from a low platform such as a swim grid. Four electric thrusters are vectored in the
vehicle’s horizontal plane, allowing responsive and powerful surge, sway, and yaw
manoeuvres. A fifth electric thruster is oriented vertically near the middle of the vehicle
to provide depth control of the typically neutrally buoyant vehicle. A single-function
manipulator can retrieve small submerged objects or can attach a winch line to heavier
18
objects. A 5-function hydraulic manipulator arm is also part of the system, allowing
more dexterous tasks.
The onboard navigation pod houses a compass, a gyroscope, and
a depth sensor. A passive sonar unit indicates the presence of nearby objects.
The ROV is connected to the ship via a tether containing power and telemetry lines.
Typical Falcon™ tethers are 350m long with neutral buoyancy in salt water and sink
slowly in fresh water. The supply voltage is boosted through the tether to mitigate line
losses, while a Line Insulation Monitor closely tracks the current and quickly shuts the
system down in the event of a fault. Falcon™ telemetry runs on an RS485 network, with
the network signals distributed to each individual device. Each device receives all the
network packets, but only responds to those specifically addressed to it.
Standard
Falcon™ tethers contain three sets of twisted pair wires for telemetry, sonar, and video
signals, in addition to the power lines.
The surface station provides an interface for the human pilot onboard the surface
vessel. A video screen displays the environment in front of the ROV. A hand controller
contains a joystick for horizontal thrust control, dials for vertical thrust and camera tilt,
along with other buttons for light intensity, manipulator control, and auto-heading and
auto-depth activation. A sonar display reveals nearby objects and houses controls for
range and refresh rate.
Typical of ROVs in its class, the Falcon™ does not have a position tracking system.
The only navigation measurements available to the pilot are the onboard compass and
depth sensor. Position estimation is made by following a sightline located with GPS
from the surface to the seafloor.
The pilot then follows a compass heading while
19
hovering close to the seafloor and visually estimates the ROV velocity to dead reckon
ROV position.
In developing the navigation suite, a DVL, an IMU, and a compass are integrated with
the Falcon™ vehicle. In addition, an acoustic transducer is attached to the vehicle. To
support this research, additional data channels were added by upgrading the tether to a
fibre-optic option and multiplexing the signals into a single fibre-optic line to send the
additional sensor measurements to the surface. A Panasonic Toughbook™ tablet PC is
added to the surface station to collect the sensor data, track the thruster commands, and
run the navigation algorithm.
1.7 Literature Review
Previous works relevant to tether management and underwater navigation are discussed
in this section. Tether management is closely related to positioning the deep end of a
submerged cable with ship and winch activity, so works of this nature are also reviewed.
Underwater position tracking and methods to improve its accuracy and update frequency
are reviewed in Subsection 1.7.2.
1.7.1 Tether Management
The influence and control of ship position and tether payout on positioning the
submerged end of a tensioned cable have been previously investigated through several
approaches. Chauvier et al. [17] developed optimization routines to schedule ship motion
and the winch payout that minimize the time taken for a towfish to pass through a
predefined set of waypoints.
Later, Williams [18] used inverse cable dynamics to
generate the ship and winch activity necessary to produce the desired towed vehicle
dynamics. However, the open-loop methods of [17] and [18] are not able to adjust for the
20
detrimental effects of unmodeled forcing such as ocean currents.
Prabhakar [15]
presented a Dahlin controller [19] that uses discrete acoustic positioning measurements to
adjust ship motion and winch activity to keep a point on a negatively buoyant ROV tether
at a desired location.
In [15], Prabhakar showed that controlling ship motion and winch activity such that the
ROV end of the tether follows the ROV trajectory can mitigate the tether disturbance.
However, the “water-pulley” effect discussed by Delmer et al. in [20] introduces delay in
off-axial motion of the tether. This delay is prolonged in neutrally buoyant tethers, such
as that of the Falcon™, to the point where positioning of the ROV end of the tether by
ship and winch motion alone is impossible.
For work class ROVs with negatively buoyant cables, one means of reducing tension at
the ROV is to induce an inverted catenary into the tether profile near the ROV.
Prabhakar [15] used simulations to position small floats along the heavy ROV cable to
create the catenary. Ship and winch activity was used to position the ship side of the
catenary a fixed distance away from a station-keeping ROV subject to a current. Similar
methods of mitigating tether disturbance on the Falcon™ and other inspection class
ROVs with neutrally buoyant tethers can be achieved with the use of a depressor mass
attached to the tether a short distance away from the ROV. This graduate research [21]
has expanded upon Prabhakar’s work in cable positioning by establishing a schedule for
desirable depressor mass positions. This schedule is employed in transit manoeuvres.
1.7.2 Underwater Position Tracking
Underwater position tracking is complicated by the attenuation of electromagnetic
waves including those used by GPS. Acoustic positioning has slow update rates and
21
exhibits significant measurement uncertainty. Typically a beacon’s position has been
trilaterated using range measurements to several reference stations based on acoustic
wave travel-time [22]. Measurement noise has also been mitigated with the use of more
sophisticated position calculations, such as using an EKF to blend the beacon position
information contained in each of the range measurements [23]. However, with just range
measurements, the EKF must assume a velocity progression in-between range
measurements, causing infrequent position updates.
Many ROV operations require more accurate position tracking, as do automatic control
and regulation schemes. Position tracking has been improved through incorporating the
measurements of additional sensors into the position estimate [24].
Velocity
measurements made by a DVL [25] or a flow meter [26] provide higher frequency
measurements, and have been integrated over time to improve the position estimate. On
work class ROVs, INS units comprised of three orthogonal accelerometers and three
orthogonal rate gyroscopes have been used [27, 28] to provide velocity and position
estimates based on integrated acceleration measurements (after removing the
gravitational bias from the accelerometers). Bias in the acceleration and angular velocity
measurements accumulates during the integration process and produces drift errors in the
INS measurements.
Drift errors in INS have been stabilized by aiding the INS
measurements with direct position and velocity measurements [29, 30, 31, 32, 26, 33,
34]. In those works, the velocity measurements are made in the body fixed coordinates,
and were rotated into an earth fixed coordinate system before integrating to complement
position measurements.
22
A KF with a kinematic model is perhaps the most commonly used complementary
filter for underwater navigation. A predominant assumption in existing KF kinematic
models [35, 36] is that the vehicle exhibits constant velocity, and this gross
approximation is used to smooth actual velocity measurements made by instruments
onboard the vehicle. The navigation system on Hydro-Quebec’s ROV [25] rotated DVL
measurements into the earth-fixed frame so that the kinematic relationship between
velocity and position was linear and a KF could be used.
Other approaches have
embedded EKFs with models that align body-fixed velocity measurements with the
navigation frame and integrate them with respect to time to augment the position estimate
[28, 30, 33, 35]. Due to nonlinearity of the rotation, employing those dynamics models
has required an EKF or other nonlinear filter.
Kinetic models have also been used to improve the KF estimate with knowledge of the
system’s dynamics.
Existing EKF implementations in [37] and [38] included the
calculation of AUV surge speed from propeller RPM to stabilize the position tracking
from a single acoustic range sensor. Also in the AUV paradigm, a kinetic model of the
HUGIN 4500 AUV was used to estimate body fixed velocities for correcting INS drift in
a KF framework [39]. The external nature of the kinetic model in this implementation
allowed the KF model to be linear, but did not produce the full error variance
minimization that would be provided by an embedded kinetic KF model.
For ROV navigation, Steinke [16] has presented the only kinetic model used to
enhance position tracking. Steinke used simulations to compare the merits of a KF and
several EKF models for tracking the position of the work class ROPOS ROV. ROPOS
uses the OCTANS INS, which has sufficient accuracy to measure the earth’s rotation,
23
resolve heading and integrate acceleration to provide low drift velocity estimates. In
[16], the performance of OCTANS eclipsed any improvements available from using a
kinetic model with DVL measurements, especially in the presence of tether disturbances
unknown to that kinetic model. However, inspection class ROVs such as the Falcon™
considered in this work are not operated with the budget or designed with the space to
install an INS, so it is anticipated that an EKF employing a kinetic model will provide
improved position tracking over the simpler kinematic KF implementation.
Infinite input response filters, such as the KF, recursively consider the entire
measurement history in their estimation strategy, and provide good smoothing
characteristics, but suffer from slow rejection of estimates with large errors. In particular,
the KF places little emphasis on an inaccurate measurement with a correspondingly large
uncertainty estimate, but an outlier measurement will taint the KF estimate for an
extended duration. The slow rejection of estimate errors has been eliminated with a
Receding Horizon adaptation of the KF in [40], but at the price of additional
computational load. Outlier rejection has also been performed by pre-processing the
measurements. The navigation suite for the Hemire ROV [28] roughly estimated the
ROV position based on a simplified hanging depressor model, and rejected measurements
outside a watch circle around that position.
The KF has also been used to estimate quantities not directly measured by a sensor.
Error state formulations [41, 26, 29, 42] of the KF have estimated sensor biases by
calculating the steady offset of sensor measurements from estimated values.
One
navigation suite [30] that has blended GPS, IMU, compass, depth, and DVL
measurements using a kinematics based EKF has also included an estimate of water layer
24
velocity to avoid errors in velocity estimation when the DVL losses bottom lock. A flow
rate sensor has also been used instead of a DVL [26]. However, the flow rate sensor
required estimation of water current to improve the AUV position dead reckoning.
1.8 Thesis Contributions
This work aims to improve the capabilities of the Falcon™ through innovative tether
management and enhanced position tracking.
Tether management schemes are
developed through numerical simulations that investigate the influence of ship position
and tether payout on the tether disturbance force. This research also expands Steinke’s
simulation based EKF navigation study [16] for a work class ROV to an inspection class
ROV and contributes experimental EKF navigation results. The technical contributions
include:
1. EKF Implementation on an inspection class ROV. The first presentation with
all of an acoustic positioning system, a DVL, and an IMU being added to the
Falcon™ ROV and identification of Falcon™ dynamics parameters.
This
thesis presents the first experimentally implemented EKF with an ROV kinetic
process model.
2. Ship and winch activity schemes to reduce tether disturbance.
In developing
tether management schemes, the influence of ship position on tether disturbance
is quantitatively derived. Schemes to actively position the ship and control the
winch are developed and compared through simulation to the conventional
operating schemes. This is the first presentation for regulating disturbance from
a neutrally buoyant tether. Operation with a depressor mass attached to the
tether is also considered.
25
3. Online tether disturbance estimation with a navigation filter. The EKF kinetic
model includes the tether disturbance, which is not measured by force sensors.
An approximate model of the temporal propagation of this disturbance is
derived, and then corrected with the dynamics mismatch observed by
navigation sensor measurements.
4. Experimental validation of EKF performance. In prior work, experimental
results have checked KF performance against GPS data [30]. In this work,
optical position measurements are used to provide a reference with much higher
accuracy and temporal resolution.
1.9 Thesis Overview
Tether management and ROV position tracking are discussed in the following chapters.
Both numerical simulation and experimental testing are employed to develop methods
and verify their performance.
Chapter 2 discusses tether management of the Falcon™ ROV’s neutrally buoyant
tether. The relative position of the ship and ROV is found to be an important influence
on the tether disturbance, as is the scope of tether between the ship and ROV. This
chapter also summarizes the tether management scheme first presented by Zand et al.
[21] which increases ROV transits speeds by using ship and winch activity to regulate
depressor position. The enhanced tether management control schemes rely on ROV
position and velocity feedback. ROV position and velocity tracking is the subject of the
remaining chapters.
Chapter 3 describes the installation of sensors on the ROV and the EKF process that
blends measurements from multiple sensors to produce accurate ROV position and
26
velocity estimates at a high update rate. It also discusses the layout of sensors on the
ROV and the communication lines which send the measurements to the surface station.
The classical KF is modified to produce an EKF embedded with an ROV dynamics
model that handles the model’s nonlinearities and asynchronous arrival of measurements.
Chapter 4 presents the identification of the constant parameters of the EKF and the
ROV model.
Measurement noise is quantified through measurements made during
shallow water tests where positions could be more accurately measured with an optical
tracking system. Thruster output, hydrodynamic drag, and added mass coefficients are
also experimentally measured using shallow water tests. Moreover, the uncertainty in the
ROV model is quantified.
Chapter 5 discusses the experimental validation of the EKF through shallow water test
measurements. Over the 1300s test, the EKF’s estimate at 10Hz has a lower Root Mean
Square (RMS) error than the stand-alone SBL measurements updated at 0.5Hz. The
DVL is shown to significantly increase the EKF position accuracy. Experimental data is
used to prove the filter could be implemented on a physical system and highly accurate
optical position measurements are used to quantify the error in the EKF position estimate.
Chapter 6 describes testing the EKF with a simulated full scale manoeuvre. Estimates
of the ROV position and velocity are compared against simulated values and found to be
reasonably accurate even though the full deepwater configuration significantly degrades
acoustic positioning accuracy.
The EKF’s estimate of tether disturbance is also
reasonable, even without providing force measurements to the EKF algorithm
Chapter 7 summarizes the main achievements and research findings and discusses
topics needing further research.
27
Chapter 2. Tether Management
The aim of tether management is to mitigate the tether’s negative impact on ROV
manoeuvrability. Conventional tether management practice for inspection class ROVs
uses observations made only at the surface to coordinate piloting of the surface ship and
tending of the tether. In this chapter, numerical simulation is used to investigate tether
management schemes that exploit knowledge of the ROV position.
Section 2.1 describes the model of the Falcon™ ROV system used in the numerical
simulation and the ROV manoeuvres simulated to demonstrate the tether management
schemes. Section 2.2 introduces the conventional tether management scheme. Section
2.3 derives optimal ship locations (relative to a known ROV location) that minimize
tether disturbance for sustained transects and maximize sustainable transit speed. The
optimal ship locations calculated in Section 2.3 form the basis for advanced tether
management schemes applied to the demonstration manoeuvres in Section 2.4. Applying
a depressor mass to the otherwise neutrally buoyant tether allows for even higher
sustainable transit speeds.
Tether management for operation with a depressor was
presented in a journal article by Zand et al. [21]. Section 2.5 summarizes the ship and
winch regulation scheme developed in that article and applies the scheme to the transit
demonstration manoeuvre.
28
2.1 Numerical Simulation of the ROV System
In this chapter, typical inspection class ROV manoeuvres are analysed using the
ProteusDS™ numerical simulation methodology described in Section 1.5.
The
simulation framework is based on parametric dynamics models that are applicable to a
wide range of submerged equipment. For this research, the ProteusDS™ underwater
vehicle and cable models are tailored to reflect the dynamics of the Falcon™ ROV
through identification of the vehicle and cable dynamics parameters. The following
subsections discuss the simulation of the tether and vehicle components of the ROV
system and the manoeuvres selected to demonstrate the tether management schemes.
2.1.1 Tether Simulation
The simulation uses a lumped mass finite element tether model [14]. The model
includes axial, torsional and bending stiffness particularly prevalent in the slack tethers
often encountered during ROV deployments. Payout and retrieval of the tether during a
manoeuvre is simulated with use of a variable length tether element at the connection to
the surface vessel [15]. The surface end of the tether is kinematically controlled to mimic
the ship activity prescribed for the selected tether management scheme.
The tether length, diameter, and density were directly measured. The estimated normal
drag coefficient was also used by [43], [14] and [44], and is based on the measured
steady-state inclination angles achieved by a towed a cable at several towing speeds
during ocean scale tests [45]. The tether stiffness coefficients were measured with forcedeflection tests. The raw measurements are listed in Appendix B, and the resulting
mechanical properties are listed in Table 2-1.
29
Parameter
Symbol
Value
Density
ρc
1025 kg/m3
Diameter
dc
0.014 m
Normal drag coefficient
CD
1.65
Axial stiffness
EA
4.3 x 104 N
Torsional stiffness
GJ
0.4 Nm2
Bending stiffness
EI
0.5 Nm2
Length
LTot
350 m
Table 2-1. Falcon™ Tether Properties.
2.1.2 ROV Simulation
The ROV is modeled as a six DOF rigid body acted upon by tether disturbance,
hydrodynamic drag, buoyancy, and thruster propulsion [16]. The force and moments
generated at the attachment point of the tether on the ROV are calculated and applied to
the two objects. Hydrodynamic drag force is modeled as a quadratic function of velocity.
The Falcon™ ROV is trimmed for neutral buoyancy, so the simulated buoyancy forcing
is equal to the weight of the ROV. Propulsive forces of the four horizontal thrusters and
the single vertical thruster on the Falcon™ are modeled as equivalent point loads on the
rigid body.
The experimental parameter identification for the Falcon™ ROV was conducted in a
shallow water test facility as discussed in Section 4.3. The measured surge and heave
thrust saturation limits were 401N and 124N respectively. The identified hydrodynamic
drag coefficients are listed in Table 4-11 and the ROV inertias with added mass are listed
in Table 4-12.
30
2.1.3 Demonstration Manoeuvres
Two manoeuvres are considered for evaluating the tether management methodologies.
Both manoeuvres start with the ROV 200m directly below the ship with a 20N tension in
the tether. The ROV waits at the starting position for 10s before traveling to the next
waypoint 600m ahead while maintaining the 200m depth. One manoeuvre is a transect.
Transects are performed at low speed (0.2m/s) to provide the ROV pilot sufficient time to
identify and assess the surrounding environment. The other manoeuvre is a transit, where
the ROV is driven to reach the final waypoint as quickly as possible.
An ROV controller embedded in the ProteusDS™ simulation software schedules the
thruster activity that produces the desired ROV manoeuvre. To simulate the transect
manoeuvre, the ROV controller uses Proportional-Integral-Derivative (PID) control to set
surge thrusts that make the ROV surge speed approach the desired 0.2m/s transect speed
until the ROV reaches the destination. To simulate the transit manoeuvre, the ROV
controller attempts to apply maximum surge thrust within the constraints of maintaining
correct ROV depth and heading.
2.2 Analysis of the Conventional Tether Tending Method
Typically the tether is tended to maintain a low tension at the surface. It is released
when the tension measured at the surface rises and it is retrieved when tension decreases.
For low currents and short manoeuvres, this methodology produces a mild tether pull on
the ROV, allowing high manoeuvrability without dragging the tether along the seafloor.
Piloting the surface vessel to stay near the ROV prolongs the occurrence of the entire
tether being deployed during long transits. Once the entire tether is deployed, the low
tension state at the surface can no longer be maintained, and the tether disturbance on the
31
ROV rises quickly. Conventional operations do not track the ROV position, so the ship
pilot’s best indicator of ROV position is the direction which the tether is leaving the
vessel. Conventional operating practice is to drive the ship in the direction of the tether
tangent, such that the near surface portion of the tether is vertical.
In the simulation studies of conventional tether management, the winch is used to
maintain a constant low (20N) tension.
The ship is driven only to maintain a near
vertical orientation of the tether near the surface. This currently accepted practice does
not rely on ROV position tracking, but as shown in the following subsections, produces
large tether disturbances during long manoeuvres.
2.2.1 Conventional Tether Management during Transect Manoeuvres
A transect manoeuvre where the ROV waits at the starting position for 10s and then
proceeds to the next waypoint 600m ahead at 0.2m/s is simulated in this subsection. The
tether profiles, deployed tether scope, and tether disturbance occurring during the
manoeuvre are shown in Figure 2-1.
32
Depth (m)
0
50
10s 800s
100
1600s
2539s
3014s
4000s
150
200
0
100
Ship
a) Tether Profiles-
200
300
Position (m)
Tether
400
500
ROV
600
ROV Path
Tether Scope (m)
350
300
250
200
0
500
1000
1500
2000
Time (s)
2500
3000
3500
4000
500
1000
1500
2000
Time (s)
2500
3000
3500
4000
Tether Disturbance (N)
b) Tether Scope
60
40
20
0
0
c) Tether Disturbance
Figure 2-1. Conventional Transect. The tether tension at the surface is regulated at 20N
and the ship drives in the direction the tether is entering the water. 10s: The ROV starts
from rest. 2539s: The tether length limit is reached. 3014s: The ROV stops at the waypoint.
4000s: The ship approaches overhead of the ROV and tether is retrieved.
Without disturbance, the ROV should reach the waypoint 3010s into the manoeuvre.
However, the ROV leads the ship by such a distance that all 350m of the tether gets
deployed 2539s into the manoeuvre, at which point the low tension state at the ship
33
cannot be maintained and the tether tension rises throughout the system. The tether
disturbance increases to 43N, making it difficult for the pilot to keep a steady course.
2.2.2 Conventional Tether Management during Transit Manoeuvres
A manoeuvre where the ROV waits at the starting position for 10s before proceeding to
the next waypoint 600m ahead is again simulated, but this time the pilot is requested to
transit the ROV as fast as possible. Figure 2-2(a) shows the ROV, ship and tether
motions that occur following the conventional tether management methodology. As the
ROV surges forward, the tether is paid out as shown in Figure 2-2(b). Initially the tether
tends to trail the ROV, but at 191s the tether length limit is reached and the ROV begins
to draw the tether straight. At this point, tension regulation is impossible and the
disturbance on the ROV rises dramatically as shown in Figure 2-2(c). The increased
tether disturbance slows down the ROV. At 694s, the ROV is pulled off depth because
the vertical thruster is saturated and the ROV controller reduces forward thrust to
maintain depth. At the end of the manoeuvre, the ship approaches the ROV and retrieves
the excess tether.
34
Depth (m)
0
50
400s
10s
100
694s
961s
1200s
191s
150
200
0
100
200
Ship
a) Tether Profiles -
300
Position (m)
400
Tether
ROV
500
600
ROV Path
Tether Scope (m)
400
300
200
100
0
200
400
600
Time (s)
800
1000
1200
200
400
600
Time (s)
800
1000
1200
Tether Disturbance (N)
b) Tether Scope
400
300
200
100
0
0
c) Tether Disturbance
Figure 2-2. Conventional Transit. The tether tension at the surface is regulated at 20N and
the ship drives in the direction the tether is entering the water. 10s: The ROV starts from
rest. 191s: The tether length limit is reached. 694s: The ROV vertical thruster is saturated;
surge thrust is reduced to maintain depth. 961s: The ROV stops at the waypoint. 1200s:
The ship approaches overhead of the ROV and tether is retrieved.
35
2.3 Analysis of the Tether Disturbance
In this section, investigative simulations and empirical models are utilized to develop
more advanced tether management schemes with reduced tether disturbance.
Ship
position and tether scope are the two control variables that can be optimized to reduce
tether disturbance.
So long as the ship to ROV distance is less than the deployed tether scope,
hydrodynamic drag on the tether is the primary cause of tether disturbance. The tether is
streamlined along its tangent, so normal drag which results from motion of the tether
relative to the surrounding water normal to the tether tangent is often the only significant
forcing.
Deploying tether into the water to lengthen the scope reduces the tether
disturbance caused by normal drag, but increases the likelihood of snagging the tether on
the seafloor and reduces responsiveness to ROV direction changes. Also, control activity
must comply with limits on ship response and tether length.
2.3.1 Tether Disturbance during Transect Manoeuvres
In this subsection, the ship position which minimizes tether disturbance during transect
manoeuvres is sought by simulating the tether disturbance produced over the range of
possible distances by which the ship could lead the ROV. The full 350m tether length is
used since shorter tethers were found to produce more disturbances through increased
tether tension. The configurations in which the ship leads or lags the ROV by more than
287m correspond to a ship to ROV slant ranges exceeding 350m, and would pull the
tether tight and create immense tether disturbance.
The tether disturbances for the
feasible range of ship leads are mapped in Figure 2-3 and show that steady-state transects
36
of 0.2m/s can be maintained with a tether disturbance smaller than 10% of the ROV
thrust capacity.
50
10% Surge Thrust Capacity
Tether Disturbance (N)
40
Minimum of 25N at 26m
30
20
Aftward Pull
Heave Pull
Total Pull
10% Heave Thrust Capacity
10
0
-10
-300
-200
-100
0
Ship Lead (m)
100
200
300
Figure 2-3. Tether Disturbance Mapped over Ship Lead for a 0.2m/s Transect.
As shown in Figure 2-3, the aftward pull due to tether disturbance decreases with
increasing ship lead. However, the vertical pull due to tether disturbance increases with
increasing ship lead.
The magnitude of the tether disturbance can be minimized to less than 25N if the ship
leads the ROV by 26m. The next subsection extends this result to high speed transits.
2.3.2 Tether Disturbance during Transit Manoeuvres
The optimal ship lead derived in the previous subsection for transects can be extended
to high speed transits. Apart from a small amount of axial stretch, steady-state tether
profiles remain the same, regardless of transit speed. However, hydrodynamic drag
increases quadratically with transit speed. The tether disturbance for a 1m/s transit speed
(five times faster than the transect) is nearly twenty-five times greater than that of a
37
transect. Figure 2-4 shows the steady-state tether disturbance as a function of ship
position for a 1m/s transit.
1250
Aftward Pull
Heave Pull
Tether Disturbance (N)
1000
750
500
250
Heave Thrust Limit
0
-250
-300
Surge Thrust Limit
-200
-100
0
Ship Lead (m)
100
200
300
Figure 2-4. Tether Disturbance Mapped over Ship Lead for a 1 m/s Transit. Notice the
shape similarity and change of tether disturbance scale compared to Figure 2-3.
Since no ship configuration produces a tether disturbance with heave and surge
components both less than the Falcon™ ROV’s corresponding thrust capacities, 1m/s
transits with the Falcon™ ROV’s neutrally buoyant tether cannot be continuously
sustained. Also, vehicle hydrodynamic drag increases with transit speed, so the thrust
capacity that can be allocated to overcome tether disturbance is reduced in the surge
direction. Table 2-2 lists the tether and the hydrodynamic drag forces imparted on the
ROV during a transect and several transit speeds.
38
Steady-state Speed
0.2 m/s
1.0 m/s
0.8 m/s
0.67 m/s
Tether Heave
8N
188 N
120 N
84 N
Tether Surge
23 N
568 N
364 N
255 N
ROV Surge Drag
25 N
273 N
189 N
142 N
Total Surge Force
48 N
841 N
553 N
397 N
Table 2-2. Tether and Hydrodynamic Drag Forces Imparted on the ROV. Several steadystate surge speeds are considered with the ship leading the ROV by 26m and 350m of tether
deployed. Tether disturbances at 0.2m/s and 1.0m/s surge speeds were measured with
numerical simulation. Tether disturbances at 0.8m/s and 0.67m/s speeds were scaled based
on the 1m/s tether disturbance.
At 0.67m/s, the total surge force matches the thrust
capacity, but the heave force is not at the thruster’s 124N saturation limit.
The total surge force sustaining a 0.67m/s transit matches the surge thrust capacity, but
the heave force is not at the heave thruster’s 124N saturation limit. A small gain in the
steady-state transit speed can be achieved by increasing the ship’s lead on the ROV,
thereby shifting tether disturbance in the surge direction to the heave direction where
spare thrust capacity is available.
By increasing the ship’s lead to 90m, the heave thruster is nearly saturated by the tether
disturbance while the tether disturbance force in the surge direction is further reduced by
2%. This reduction in surge tether disturbance allows for a slightly faster steady transit
speed. However, this speed increase is quite small, so all ship leads from 26m to 90m
allow for nearly maximum steady-state transit speeds.
2.4 Advanced Tether Management
In this section, the optimal distances for the ship to lead the ROV derived in the
previous section are applied to the demonstration manoeuvres introduced in Subsection
2.1.3. The conventional method of maintaining low tension in the tether as measured at
the surface is retained.
39
2.4.1 Advanced Tether Management for Transect Manoeuvres
For the transect manoeuvre, the ship lead is selected to minimize the tether disturbance
at the steady-state surge speed. As per Subsection 2.3.1, this ship lead is 26m for
transects at 200m depth. For ROV surge speeds other than 0.2m/s, the optimal ship lead
is still 26m, but the steady-state tether disturbance will differ from the 25N predicted for
transects due to the change in magnitude of hydrodynamic forcing on the tether.
The advanced tether management scheme is demonstrated with the transect manoeuvre
simulated over 4000s duration, and the ROV controller is given the same instructions as
in the manoeuvre demonstrating conventional tether management. The ROV position is
assumed to be known, and the ship leads the ROV by 26m. The resulting time evolution
of the tether profile, tether scope, and tether disturbance are presented in Figure 2-5. This
transect does not cause the entire tether to be deployed and the tether disturbance is low
throughout the manoeuvre.
40
Depth (m)
0
50
1000s
10s
100
2000s
3010s
4000s
150
200
0
100
Ship
a) Tether profiles -
200
300
Position (m)
400
Tether
ROV
500
600
ROV Path
Tether Scope (m)
350
300
250
200
0
500
1000
1500
2000
Time (s)
2500
3000
3500
4000
Tether Disturbance (N)
b) Tether scope with advanced (solid) and conventional (dotted) tether management
60
40
20
0
0
500
1000
1500
2000
Time (s)
2500
3000
3500
4000
c) Tether disturbance with advanced (solid) and conventional (dotted) tether management
Figure 2-5. Transect with Advanced Tether Management. The tether tension at the surface
is regulated at 20N and the ship leads the ROV by 26m. 10s: The ROV starts from rest.
3010s: The ROV stops at the waypoint. 4000s: The ship approaches overhead of the ROV
position and tether is retrieved.
41
2.4.2 Advanced Tether Management for Transit Manoeuvres
For the transit manoeuvre, the ship is set to lead the ROV by 90m in an attempt to
maximize surge speed. This ship lead was derived in Subsection 2.3.2 to distribute the
tether disturbance in proportions that use the full thrust capacity of both the surge and
sway thrusters at the maximum sustainable transit speed. Figure 2-6 shows the resulting
time evolution of the tether profile, the tether scope, and the tether disturbance.
A transit with this advanced tether management scheme causes all 350m of tether to be
deployed sooner than the conventional method because the ship starts the manoeuvre by
driving ahead of the ROV. However, this configuration reduces the sustained tether
disturbance to less than 280N, allowing the ROV to reach its destination in only 728s 233s faster than when using the conventional tether management method.
42
Depth (m)
0
10s
50
55s
400s
100
728s
1200s
150
200
0
100
Ship
a) Tether profiles Tether Scope (m)
200
300
400
Position (m)
Tether
500
ROV
600
700
ROV Path
300
200
100
0
200
400
600
Time (s)
800
1000
1200
Tether Disturbance (N)
b) Tether scope with advanced (solid) and conventional (dotted) tether management
600
400
200
0
-200
0
200
400
600
Time (s)
800
1000
1200
c) Tether disturbance with advanced (solid) and conventional (dotted) tether management
Figure 2-6. Transit with Advanced Tether Management. The tether tension at the surface is
regulated at 20N and the ship leads the ROV by 90m. 10s: The ROV starts from rest. 55s:
The tether length limit is reached 728s: The ROV stops at the waypoint. 1200s: The ship
approaches overhead the ROV and tether is retrieved.
2.5 Depressor Effects
Further tether disturbance reductions and corresponding transit speed increases can be
achieved with the use of a depressor mass. Adding a clump weight depressor to the
tether a short distance away from the ROV ensures that the tether hangs almost vertically
43
from the ship, and allows ship motion to be used to position the depressor near the ROV.
If the depressor is positioned correctly, the ROV is subjected only to the tether
disturbance created by the hydrodynamic drag on the tether between the depressor and
ROV. A tether management scheme was developed and presented by Zand et al. in [21]
for Falcon™ manoeuvres with a depressor mass attached to the otherwise neutrally
buoyant tether. The governing equations of this tether management scheme are presented
in Subsection 2.5.1. Subsection 2.5.2 presents the application of the depressor tether
management scheme to the transit demonstration manoeuvre defined in Subsection 2.1.3.
2.5.1 Depressor Tether Management
A depressor with the properties listed in Table 2-3 is added to the Falcon™ ROV’s
otherwise neutrally buoyant tether. The depressor is attached to the tether with 50m
scope to the ROV. This amount of scope was found [21] to remain slack even during
sudden ROV stopping manoeuvres.
Parameter
Value
Diameter
0.40 m
Mass
260 kg
Added Mass
17 kg
Scope to ROV
50 m
Table 2-3. Depressor Properties
Ship motion is scheduled to regulate the depressor’s horizontal offset from the ROV,
denoted +x . Winch actuation regulates the depressor’s vertical offset from the ROV,
denoted +z . In [21], desired offsets are calculated which mitigate tether disturbance on
the ROV during transits and ensure the depressor does not collide with the ROV during
operation. The shortest distances in which the depressor could be stopped using ship
44
motion were derived as a function of transit speed, u. In order to allow depressor
overshoot to occur without tightening the tether leading to the ROV, the desired
depressor horizontal offset was selected to be half of these stopping distances:
+x∗ = -14.5 u u - 2.25u
(2.1)
The superscript ( ⋅) denotes desired value. To avoid collision of the depressor with the
∗
ROV, the depressor depth was set as high as possible while allocating only 1% of heave
thrust capacity to offset the vertical tether disturbance. The desired depressor depth
offset is a function of the depressor’s horizontal offset:
3
2
+Z∗ = 0.0002 +X − 0.029 +X + 1.65 +X − 31
(2.2)
The water pulley effect [20] limits the horizontal acceleration of the depressor
achievable through ship motion. Since abrupt changes to depressor position are not
possible with ship and winch activity, the desired depressor offsets are low pass filtered
according to:
+ X∗ +100 ⋅+ X* =+X*
+ Z* +10 ⋅+ Z* =+Z*
(2.3)
The overhead tilde ( ⋅ ) indicates a smoothed quantity and the overhead dot indicates a
partial differential with respect to time. The time constants of the filters in Equation (2.3)
were optimized through iterative simulation of the depressor system’s response to control
inputs.
Depressor depth is achieved by setting the winch payout rate, s , as the sum of the error
in depressor depth and the rate of increase of depressor vertical offset:
s = ( + z* −+z ) + ( w − wDPR )
(2.4)
45
In Equation (2.4), w denotes the ROV heave velocity and wDPR denotes the depressor
heave velocity.
Depressor horizontal positioning is achieved by determining a desired ship speed and
enacting that ship speed with ship propulsion.
The desired ship speed is a linear
combination of ROV speed, the depressor horizontal position error, and the rate of
increase of depressor horizontal offset:
uS = u + 0.05 ( + *X −+
X
) + 4.0 ( u − u )
DPR
(2.5)
The constant coefficients in Equation (2.5) were selected through iterative simulation
to optimize depressor positioning response. Equations (2.1) through (2.5) govern the
depressor tether management scheme presented by Zand et al. in [21].
2.5.2 Demonstration Manoeuvre with Depressor Tether Management
The depressor tether management scheme [21] was applied to the transit demonstration
manoeuvre. Figure 2-7(a) shows the tether profiles at key times in the manoeuvre.
During the first 10s of the manoeuvre, the ROV is stationary, and the ship hangs the
depressor 31m above the ROV. As the ROV starts the transit and increases its velocity,
the ship leads by over 150m to accelerate the depressor. Meanwhile, the winch releases
tether to drop the depressor towards the ROV depth to streamline the tether between the
depressor and the ROV. The ROV reaches the destination waypoint at 542s and the
system settles to the stationary equilibrium position. Figure 2-7(b) compares the tether
scope deployed using the depressor tether management scheme to the tether scope
deployed using the tether management schemes with neutrally buoyant tethers. The
depressor tether management scheme uses less tether scope and does not reach the tether
length limit. Figure 2-7(c) shows the tether disturbance generated using the depressor
46
tether management scheme is significantly less than the tether disturbances generated by
the tether management schemes with neutrally buoyant tethers.
47
Depth (m)
0
10s
50
300s
84s
524s
750s
100
580s
150
200
0
100
200
300
400
Position (m)
500
600
700
a) Tether profiles
Ship
Tether
Depressor
ROV
ROV Path
Depressor Path
Tether Scope (m)
400
300
200
100
0
200
400
600
Time (s)
800
1000
1200
Tether Disturbance (N)
b) Tether scope with advanced (solid), conventional (dotted) and depressor (dashed) tether
management
600
400
200
0
-200
0
200
400
600
Time (s)
800
1000
1200
c) Tether disturbance with advanced (solid), conventional (dotted), and depressor (dashed)
tether management
Figure 2-7. Transit with Depressor. Ship and winch activity was regulated according to the
depressor tether management scheme summarized in Subsection 2.5.1. The demonstration
manoeuvre proceeds as follows: 10s: The ROV starts from rest; the ship surges ahead,
deploying tether in its wake. 84s: Depressor speed reaches ROV speed and tether retrieval
begins. 524s: The ROV stops at the waypoint. 580s: The depressor comes to a stop. 750s:
The system regains stationary equilibrium.
48
The tether disturbance reduction realized with the depressor tether management scheme
allows the ROV to sustain a transit speed in excess of 1m/s.
2.6 Tether Management Remarks
Excessive tether disturbance often limits the ROV manoeuvre speed or length. The
tether disturbance can be reduced by releasing more tether from the ship, but tether
disturbance increases quickly when the entire length of tether is deployed. Transects with
low tether disturbance and transits at moderate speeds can be achieved by having the ship
lead the ROV by prescribed amounts. The ROV surge speeds for long transits can be
further increased with the use of a depressor.
Tether position regulation schemes based on ship and winch activity have been
introduced for small inspection class ROVs. Slow response of the tether in the normal
direction requires the ship commands to react quickly in order to keep up with ROV
course changes. The advanced tether management schemes and the depressor tether
management scheme require tracking the ROV position.
The depressor tether
management scheme also requires tracking the ROV velocity. The accomplishment of
this requirement is discussed in the following chapters, which present the implementation
and testing of a position and velocity tracking system.
49
Chapter 3. Navigation Estimation
Towards the implementation of advanced tether management schemes, efficient
seafloor surveys, and successful object recoveries discussed in previous chapters, the
position and velocity of the ROV must be accurately tracked at a high update rate. As
discussed in Section 1.3 all position, velocity and inertial motion sensors used on
underwater vehicles have performance limitations. Acoustic positioning has high
measurement noise and slow update rates; ROV positions dead reckoned from DVL
body-fixed
velocity
measurements
accumulate
bias
and
truncation
errors.
Complementary filtering of the ROV position, velocity, attitude, and rotation rate
measurements provided by an SBL acoustic positioning system, a DVL, a compass, and
an IMU respectively, is anticipated to estimate the position of the ROV with the long
term stability of acoustic positioning at the high update rate of dead reckoning.
This chapter describes the sensor suite, filtering algorithm, and dynamics model used in
the ROV tracking solution. The sensor setup on the Falcon™ and the collection of
measurement are described in Section 3.1.
The principles of Kalman filtering are
presented in Section 3.2, and are modified in Section 3.3 to produce an EKF which
accounts for nonlinear ROV dynamics and asynchronous measurements.
The ROV
dynamics used to propagate the EKF estimate through time are introduced in Section 3.4.
50
3.1 Sensor Installation
ROV kinematic measurements are collected and processed to accomplish the objectives
of this work. An SBL, a compass, a DVL, and an IMU are used in conjunction with the
Falcon™ ROV’s onboard compass and depth sensor.
Instrumenting the Falcon™
requires enclosing the sensors in waterproof containers and routing the data stream to the
surface computer. The compass and depth measurements standard for Seaeye vehicles
are collected by monitoring the Falcon™ ROV’s existing telemetry network, as described
in detail in Subsection 3.1.3. The ROV mounted acoustic transducer, which is part of the
SBL system, is self contained, battery powered, and communicates acoustically with the
reference transducers at the surface. A waterproof housing was designed and built for the
DVL and IMU. A Sparton™ compass manufactured by Sparton Corp. was also installed
in the housing. Communication between these sensors and the surface computer is
accomplished using additional digital communication channels available through a fibreoptic tether purchased for the project.
3.1.1 Subsea Sensor Pod
The subsea sensor pod shown in Figure 3-1 was designed for ease of machining. It
consists of an aluminium casing with two end caps. The bottom cap is bored to hold the
DVL transducer head. The aluminum housing is anodized to prevent corrosion. The
caps are held together with two stainless steel threaded rods which also guard the DVL
transducer. When submerged, water pressure helps to hold the assembled pod together.
A single radial o-ring seals each cap-casing interface.
51
#
1
2
3
4
5
6
7
8
9
10
11
Description
Top Cap
IMU
Circuit Board Standoffs
Circuit Board – Base for Sparton Compass
and Voltage Converters
Aluminum Casing
Exterior Stainless Steel Rods
DVL Electronics
DVL Electronics Standoffs
Bottom Cap
DVL Transducer Head
DVL Guard
(a) Assembly Drawing of the Sensor Pod
(b) Rear View
(c) Plan View
Figure 3-1. Sensor Pod. The sensor pod contains the Explorer™ DVL, Sparton™ compass,
and MMQ50™ IMU. Also shown is the SBL target transducer on the port rear corner.
52
During deployment, the pod’s impact on ROV buoyancy is reduced by ballasting the
pod for neutral buoyancy. With the DVL, compass, and IMU installed, the pod exhibits
slightly positive buoyancy. A 600g lead block attached to one of the stainless steel rods
makes the pod neutrally buoyant in fresh water. An additional 230g lead block is
attached to one of the stainless steel rods for saltwater operation. As more sensors are
added to the pod, the ballasting weights can be reduced to preserve neutral buoyancy.
Radial o-rings were selected for ease of assembly. Radial o-rings are easier to install
than face o-rings, as they do not fall out of their groove when disassembled. A vent plug
was installed, but found to be unnecessary due to the open (compressible) volume in the
pod being much larger than the volume displaced during cap installation.
A Subconn underwater cable with twelve wires penetrates the top cap and links with a
wet-mateable connector on the Falcon™ junction box. Two wires supply the sensor pod
with 48V DC power, and nine others connect the three RS232 channels to the fibre-optic
multiplexer in the ROV junction box. Two DC to DC voltage converters supply the
+12V and –12V power requirements of the DVL, IMU, and Sparton™ Compass.
3.1.2 Instrument Placement
The standard Falcon™ instruments are located within the ROV’s open frame. A
cowling mounted above the syntactic foam protects the onboard cables and instruments.
The imaging sonar transducer protrudes through the top of the cowling to provide a clear
path for the sonar signals, whereas the rest of the unit is protected within the cowling.
The water column below the top-center mounted vertical thruster is kept clear to avoid
hindering the thruster wash.
Protecting instrumentation from exterior impacts and
53
maintaining sleekness to avoid subsea entanglement are major design considerations for
selecting locations for additional instrumentation.
Another important consideration during instrument placement is the function of the
instrument. The compass needs to be placed far away from transient magnetic field
sources, such as the electric thrusters. The DVL transducers require a clear view of the
seafloor.
The SBL target transducer must have unobstructed paths to the surface
mounted reference stations.
Instrument placement is important for the dynamics model as well.
The ROV
coordinates (shown in Figure 3-2) were defined with an origin at the vehicle’s center of
mass and the x, y, and z coordinates representing surge, sway, and heave directions
respectively. Offsetting the SBL and DVL from the origin of the ROV coordinate frame
leads to differences between the sensor measurements and the corresponding state
measurements at the ROV mass centre. Since the DVL cannot be placed at the origin of
the ROV coordinate frame, the ROV rotation rates must be tracked and combined with
the DVL measurements to calculate the ROV velocity. The tether’s attachment point to
the ROV dictates where the disturbance force is applied. Since this point is not at the
origin of the ROV, a torque is induced by the tether disturbance. Table 3-1 lists the
positions of the important instruments in ROV coordinates.
54
Navigation Pod
Sensor Pod
y
Junction
Box
x
Target Transducer
a) Falcon™ Top View
y
z
b) Falcon™ Side View
Figure 3-2. Falcon™ Instrument Layout. The ROV coordinate frame’s origin is located at
the mass centre, just below the vertical thruster. The SBL target transducer and the sensor
pod containing a DVL, a compass, and an IMU are fastened to the rear corners of the
vehicle. The navigation pod containing a compass, a depth sensor, and a gyroscope is
located under the vehicle cowling (removed) to starboard of the vertical thruster.
55
Instrument
Parameter
Value (m)
xDVL
yDVL
z DVL
-0.59m
0.30m
0.35m
SBL Target
Transducer
xTARGET
yTARGET
zTARGET
-0.45m
-0.34m
-0.15m
Tether
Shackle
xSHACKLE
ySHACKLE
zSHACKLE
0.14m
0.00m
-0.22m
xIMU
yIMU
z IMU
-0.58m
0.30m
-0.17m
Sparton™
Compass
xSPARTON
ySPARTON
zSPARTON
-0.59m
0.30m
-0.07m
Seaeye
Navigation
Pod
xNAVPOD
yNAVPOD
z NAVPOD
0.00m
0.18m
-0.16m
DVL
IMU
Table 3-1. Instrument Locations. The values are measured in ROV coordinates.
3.1.3 Sensor Telemetry
Measurements are transmitted from the instruments onboard the ROV to the navigation
laptop through three paths: (1) the standard Falcon™ sensors in the navigation pod send
their measurements through the tether using the Falcon™ ROV’s telemetry channel; (2)
the instruments in the sensor pod have dedicated RS232 channels also sent through the
tether; (3) the SBL acoustic position tracking system is independent of the Falcon™
hardware and sends data through the water using acoustic communication.
Each
measurement stream is collected by its respective monitoring thread within the Kalman
software. These monitoring threads parse the data into measurements, apply scaling and
alignment, and add each measurement to the measurement buffer for subsequent
56
processing by the EKF algorithm. Figure 3-3 shows a schematic of the measurement
collection process.
Kalman Software
Measurement Buffer
SBL
Monitor
Falcon
Monitor
DVL
Monitor
Compass
Monitor
SBL Software
Divebase
IMU
Monitor
Systron Donner
Active X
Navigation Laptop
SBL Surface
Hardware
Fibre-optic
Surface Multiplexer
Above Surface
Below Surface
SBL Ref
Stations
DVL
SBL Target
Transducer
IMU
Falcon Depth
Fibre-optic
Subsea
Multiplexer
Falcon Thrusters
Sparton
Compass
Sensor Pod
Falcon Compass
Junction Box
Falcon ROV
Figure 3-3. The Sensor Data Flow used by the EKF. The Falcon™ sensor and thruster
commands are read into the navigation laptop through the RS485 telemetry network sent
through the tether. The sensor pod instruments are linked to the navigation laptop through
the tether on individual RS232 channels. The SBL target transducer communicates with
the SBL reference stations with in-water acoustic signals, and its signal is processed by the
SBL equipment before being presented to the navigation laptop. The Kalman software
processes the signals and stores them in a measurement buffer.
57
The standard Falcon™ sensors, specifically the compass and depth sensor, are located
in the Seaeye navigation pod mounted beneath the top cowling, on the starboard side of
the vehicle (see Figure 3-2(a)). Each sensor connects to the Falcon™ telemetry via its
dedicated RS485 node within the navigation pod. The RS485 network connects through
the Falcon™ junction box, where it is distributed to the onboard actuators including
thrusters, lights, manipulator, and others. This network is also connected to the surface
hardware by multiplexing it along with a second RS485 channel used for the sonar, four
RS232 channels used with the instruments in the sensor pod, and the video channels. The
multiplexed channels are sent up the tether through a fibre-optic line and separated into
their original channels inside the Seaeye cabin junction box. The Falcon™ telemetry,
back in its RS485 form, connects to the master node within the surface station. This node
sends, requests, and receives data based on the ROV pilot’s control inputs. Within the
cabin junction box, the Falcon™ RS485 telemetry is yoked and the second line is
converted to a RS232 channel with only the receive line, allowing the Falcon™ telemetry
to be read but not changed. This channel is connected to the navigation laptop, where it
is read with the Falcon™ Monitor.
The Falcon™ Monitor is a thread within the
navigation software which reads every character of the Falcon™ telemetry, parses the
compass and depth measurements, converts the thruster commands into thruster forces,
and discards the rest. The measurements and thruster commands are time-stamped and
stored in the measurement buffer.
The sensor pod instruments, namely the Sparton™ compass, MMQ50™ IMU, and
Explorer™ DVL, output measurements on individual RS232 channels. These signals are
58
transmitted to the Falcon™ junction box through a twelve wire Subconn® cable with a
wet-mateable connector. The channels are multiplexed along side the Falcon™ RS485
telemetry within the junction box, are transmitted through the tether via a fibre-optic line,
and then are demultiplexed at the surface.
Once back into their individual RS232
channels, the three sensor channels are connected to the navigation laptop. Each sensor
channel is monitored by a dedicated thread within the Kalman software. The Compass
Monitor removes measurement bias caused by misalignment between the Sparton™
compass coordinates and the ROV coordinates and provides a final heading result
between 0deg and 360deg. The DVL Monitor aligns the velocity measurements to the
ROV coordinates, removes bad measurements caused by loss of bottom lock, and
converts the measurement units to m/s. Systron Donner’s ActiveX controller converts
raw MMQ50™ IMU data to calibrated measurements in m/s2 and deg/s and provides
them to the IMU Monitor. The IMU Monitor aligns the gyroscope measurements to the
ROV axes, and submits the corrected spatial rotational velocity to the measurement
buffer. The IMU’s acceleration measurements are not used.
Acoustic position tracking is done using Desert Star System’s PILOTTM SBL system.
This system operates independently of the Falcon™ ROV equipment and bypasses the
tether by using acoustic communications between the target transducer on the ROV and
the reference stations. The range between the target transducer and each reference station
is measured by tracking the time it takes an acoustic signal to travel between the two
transducers. The measurement process starts with a reference station transmitting an
acoustic pulse into the water. When this signal is received by the target transducer, the
target transducer replies with a similarly identifiable signal, and also includes a signal
59
indicating the depth of the target transducer measured by a pressure sensor.
The
reference stations not only transmit the interrogation signal, but also listen for replies
from the target transducer. The PILOTTM SBL’s STM-10™ surface station analyzes the
acoustic signals, already converted to a voltage by each reference transducer.
The
surface station connects to the navigation laptop with a serial connection and interfaces
with Desert Star System’s Divebase™ acoustic positioning software. The reference
station locations are entered into Divebase™ and used to calculate the target transducer’s
position.
Divebase™ exports the range measurements and if available, a position
measurement, to a communications socket.
This socket is monitored by the SBL
Monitor, which ensures that the range measurements are valid and enters them in the
measurement buffer along with a time-stamp and the location of the associated reference
station.
The measurement buffer stores the measurements until the filtering algorithm uses
them. All measurements in the buffer are time-stamped and indexed according to the
instrument they were made by.
3.2 Kalman Filter Fundamentals
Kalman Filters [12] are widely used complementary filters that draw on a process
model and assistive sensor measurements to propagate a system state estimate through
time. At each time-step, tk, the vector of sensor measurements, zk, and the predicted state
estimate, xˆk− , are combined through weights called the Kalman gains. These gains are
based on the relative estimated uncertainties of the state estimate and of the
measurements. The Kalman gains minimize the variance of the error of the state estimate
subject to the following constraints [46]:
60
•
Linear process model dynamics:
xk = Φ ⋅ xk −1 + wk
•
(3.1)
Gaussian process model errors, w, with zero-mean and variance Q:
Qk = E[ wk wkT ]
•
(3.2)
Gaussian measurement errors, v, with zero-mean and variance R:
zk = H ⋅ xk + vk
(3.3)
Rk = E[vk vkT ]
•
Measurement error independent of process error:
E[ wk vkT ] = 0
(3.4)
The notation used in the KF is as follows: x is the KF state, Φ is the KF process state
transition matrix, w is the KF process error, Q is the KF process error covariance matrix,
z is the KF measurement vector, H is the KF measurement matrix, v is the measurement
error, R is the measurement error covariance matrix, a k subscript represents the value at
the time tk, an overhead hat (^) represents an estimated value, the superscript
( ⋅)
T
represents transpose, and the superscripts ( ⋅) and ( ⋅) represent the value before and
−
+
after the state estimate is corrected with measurements, respectively.
During each time-step tk of the discrete KF, an initial state estimate is calculated by
applying the state transition matrix, Φ , to the optimal estimate of the state made at the
previous time-step:
xˆk− = Φ ⋅ xˆk+−1
(3.5)
61
The state estimate error covariance matrix, denoted Pˆk− , is calculated by manipulating
the error covariance estimate at the previous time-step, Pˆk+−1 , to account for state changes
and by adding the process uncertainty to the result:
Pˆk− = ΦPˆk+−1ΦT + Qk
(3.6)
The measurements received at the current time-step are listed in the measurement
vector, zk, and dictate the assembly of the measurement matrix Hk and the measurement
covariance matrix Rk.
The innovation vector, ek, is the difference between the
measurement values and the KF’s expectations for the measured values.
ek = zk − H k xˆk−
(3.7)
The optimal Kalman gain, Kk, is calculated based on the measurements available, the
uncertainty of those measurements, and the uncertainty of the initial state estimate:
K k = Pˆk− H kT  H k Pˆk− H kT + Rk 
−1
(3.8)
A refined estimate, xˆk+ , is then computed by adjusting the initial estimate with the
measurement innovations:
xˆk+ = xˆk− + K k ek
(3.9)
The estimated error covariance of the initial state estimate is used to calculate the error
covariance, Pˆk+ , of the refined state estimate:
Pˆk+ = [ I − K k H k ]Pˆk−
(3.10)
The state estimate at the next step can then be calculated by repeating equations (3.5)
through (3.10). Figure 3-4 shows the steps of the recursive KF process.
62
Initialize
Estimate of state, x̂0+
Uncertainty of state, P0
Predict
xˆk− = Φ ⋅ xˆk+−1
Pˆk− = ΦPˆk+−1ΦT + Qk
Advance
Compute Gain
k = k +1
K k = Pˆk− H kT  H k Pˆk− H kT + Rk 
−1
Blend
xˆk+ = xˆk− + K k  zk − H k xˆk− 
Pˆk+ = [ I − K k H k ]Pˆk−
Figure 3-4. The Standard KF Process.
Both direct state and error state formulations of the KF are prevalent in practice. Direct
state formulations, such as those presented in [25] and [37], and the one used in this
work, employ state dynamics to propagate the state. Error state formulations propagate
an estimate of the measurement error using a model of the measurement error in the KF.
Error state formulations correct for measurement error by subtracting the estimated error
from the measurement values [26, 29, 42]. Direct state formulations work best for
applications using a wide range of measured quantities with sophisticated system models
because they provide the framework to relate the measurements from the various sensors,
and account for uncertainty in the relationships. Error state formulations are better suited
63
to model instrument behaviour, such as time varying gyroscope biases, because they
provide the framework to model the progression of measurement error.
3.3 The Extended Kalman Filter
The basic KF works well for linear systems. Consider an acoustic tracking system
being aided by DVL measurements and highly accurate orientation measurements. The
orientation measurements could be used to transform the body-fixed DVL measurements
into earth frame coordinates. A linear state transition matrix could then be formulated for
the kinematics relating ROV position to ROV velocity and a KF could be used to find the
optimal ROV position and velocity given the measurements provided. However, if
accurate ROV orientation tracking is not available, a more accurate filter would include
the ROV Euler angles as states and transform the DVL velocity to earth coordinates
within the KF framework. Unfortunately, transforming the velocity to earth coordinates
is a nonlinear calculation, and including it in the KF state transition matrix would violate
the constraint defined by Equation (3.1).
The KF principles can be applied to filter non-linear systems by using an EKF, which
linearizes the state dynamics and measurement functions about the state estimate at each
time-step. The nonlinear state dynamics and measurement functions violate the Gaussian
noise requirement for Kalman optimality, so the EKF estimate is not guaranteed to be the
minimum error variance estimate. However, proper estimation of the process uncertainty
ensures near optimality for smoothly varying systems. Alterations or approximations
must also be made to account for asynchronous measurements and for measurement
delays.
64
3.3.1 Linearization about the Current State Estimate
Applying the KF methodology to linearized state relationships produces an EKF [13].
An EKF uses the following state and measurement functions.
x = f ( x, t )
zˆ = h( x, t )
∂f ( x, tk )
Fk =
∂x
T
∂h( x, tk )
Hk =
∂x
(3.11)
x = xˆk−
T
x = xˆk−
In Equation (3.11), the system dynamics are embedded in the set of nonlinear functions
denoted by f, which model the time rate of change of the state. The Jacobian of the
dynamics of f is denoted by F. The measurements collected by an EKF can be nonlinear
functions of the state, with the relationships modeled by the Kalman measurement
functions h( x) . The EKF prediction equations become:
xˆk− = xˆk+−1 +
tk
∫
f ( xˆ, t )dτ
tk −1
Pˆ = Pˆ +
−
k
+
k −1
(3.12)
tk
∫ ( FP + PF
T
+ Q )dτ
tk −1
For small time-steps, +t , forward Euler integration is found to suffice, and the
prediction equations simplify to a discrete form:
xˆk− = xˆk+−1 + f ( xˆ, t ) ⋅+t
Pˆk− = ( I + F ⋅+t ) ⋅ Pˆk+−1 ⋅ ( I + F ⋅+t )T + Q +t
(3.13)
+t = tk − tk −1
The linearization process alters neither the Kalman gain nor the blending equations.
However, the assembly of the H and R matrices needs to be generalized to account for the
asynchronous nature of the measurements provided by the digital sensors.
65
3.3.2 Measurement Innovation Collection
Measurements close the state estimation propagation loop, providing feedback that
keeps the estimate accurate even in the presence of model inaccuracies.
The
measurements arrive in the measurement buffer asynchronously and at different rates, as
described in Section 3.1, and those arriving since the last time-step are processed at the
current time-step.
The innovation of a single measurement, denoted by m ek where the superscript
m
( ⋅)
denotes the mth measurement received since the last time-step, is the difference between
the measurement and the estimate of the measurement.
The scalar measurement
function, mh , uses the state estimate to calculate the estimate of the measurement.
m
ek = m zk − m h( xˆk− )
(3.14)
Unlike the linear KF, which calculates the innovation vector, ek , from the
measurement vector using Equation (3.7), the EKF assembles the innovation vector from
the innovation of individual measurements.
ek {m} = m ek
(3.15)
In Equation (3.15), {m} represents the mth entry of the vector. The innovations of the
other measurements received at time-step k are the remaining entries in ek .
The measurements arrive in the measurement buffer with delay. For most sensors, the
delay is small, and the error caused by ignoring it is negligible compared to the
measurement uncertainty. However, the delay is significant for sensors with low update
rates, most notably the acoustic positioning sensor. To account for the delay, the state
estimate, m xˆ − , at the measurement time, mt , is calculated by propagating the current state
66
estimate back to the measurement time using state dynamics linearized about the current
state estimate:
m
xˆ − = xˆk− − f (tk , xˆk− , uk ) ⋅ (tk − mt )
(3.16)
The measurement innovation is then calculated with Equation (3.14) augmented to use
the state estimate at the measurement time:
m
ek = m zk − m h( m xˆ − )
(3.17)
Other methods of estimating the state at the measurement time, such as keeping a short
history of the state estimates as done in [23] and [25], would avoid linearization errors,
but would add computational burden and may cause instability in cases with large errors
in the estimate history.
3.3.3 Assembly of Measurement Matrices
The measurement sources dictate the assembly of the measurement matrix, H, and
measurement covariance matrix, R. The measurements are discrete and typically not
synchronised. For example, the DVL outputs translational velocity at 2Hz, while the
IMU reports angular velocity at 20Hz.
measurements are possible.
As a result, multiple combinations of
Time-steps at 0.1s intervals will contain several IMU
measurements, and many will not have a DVL measurement at all. Thus, the number of
measurements in z and the entries in e, H and R can vary.
For each measurement’s innovation, mek , a corresponding row in H k , denoted
m
Hk ,
represents the local gradient of the associated measurement function:
m
∂ ( m h( x, mt ))
Hk =
∂x
T
(3.18)
m
x= x
67
For a measurement that is a linear combination of the state variables, m H k is constant
and can be pre-calculated. However, for a measurement that is a non-linear combination
of the state variables, m H k is state dependent and must be calculated as the measurement
is received. Once calculated, m H k is added to the measurement matrix:
H k {m,1: n} = m H k
(3.19)
In Equation (3.19), notation is as follows: {i,j} represents the matrix cells in the ith
row(s) and jth column(s); i:j represents a list of integers starting at i and ending at j; n is
the number of states in the EKF.
Each measurement also has an associated uncertainty, quantified as an error variance,
σ k 2 . For a single independent measurement, a row and a column are added to the
m
measurement covariance matrix, Rk. The entries of the row and column are zero except
the last entry which lies on the diagonal of Rk and is the estimated error variance of the
measurement.
Rk {1: m − 1, m} = 0m −1,1
Rk {m,1: m − 1} = 01,m −1
(3.20)
Rk {m, m} = mσ k2
In Equation (3.20), 0i , j represents a matrix of zeros with i rows and j columns.
The zeros signify that there is no correlation between this measurement and those from
other entries in the measurement buffer. This is a reasonable assumption since the
measurement buffer entries are either made at different times or by different instruments
with independent bias and noise properties. In the case of several values being measured
68
by the same instrument, a square matrix containing the expected values of the outer
product of the measurement errors, wmeas , is added to Rk in block diagonal form.
Rk {1: m − 1, m : p} = 0m −1, p
Rk {m : p,1: m − 1} = 0 p , m −1
(3.21)
Rk {m : p, m : p} = E[ m: p wk ⋅ m: p wkT ]
In Equation (3.21), p represents the number of measurements being added as a set.
This method of assembling Rk adjusts for the variability of the measurement
combinations.
3.4 The EKF for ROV Navigation
The EKF developed in this work uses a suite of sensors tracking a variety of states to
accurately estimate ROV position and velocity. Tether disturbance is also estimated with
the EKF, even though no force sensors are used. Velocity and tether disturbance states
are observed in the ROV reference frame attached to the ROV at the mass centre, and
position states are observed in the inertial reference frame. The two frames are related by
the Euler angles which are also included in the EKF states. The EKF state vector
includes the velocity (u, v, w, p, q, r) in ROV coordinates, position (X, Y, Z) in earth
coordinates, Euler angles (φ, θ, ψ), and 3 tether disturbance parameters.
x ≡ [u v w
p q r
X
Y
Z φ θ ψ
T α
β]
T
(3.22)
Of the three tether disturbance parameters, T represents tether tension, where as
α and β represent the bearing and inclination angles of the tether at the attachment point
on the ROV. The state variables and coordinate systems are shown graphically in Figure
3-5.
69
X
North
Y
East
β
Z Down
Earth Coordinates
α
p
y, v
sway
q
surge
x, u
r
z, w
heave
ROV Coordinates
Figure 3-5. ROV Nomenclature Diagram
The ROV dynamics are embedded in the KF to propagate the state through time. The
kinetic dynamics that propagate the translational velocity are discussed in Subsection
3.4.1.
The kinematic dynamics governing the remaining states are discussed in
Subsection 3.4.2.
3.4.1 ROV Kinetics
The time rates of change of the velocities are the accelerations in ROV coordinates,
estimated through a kinetic model. An ROV model similar to [16] is selected that
70
calculates ROV acceleration in ROV coordinates accounting for Coriolis accelerations,
thrust forces, tether disturbance, hydrodynamic drag, and added mass.
u = (v ⋅ r − w ⋅ q ) + ( FThrustu + T cos(α ) cos( β ) − FDu ) / mu
v = ( w ⋅ p − u ⋅ r ) + ( FThrustv + T sin(α ) cos( β ) − FDv ) / mv
(3.23)
w = (u ⋅ q − v ⋅ p) + ( FThrustw + T sin( β ) − FDw ) / mw
In Equation (3.23), notation is as follows: FThrustu , FThrustv , and FThrustw are the applied
thruster forces in the surge, sway, and heave directions respectively; FDu , FDv , and FDw
are the drag forces in the surge, sway, and heave directions respectively; mu , mv , and
mw are the total inertia of the ROV with added mass.
The applied thruster forces, FThrustu , FThrustv , and FThrustw , are tracked with the Falcon™
Monitor and directly influence the EKF process model of the velocity states.
The
proportion of the applied thrust each thruster exerts in the forward, lateral, and vertical
directions are determined by the thruster installation coefficients: η , κ and λ .
FThrustu = η FThrust
FThrustv = κ FThrust
(3.24)
FThrustw = λ FThrust
The thrust reported by the Falcon™ Monitor is the total thrust in the surge, sway, and
heave directions, i.e., a linear combination of the thrusts produced by each thruster:
 FThrustu  η PF

 
 FThrustv  = κ PF
 FThrustw   λPF
η SR η SF η PR
κ SR κ SF κ PR
λSR λSF λPR
 FThrustPF 
ηV   FThrustSR 
κV   FThrustSF 


λV   FThrustPR 
 FThrustV 
(3.25)
The hydrodynamic drag forces, FDu , FDv , and FDw , are modeled as quadratic functions
of the ROV speed:
71
FDu = Du u + Duu u u
FDv = Dv v + Dvv v v
(3.26)
FDw = Dwu + Dww w w
This model does not account for ocean currents, which lead to differences between the
ROV’s speed relative to the water and its absolute over-ground speed. The dynamics of
the unmodeled phenomena are similar to the tether disturbance dynamics, so significant
ocean currents will taint the EKF’s estimate of the tether disturbance.
The total inertias of the ROV, mu , mv , and mw , are the sum of the mass of the ROV
and the added mass due to the pressure force of water surrounding the ROV during
acceleration.
3.4.2 ROV Kinematics
Kinematic models govern the remaining EKF state variables, namely the rotational
rates, the position, the Euler angles, and the tether disturbance.
A constant rotation rate model is used, which relies on measurements to introduce any
rotational acceleration into the EKF’s estimate:
p = 0
q = 0
(3.27)
r = 0
The constant angular velocity approximation is acceptable because the IMU’s rate
gyroscopes provide high frequency measurements. A more sophisticated rotation rate
model, which calculates rotational accelerations based on net torques on the ROV, would
make the EKF more robust to IMU measurement dropout and improve tether disturbance
force estimation. However, a kinetic rotation rate model would require identification of
72
rotational inertias, thruster force lines of action, and hydrodynamic centers of pressure on
the ROV projected faces.
The coordinate transformation matrices T1 and T2 map values from ROV coordinates
to the earth coordinates [16]:
cosψ cosθ cosψ sin θ sin φ − sinψ cosφ cosψ sinθ cosφ + sinψ sin φ 
T1 =  sinψ cosθ sinψ sin θ sin φ + cosψ cosφ sinψ sinθ cosφ + cosψ sin φ 
 − sin θ

cosθ sin φ
cosθ cosφ
1 sin(φ ) tan(θ ) cos(φ ) tan(θ ) 
T2 = 0
cos(φ )
− sin(φ ) 
0 sin(φ ) / cos(θ ) cos(φ ) / cos(θ ) 
(3.28)
(3.29)
The time rates of change of the position are calculated by using T1 to map the
translational velocity into earth coordinates:
 X 
u 
 
 
 Y  = T1  v 
 Z 
 w
 
(3.30)
The time rates of change of the Euler angles are calculated by using T2 to map the
rotational rates into earth coordinates:
 φ 
 p
 
 
 θ  = T2  q 
ψ 
 r 
 
(3.31)
As demonstrated in Chapter 2, tether disturbance forces can significantly influence the
ROV dynamics. These forces are difficult to model accurately, as they depend on the
often contorted profiles formed by the flexible neutrally buoyant tether. Given the
modelling difficulties, a sophisticated tether model is not anticipated to provide
73
significant additional information over the rudimentary model used in this work, which
simply describes how this force is likely to vary. Within the EKF process model, the
magnitude of the tether tension is assumed to remain constant:
T = 0
(3.32)
The tether direction is separated into bearing and inclination represented by α and β
(see Figure 3-5). The tether tangent at the vehicle connection is assumed to rotate much
more slowly than the vehicle, and thus, is approximated as stationary in the earth-fixed
frame. Then the rate of change of α and β are equal to the reverse of the ROV angular
velocity:
α = −r
β = − p sin α − q cos α
(3.33)
Low confidence in the accuracy of the tether disturbance model is relayed to the EKF
by setting the corresponding entry in the Q matrix appropriately high. This weighting
attributes most of the mismatch between the model-propagated state and the
measurement corrections to the tether disturbance states. For example, a sustained ocean
current will bias the expected vehicle forcing in much the same way as a tether
disturbance, and this bias will appear in the tether disturbance estimate.
3.4.3 Measurement Collection
The Falcon™ ROV’s standard navigation pod contains a compass and a depth sensor,
which directly measure ψ and Z respectively. The addition of an IMU and a Sparton™
compass provides direct measurements for the six orientation states. The DVL and SBL
measure combinations of EKF states.
74
The rows of H corresponding to measurements directly correlated to the state have a
single unity element in the column of the corresponding state, and zeros in the other
columns:
Depth
H k = 01,3
IMU
01,3
H k = 03,3
Sparton
H k = 03,3
[0
I 3,3
03,3
0 1] 01,3
03,3
03,3
03,3
I 3,3
01,3 
(3.34)
03,3 
(3.35)
03,3 
(3.36)
In Equations (3.34) to (3.36): I i ,i represents an identity matrix of size i;
IMU
H k , and
Sparton
H k represent the measurement matrix entries,
m
Depth
Hk ,
H k , for the Depth
sensor, IMU, and Sparton™ compass measurements respectively.
The IMU gyroscopes measure rotation rates in the inertial reference frame, so their
measurements include the earth’s rotation. The earth’s rotation rate is approximately
4x10-3 deg/s and the bias it causes in the gyroscope measurements is distributed between
the pitch, roll, and yaw axes and depends on the IMU’s latitude and heading. The bias in
yaw rotation was removed through calibration. The influence on pitch and roll rate
measurements is neglected because the components of earth’s rotation in these directions
are less than the measurement noise quantified and presented later in Table 4-9.
The DVL measures its velocity relative to the earth when the instrument is within
100m of the seafloor.
The DVL Monitor aligns this measurement with the ROV
coordinates, but ROV translation and rotation both contribute to the instrument’s
measurement.
u DVL
 u   0 −r
0
=  v  +  r
 w  − q p
q   xDVL 
− p   yDVL 
0   z DVL 
(3.37)
75
Thus, DVL velocity is a linear combination of the rotation rates and the translational
velocities. The DVL’s measurement matrix entries ( DVL H k ), are a function of the DVL
position ( xDVL , yDVL , z DVL ), in ROV coordinates:
DVL


H k =  I 3,3

 0
− z
 DVL
 yDVL
− yDVL 
xDVL  03,3
0 
z DVL
0
− xDVL
03,3


03,3 

(3.38)
The measurement function for the acoustic ranges, hSBL , is a non-linear combination of
the ROV position and orientation. The earth-fixed location of the target transducer,
rTARGET , is found using the ROV position, orientation, and offset to the target transducer
( xTARGET , yTARGET , zTARGET ):
rTARGET = [ X
Y
Z ] + T1 ⋅ [ xTARGET
T
yTARGET
zTARGET ]
T
(3.39)
The distance from the target transducer to each reference station location, rREF , is
measured, and the measurement function calculates the expected value:
hSBL = rREF − rTARGET
Lastly,
SBL
(3.40)
H k is the local gradient of this range over the state-space:
SBL
∂hSBL ( x, SBLt )
Hk =
∂x
T
(3.41)
x = SBL xˆk−
However, the dependence of hSBL on the Euler angles is neglected in calculation of
SBL
H k because the gradient is algebraically complex and the effect is negligible since the
target transducer offset is much smaller than the distance between the target and
reference transducers.
76
SBL

H k = 01,3

01,3
01,3
rTARGET − rREF
rTARGET − rREF

01,3 

Unlike the entries of the H matrix for the other sensors,
(3.42)
SBL
H k is not constant.
3.5 The ROV EKF Algorithm
The ROV EKF algorithm is schematically depicted in Figure 3-6. The algorithm starts
with an initial rough estimate of the state, x̂0 , used instead of the refined estimate of the
last time-step, xˆk+−1 , and correspondingly high estimated error variances on the diagonal
of the state error covariance matrix P. This setting makes the EKF rely on initial
measurements for early state estimates.
At each step, measurements are collected in the measurement buffer for one time-step
while the state estimate is advanced using the dynamics described in Subsection 3.4.1 and
Subsection 3.4.2 to form an initial estimate, xˆk− . The measurements are then processed
sequentially with the difference between measured and estimated values filling in the
innovation vector, ek . The H and R matrices for this time-step are assembled at this time
based on the measurement types received. The Kalman gain is calculated, and the refined
estimate, xˆk+ , is calculated by adjusting the initial estimate with the innovation vector.
The current time-step’s refined state estimate is integrated forward to become the initial
estimate of the next time-step. The process then repeats itself recursively.
77
Initialize
Initial estimate of state, x̂0
High uncertainty of state, P̂0
Start measurement collection
Predict
xˆk− = xˆk+−1 + f ( xˆ , t ) ⋅+t
Pˆk− = ( I + F ⋅+t ) ⋅ Pˆk+−1 ⋅ ( I + F ⋅+t )T +
+t = tk − tk −1
Measurement Buffer
Contains pre-processed
measurements received
since the last time step
Collect
For each measurement:
Advance
k = k +1
•
∂hm ( x, mt )
Add row to H k :
∂x
T
x = m xˆk−
•
Add measurement uncertainty to Rk diagonal
•
Add measurement innovation
meas
ek = meas z − h( meas xˆ )
Compute Gain
K k = Pk− H kT  H k Pk− H kT + Rk 
Blend
xˆk+ = xˆk− + K k ek
Pˆk+ = [ I − K k H k ]Pˆk−
Figure 3-6. The Kalman Flowchart for ROV Navigation
−1
78
Chapter 4. System Identification
A series of shallow water tests were performed to identify the constants specific to the
Falcon™ ROV in the EKF developed in Chapter 3. This chapter presents the test
conditions and identifies the parameters. The accuracy of each sensor is estimated in
Section 4.2 by comparing measurements with more accurate values. Accurate values on
which to evaluate measurement noise are not available during regular deepwater
operations. The shallow water tests were conducted in a controlled setting and an optical
motion measurement system was used to provide a reference position signal against
which the individual sensors, and the EKF as a whole, could be judged. The parameters
of the ROV dynamics model are identified in Section 4.3 by analysing measurements
made by the onboard sensors during identification manoeuvres in the shallow water test
facility. Model errors are characterized in Section 4.4 by scrutinizing the EKF’s estimate.
4.1 The Shallow Water Test Facility
Shallow water testing was performed in a 12m long by 5.5m wide boathouse at a
saltwater marina. The boathouse provided an enclosed test range with a controlled
climate, still water and a surrounding deck that provided room to set-up the ROV and the
optical motion measurement system. The SBL reference stations were fixed to the
79
boathouse enclosure. Thus, acoustic position measurements were obtained in earth
coordinates rather than in coordinates moving with a surface vessel. When submerged
below the 0.3m depth of the boathouse floats, the vehicle operated in a wide expanse of
water. As a result, the acoustic reverberation challenges encountered with pool testing
were avoided. Furthermore, covering the boat access and skylights eliminated most
ambient light and improved the performance of the optical motion measurement system
in daylight hours.
4.1.1 Testing Field
The Falcon™ ROV and its surface equipment were mobilized in the boathouse along
side the optical motion measurement system. The water depth was 3m at low tide and
5m at high tide. A walkway lined the edge of the boathouse, leaving a 4.2m wide by 11m
long water surface.
The earth fixed coordinate system was aligned with the walkways.
The SBL positions and compass headings were transformed by their respective
monitoring algorithms to be in the X-Y coordinate frame shown in Figure 4-1.
80
Y Position (m)
0
1
2
3
4
5
0
2
4
6
X Position (m)
8
10
Figure 4-1. Boathouse Layout showing the coordinate system (dashed grid), the dock edges
(solid), the optical measurement system’s field of view (dotted trapezoid), the optical
coordinate markers (circles) and the SBL reference stations (stars). Boat access is from the
right side of the figure.
4.1.2 Optical Motion Measurement System Setup
The VZ3000 VisualeyezTM tracking system by Phoenix Technologies Inc. was used to
accurately track the ROV position to provide a reference for raw acoustic position
measurements and for the EKF estimate. This tracking system measures the position of
markers (LED light sources) by viewing them on three cameras at calibrated positions.
For the system to determine a marker’s location, other light sources must be dimmed
below the detection threshold, and line of site must be maintained between the marker
and all three cameras. The camera unit was mounted high up the boathouse wall, and
faced downward to minimize the influence of ambient light.
As the optical motion measurement system is based on light transmission, the system
only works above the water surface. A mast (shown in Figure 4-2) was constructed of
thin aluminium tubing and attached to the ROV at the tether attachment point. The mast
held the optical markers at fixed locations above the ROV. The mast was stiffened with
81
guy wires running from the base of the cross on the mast to the forward rails on the ROV.
Additional guy wires running aft may have further strengthened the mast but would have
occasionally contacted the ROV tether, jolting the mast off location. The mast base was
anchored to the ROV’s syntactic foam and the tether attachment bracket counteracted the
forward pull of the guy wires.
One forward facing and one rear facing marker were placed at each of the three above
surface extremities of the mast. The markers were aimed 30deg above horizontal to
reduce reflections off the water surface.
Rear Marker
Front Marker
a) Mast to Hold the Markers
b) Port Side Markers
Figure 4-2. Optical Markers Mounted to the ROV. The optical markers were attached to
an aluminum mast which held the markers above the water throughout the tests.
Stationary markers were fixed to the boathouse walkway to align the optical motion
measurements with the boathouse reference frame shown in Figure 4-1. Table 4-1 lists
the marker locations; the X-axis was marked with two markers, and the XY plane was
marked by a third marker located on the far side of the boathouse.
82
Marker
Reference
X Location
(m)
Y Location
(m)
Height –Z
(m)
Offset Origin
3.194
0
0.65
X axis Direction
4.905
0
0.65
XY Plane
4.045
4.2
0.65
Table 4-1. Visualeyez™ Stationary Marker Locations.
4.1.3 Processing Optical Motion Measurements
The ROV position was extracted from the marker position measurements of the optical
motion system using several ROV-fixed reference frames. First a pair of mast-fixed
coordinate systems were defined, one based on the front markers, and another in terms of
the rear markers. The origins were at the centres of the triangles formed by the top, port,
and starboard markers of each side. The x-axis pointed to the top marker, and the y-axis
lay in the plane of the triangle. A matrix was defined that transformed the mast-fixed
coordinates the ROV coordinates.
The relative orientations and offsets of the mast coordinates to the ROV coordinates
were defined through a set of optical motion measurements of the ROV when stationary
and above water. During the stationary test, the optical measurement cameras could view
the markers on the mast simultaneously with temporary markers placed on the ROV. The
temporary markers were placed on the ROV at the locations listed in Table 4-2.
83
Marker Location
x Location
(m)
y Location
(m)
0
0
Wide Angle Camera
Top Center
0.48
0
0.18
Target Transducer
Top Center
-0.45
0.34
0.15
Sensor Pod Top
Center
-0.59
-0.30
0.19
Vertical Thruster
Top Center
Height -z (m)
0.18
Table 4-2. Temporary ROV Marker Locations (in ROV coordinates) used in the
transformations that map the two mast coordinate systems to the ROV coordinates.
The transformation matrices were found by rotating and offsetting the mast coordinate
systems until they lined up with the temporary markers on the ROV. This procedure
eliminated any misalignment of the markers on the mast and any imperfections in the
mast’s equilibrium profile. So long as the markers on the mast remained stationary
relative to the ROV, the derived transformation matrix calculated the submerged ROV
coordinate system location based on the visible mast markers. The calculated ROV
positions were not as accurate as the individual marker measurements because the
calculation not only relied on mast marker positions, but also on the mast coordinate
system orientation, which was poorly conditioned due to limited spacing of the mast
markers.
An additional coordinate system with origin at the SBL target transducer was tracked
using coordinate transformation matrices calculated in the same way as the ROV
coordinate system. This coordinate system was used to evaluate the SBL measurement
accuracy.
To resolve each marker’s location, all three optical measurement cameras needed to
simultaneously view the marker. This limited the optical system’s field of view to
84
roughly a 4m by 4m square. The ROV mounted sensors functioned correctly outside of
this area, but optical motion measurements were not available to verify accuracy.
Reflections off the water surface and the aluminum boathouse walls caused occasional
inaccurate marker position measurements.
Inaccurate position measurements were
eliminated with a Matlab™ script that removed measurements made at times when
calculated distances between the mast markers deviated in excess of 0.01m from the
actual distance between the markers. When one or more markers defining the ROV
position was not found, the Visualeyez™ software assumed the ROV had not moved. At
these times, the marker measurements were tagged as a ‘bad’ position measurement, and
the associated motion measurements were also rejected by the Matlab™ script. A sample
of acceptable and rejected measurements of ROV position using both the forward and
rear facing markers are shown in Figure 4-3.
Usually, either all forward facing markers or all rear facing markers faced the cameras
and could be tracked, providing frequent ROV position fixes while the ROV mast was
within the three cameras’ field of view.
The filtered optical motion measurements
provided highly accurate ROV position fixes at 100Hz. These position fixes were later
used as an accurate reference against which to compare the SBL measurements and the
EKF estimates.
85
6.5
6
ROV X Position, X (m)
5.5
5
4.5
Multipath
4.8
4
3.5
4.7
3
Occlusion
4.6
2.5
680
2
674
676
678
680
682
Time (s)
680.1
684
680.2
686
680.3
688
690
Figure 4-3. Optical Motion Measurements of ROV using forward (dark) and rear (light)
facing markers. Good data are shown as dots; rejected data are shown as circles. Up to
679s, the ROV faced the cameras, so only the forward facing markers were correctly
tracked. From 679s to 681s the ROV was broadside the cameras, so both sets of markers
were visible, but many multipath reflections occurred as the light signal was weak. After
681s the ROV faced away from the cameras, so only the rear markers were correctly
tracked. After 684s the ROV moved beyond the field of view of the cameras and no optical
position fixes were available.
4.2 Measurement Modeling
The EKF needs to know how much confidence to put into measurements when
computing the Kalman gain. This confidence is quantified as the measurement error
variance and is specified in the measurement covariance matrix R in Equation (3.21).
86
Measurement error cannot be identified without knowing the exact value of the
quantity being measured. Even in the controlled environment of the boathouse, random
errors, time varying biases, and unidentified sensor misalignment caused measurement
inaccuracies. Even the optical motion measurements, which provided highly accurate
and high frequency ROV positions, were not well suited for tracking other quantities,
such as body fixed velocities.
Numerical differentiation of the optical position
measurement to produce velocities in earth coordinates amplified noise and was also
sensitive to errors in the measurement time-stamps. The rotation to ROV coordinates
relied on Euler angles, which were also difficult to accurately measure.
To mitigate measurement error, it is important to match the sensing method to the
sought after quantity. Measurements of the ROV position, orientation, and velocity
provided feedback for the EKF. The estimation of the accuracy of the instruments
sensing each of these quantities is explained in the following subsections.
These
estimated accuracies were used in computing the Kalman gains. The data collected from
a 1562s identification manoeuvre where the ROV was piloted throughout the shallow
water test facility were used to calculate measurement error properties and identify the
system dynamics parameters.
4.2.1 Acoustic Ranging
The PILOTTM SBL tracking system tracked the position of an ROV mounted target
transducer (TLT-1) through acoustic interrogation.
The ranges between the target
transducer and three reference transducers at known locations were measured by time of
travel of an acoustic pulse emitted from a reference station, repeated by the target
transducer, and received by each reference station.
87
The SBL system provided measurements at a slower rate than the other sensors. This
was because the interrogating transducer required a delay to switch from transmit to
receive in order to avoid false readings when beginning to listen for the response signal.
Also, the SBL system operated on a dedicated ping frequency, so only one ping was
intended to be propagating through the water at any time. Thus the system had to wait
for each ping to travel between transducers, and dissipate sufficiently before sending the
next ping. The system was configured for transducer ranges on the order of 100s of
meters, where round trip travel times could take nearly 1s at a nominal in-water sound
speed of 1500m/s. The average update rate was 0.42Hz during the shallow water tests.
During the shallow water tests, the reference stations were hung from the boathouse
walkway, at the corners of the boathouse. The reference stations were located at the
coordinates listed in Table 4-3.
Reference
Station #
X Location
(m)
Y Location
(m)
Depth (m)
1
9.50 m
4.21 m
0.52 m
2
1.32 m
3.49 m
0.36 m
3
9.51 m
0m
0.65 m
Table 4-3. SBL Reference Station Locations. Reference stations were hung at surveyed
corners of the boathouse.
Stationary tests were performed to check the acoustic positioning system measurements
against directly measured target transducer positions. During these tests, the target
transducer was held for several minutes at each of several accurately measured locations
while the SBL measured the transducer’s range to the each of the three reference stations
and calculated its location. Figure 4-4 compares the range measurements made by one of
88
the reference stations to the true range, and shows a bias. Table 4-4 presents the errors of
the ranges measured by each reference transducer for all four static tests.
4.5
Acoustic Ranging
Accurate Value
Mean Measurement
Range (m)
4
Range Bias
3.5
3
0
50
100
150
200
250
Time (s)
Figure 4-4. Range Measurement Bias Observed during Stationary Testing.
Target Transducer
Position
Reference Station 1
Reference Station 2
Reference Station 3
X
Y
Z
True
Meas
Diff
True
Meas
Diff
True
Meas
Diff
3
0
0.82
7.75
7.31
0.44
3.90
3.44
0.46
6.51
6.09
0.42
8
0
0.82
4.48
4.03
0.45
7.55
7.16
0.39
1.51
0.94
0.57
3
0
0.82
7.75
7.44
0.31
3.90
3.44
0.46
6.51
6.15
0.36
8
-4.2
0.82
1.53
1.02
0.51
6.73
6.28
0.45
4.46
3.98
0.48
Mean Bias
0.43
0.44
0.46
Table 4-4. Range Measurement Bias Observed with Stationary Tests. All values in meters.
All range measurements were shorter than the actual ranges by approximately 0.4m.
This constant error was removed during the pre-processing step in the SBL Monitor.
The SBL ranges were also compared against optical motion measurements to observe
the effect of motion on the range measurements. The SBL measurements were observed
to lag the optical motion measurements by 0.7s, so this delay was subtracted from the
89
SBL time-stamp before comparing the two measurement series. Figure 4-5 shows the
SBL range measurements from each reference transducer, and the more accurate ranges
calculated from the optical motion measurements. The variance of the range error was
computed by interpolating the optical motion measurements corresponding to the SBL
ranges within 0.1s of valid optical motion measurements.
90
Range (m)
9
7
5
3
1
600
700
800
900
800
900
800
900
Time (s)
a) Reference Station 1
Range (m)
9
7
5
3
1
600
700
Time (s)
b) Reference Station 2
Range (m)
9
7
5
3
1
600
700
Time (s)
c) Reference Station 3
Figure 4-5. Dynamic Test of SBL Range Accuracy. SBL ranges (star) were compared with
ranges calculated from the optical data (broken line). Ranges could only be calculated from
the optical data when the ROV optical markers were tracked, so the resulting series appear
as broken lines. The range measurements are shown for each reference station.
91
During the 1562 second identification manoeuvre, 1956 valid range measurements
were made by the SBL system. Of these, 1432 range measurements were made when
valid optical data were available to use as a reference in calculating the measurement
error.
The other SBL range measurements were made when neither set of optical
markers on the ROV mast was sufficiently visible to make an accurate optical position
measurement. Table 4-5 lists the errors in SBL measurements observed during the
shallow water identification manoeuvre.
Reference
Station #
# of
comparable
measurements
Range Bias
(m)
Range Error
Variance
(m2)
1
500
0.33m
0.64m2
2
470
0.34m
1.01m2
3
462
0.09m
0.58m2
Table 4-5. SBL Acoustic Ranging Errors
Even though the range measurement bias observed during the stationary test was
removed, a bias was observed in the shallow water identification manoeuvre. The bias
may be caused by velocity dependence of the measurement delay or measurement errors
in surveying the reference station locations.
Fluctuating measurement errors were quantified as error variance. The range error
variances measured in the shallow water test became the entries in the Kalman
measurement covariance matrix, R, associated with each reference station range
measurement.
The Divebase™ software processed the SBL ranges as they were measured and
computed a position measurement when all three reference stations received enough
information to calculate their range to the target transducer. The measurements of the
92
depth sensor on the target transducer were also included in the position measurement
computation. However, theses position measurements were recalculated to remove error
caused by the constant bias observed in Table 4-4. The SBL position measurements were
considered as a benchmark on which to compare the EKF performance.
4.2.2 Depth Sensors
The SBL depth sensor was located in the target transducer and the ROV depth sensor
was located in the Seaeye navigation pod. Both sensors measured the ambient water
pressure to determine depth. The SBL depth sensor measurements were acoustically
transmitted to reference stations, collected by the Divebase™ software, and used in the
SBL position calculation. The ROV depth sensor measurements were transmitted to the
surface station using the ROV’s telemetry, which allowed higher update rates, better
resolution, and more robust measurements than the SBL depth measurements. The
optical motion measurement system also tracked ROV depth at a rate and accuracy far
exceeding the measurements of the two depth sensors. ROV depth measurements made
during the shallow water identification manoeuvre are compared in Figure 4-6.
93
1.2
1
Depth (m)
0.8
0.6
0.4
0.2
0
-0.2
600
605
610
615
620
625
630
Time (s)
635
640
645
650
Figure 4-6. Depth Sensor Test. ROV depth measurements made by the depth sensor in the
Seaeye navigation pod (stars) and by the SBL depth sensor (circles) were compared with the
more accurate optical motion measurements (dark line).
The errors in both the ROV depth sensor measurements and the SBL depth sensor
measurements were calculated by using the optically measured ROV depth as the
reference values. As with the range errors presented in Subsection 4.2.1, the optically
measured depths were interpolated to synchronise with the ROV depth sensor and SBL
depth sensor. Table 4-6 lists the measurement rates and the error variances observed for
both depth sensors during the 1562s test.
Sensor
Measurement
Rate
Error
Variance
ROV Depth
10 Hz
0.036 m2
SBL Depth
0.5 Hz
0.2 m2
Table 4-6. ROV Depth Measurement Properties.
The measurement rate and accuracy of the ROV depth sensor were far superior to the
SBL depth measurements. The error variances presented in Table 4-6 became the entries
of the EKF measurement covariance matrix, R, associated with the depth measurements.
94
4.2.3 Doppler Velocity Log
The DVL measured its velocity by transmitting acoustic pulses, and analyzing echoes
off the sea floor. By measuring the frequency shift between the transmitted pulse and the
received echo, the DVL calculated its speed along the direction of the acoustic beam.
The DVL utilized several beams to resolve its velocity into vehicle fixed coordinates.
Each of the four circles shown in Figure 4-7 is a transducer that measures the vehicle’s
speed normal to the transducer’s face.
Figure 4-7. Doppler Velocity Log Transducer Head.
The uncertainty of the DVL measurements was estimated by holding the unit stationary
and recording the measurements. The resulting characteristics of the measurement series
for the zero velocity condition are given in Table 4-7 and were assumed to apply for the
non-stationary case as well. A 0.4s measurement delay of the DVL was observed during
the shallow water identification manoeuvre, as shown later in Figure 4-11.
95
Measurement
Quoted Accuracy
(m/s)2
Stationary Variance
(m/s)2
Bias
(m/s)
Surge, u
1.44x10-4
4 x 10-5
1.5 x 10-4
Sway, v
1.44x10-4
8 x 10-5
0.7 x 10-4
Heave, w
1.44x10-4
1 x 10-5
0.5 x 10-4
Table 4-7. DVL Measurement Error
The DVL was configured to ping as fast as possible, and create an ensemble containing
the instrument-fixed velocity with every complete set of echoes received.
configuration produced DVL measurements at a rate of 2Hz.
This
Measurement error
variance could be reduced by averaging multiple sets of pings into an ensemble, but
response to velocity changes would be reduced by the averaging procedure.
4.2.4 Magnetic Compasses
Electronic compasses employ magnetometers to sense the magnetic field as a voltage
signal. The magnetic field in the horizontal plane indicates north. Most electronic
compasses, including the ones used in this work, use a three axis magnetometer to
measure the complete magnetic field and an accelerometer to determine the vertical
direction.
Typically the magnetometer is in the form of a flux gate, which is a
magnetically permeable material wrapped with several coils of wire. An oscillating
voltage applied to one coil induces a fluctuating magnetic field in the material, which is
sensed by the other coils. The superposition of the applied field to the ambient magnetic
field causes the coils aligned with the north-south direction to saturate sooner than those
out of alignment.
The Sparton™ compass in the navigation pod output pitch and roll determined with a
set of accelerometers, and heading determined from a three axis magnetometer. The
Falcon™ onboard compass operated in a similar way, but the pitch and roll
96
measurements were not entered into the measurement buffer. Measurements from both
instruments were reported to their respective monitoring threads at 10Hz.
When either compass was stationary, its measurements had low variance. In this
regime, pitch and roll were measured accurately because the only acceleration is gravity.
Accurate measurement of compass orientation improved the calculation of heading which
required projecting the three dimensional magnetic field onto the horizontal plane. Also,
constant magnetic anomalies could cause a bias, but would not add to the variance of the
compass measurements when stationary.
The Sparton™ compass was rated to have a 1 x 10-4rad2 (0.52deg2) error variance for
stationary heading measurements. When held stationary, its 10Hz measurements had an
8.5 x 10-5rad2 heading variance, which agreed with the specification. The manufacturer
of the Falcon™ compass was unknown, so accuracy ratings could not be found.
However, a stationary test produced measurements with 5.4 x 10-5rad2 heading variance,
suggesting the Falcon™ compass was slightly more accurate than the Sparton™
compass.
Dynamic compass measurements were subjected to higher noise. The pitch and roll
finding accelerometers could not distinguish between body acceleration and gravitational
acceleration, creating uncertainty in the pitch and roll measurements.
Unmodeled
magnetic anomalies, which merely cause a bias in the stationary test, would become
dynamic errors if the anomalies were not constant through space.
The optical motion measurements, which worked well as a reference for the
positioning system, were poorly conditioned for orientation measurements because the
mast markers were close together. Consequently, headings calculated from the optical
97
measurements were not noticeably more accurate than the compass measurements.
Instead, the measurements of the Sparton™ and Falcon™ compasses were compared
against each other to estimate the measurement error variances of each sensor.
The measurement errors of the Sparton™ compass were assumed to be independent of
the Falcon compass’ measurement errors, so a differencing approach could be used to
calculate the error variance. Subtracting the Falcon™ compass measurements from the
Sparton™ compass measurements removed the dynamic true heading, and only the
difference of the two measurement sets’ errors remained. The variance of the difference
of two uncorrelated random variable sets is the sum of each set’s variance. This result
was manipulated to express the Sparton™ compass’ heading measurement error
2
2
, in terms of the calculable variance of the difference, σ Spar
, and the
variance, σ Spar
ψ
ψ − Falψ
2
.
Falcon™ compass’ error variance, σ Fal
ψ
2
2
2
σ Spar
= σ Spar
− σ Fal
ψ
ψ − Falψ
ψ
(4.1)
The dynamic response of both sensors was assumed to be sufficiently similar that the
ratio of the two sensors’ variances calculable for the stationary case remained the same
for the moving compass:
2
σ Spar
ψ
2
σ Fal
ψ
=
8.4 × 10−5
5.4 ×10−5
(4.2)
This relationship between the error variances of the two compasses allowed Equation
(4.1) to be solved for both error variances.
estimated error variances of both compasses.
Table 4-8 presents the measured and
98
Measurement
Symbol
Quoted
Stationary
Dynamic
2
σ Spar
ψ
8 x 10-5 rad2
Static
8.4 x 10-5 rad2
3.3 x 10-2 rad2
Sparton Pitch and
Roll
2
2
σ Spar
, σ Spar
φ
θ
1 x 10-5 rad2
Static
6.1 x 10-6 rad2
--
Falcon™ Heading
2
σ Fal
ψ
-
5.4 x 10-5 rad2
2.2 x 10-2 rad2
Sparton minus
Falcon™ Heading
2
σ Spar
ψ − Falψ
-
1.0 x 10-4 rad2
5.5 x 10-2 rad2
Sparton Heading
Table 4-8. Compass Measurement Error. Stationary error variances and the dynamic
variance of the difference of the two instruments were directly measured. Dynamic error
variances of the individual instruments were inferred from the ratio of the static variances
and the differenced variance.
4.2.5 Inertial Measurement Unit
The MMQ50™ IMU contained an accelerometer and a rate gyroscope on three
orthogonal axes. Only the rate gyroscopes were used for this work. Low cost IMUs are
made of micro-machined piezoelectric quartz elements that measure rotational rates and
linear acceleration. Angular velocity alters the natural frequency of these piezoelectric
elements, whose vibration is digitally measured. Like the DVL, the IMU noise was
measured by holding the unit stationary and calculating the variance of the
measurements. Table 4-9 lists the error variance and bias of each gyroscope.
Measurement
Quoted
Stationary Test
Variance
Stationary Test
Bias
X-axis Gyroscope Error
0.003(°/s)2
0.005 (°/s)2
-0.026 °/s
Y-axis Gyroscope Error
0.003(°/s)2
0.010 (°/s)2
0.025 °/s
Z-axis Gyroscope Error
0.003(°/s)2
0.008 (°/s)2
0.080 °/s
Table 4-9. IMU Measurement Error
99
IMU measurements were received by the IMU Monitor thread at 20Hz. The high
measurement rate of this sensor made it particularly useful in creating a low variance
estimate of the Euler angles.
4.3 System Identification
The parameters that match the behaviour of the dynamics model given in Subsection
3.4.1 to the Falcon™ ROV were identified through a series of repetitive tests performed
in the shallow water test facility referred to in this work as the shallow water
identification manoeuvre. System behaviour was observed with the onboard sensors, and
the only additional instrument is a strain gauge for thrust measurement.
4.3.1 Thruster Parameters
The total force exerted by the ROV thrusters as a function of the ROV pilot’s thrust
commands was needed to include thrust forces in the ROV dynamics model. This
function was found by identifying each thruster’s installation coefficients and the
relationship between pilot command and individual thruster forcing.
The thruster installation coefficients described by equation (3.25) were identified by
considering the geometry of the thrusters. Figure 4-8 shows the centreline vectors of the
ROV’s four horizontal thrusters and Table 4-10 lists the vector angles. These thrusters
were assumed to be interchangeable with no effect on the system dynamics because they
were the same model and used the same cowling. The vertical thruster was also the same
model, but its cowling was shorter and built into the syntactic foam.
100
θ PR
θ PF
Figure 4-8. The Falcon™ Thruster Arrangement.
Four thrusters provided horizontal
motion actuation. A vertical thruster provided depth control. All thrusters were the same
model.
Thruster Location
Symbol
Value (deg)
Port Forward
θ PF
36°
Port Rear
θ PR
-36°
Starboard Forward
θ SF
-36°
Starboard Rear
θ SR
36°
Table 4-10. Falcon™ Horizontal Thruster Angles
As with most thrusters, those on the Falcon™ ROV exhibit radial symmetry, so each
thruster’s force was assumed to act along its rotation axis. By considering the magnitude
of force exerted by each thruster to be that realized in the installed configuration, the
entries of equation (3.25) that convert the individual forcing of the ROV thrusters to net
force in the surge, sway, and heave directions were reduced to vector additions:
η* = cos(θ* )
κ * = sin(θ* )
λ* = 0
ηV = 0
κV = 0
λV = 1
In Equation (4.3), the subscript ( ⋅)* denotes each of the horizontal thrusters.
(4.3)
101
The other thrusters and the ROV hull can divert water flow and cause the thruster
installation assumption to be violated. However, the bollard pull tests presented next
showed the net force of all the thrusters satisfied the assumption of each thruster’s force
aligning with its rotation axis.
The relationship between the ROV pilot’s thrust commands and the force exerted by
each of the thrusters was examined with a set of bollard pull tests performed in the
shallow water test facility. For these tests, an axial load-cell was anchored to the dock
with a strap. The free end of the load-cell was attached to the ROV with a 10m rope.
The rope was attached to the rear of the ROV for the forward surge tests. It was also
attached to the front, port side, and starboard side for measuring thrusts in the reverse
surge, positive sway, and negative sway directions. Both positive and negative heave
thrusts were measured by adding steel weights to make the ROV 14kg negatively
buoyant, setting the load-cell in a vertical configuration and attaching the rope to the top
of the ROV.
For each thrust direction configuration, the load-cell signal was recorded with a timestamp synchronised with the thrust commands read off the Falcon™ ROV telemetry.
Both the thrust commands for each thruster and the load-cell voltage were recorded at
rates of 10Hz. The ROV was piloted away from the load-cell, but restrained in that
direction with the rope connecting the two.
Thrust commands were made as step inputs at multiple levels.
Each level was
sustained for approximately 10s. Figure 4-9 shows the measured thrusts resulting from
several commanded thrust step inputs. Figure 4-10 plots all measured surge thrusts over
the domain of commanded thrusts. A steep ramp in the force exerted for the upper end of
102
the commanded thrust required finer thrust steps at this range to resolve the quadratic
nature of the relationship and the saturation point of the thrusters.
450
Command (%)
Force (N)
Surge Thrust
400
300
200
100
0
0
50
100
150
Time (s)
200
250
Figure 4-9. Time-series of Commanded and Realized Thrust Forces
600
400
Force (N)
200
0
-200
-400
-600
-100
-80
-60
-40
-20
0
20
40
Pilot Command (% Force)
60
80
100
Figure 4-10. Scatter plot of Realized Thrust over the Range of Thrust Commands.
Step inputs in thrust commands were utilized to verify the synchronisation of the
commands and the load-cell, highlight the rapid response of the thrusters, and isolate the
transient effects of the thrusters. The transient data due to the steps were removed from
103
the analysis, leaving only the sustained thrust times for use in characterizing the thruster
relationship. This steady-state data exhibited a more deterministic relationship shown in
Figure 4-11.
450
Command (%)
Force (N)
Surge Thrust
400
300
200
100
0
0
50
100
150
Time (s)
200
250
400
300
Force (N)
200
100
0
-100
-200
-300
Measured
Fitted
-400
-100
-80
-60
-40
-20
0
20
40
Pilot Command (% Force)
60
80
100
Figure 4-11. Steady-state Surge Thrust Force Response to Thrust Commands. A piecewise
quadratic equation was fitted to this data to convert thrust commands into force estimates.
The surge force response had the highest signal to noise ratio, so it was used to
determine the output of a single thruster. The sway forces were 70% of the surge forces
104
realized for the same command magnitude, confirming the assumption that each
thruster’s forcing direction was along its rotation axis.
The thrusters exhibited a quick response and saturation at 90% thrust. A piecewise
quadratic curve was fitted with a least squares approach to relate the pilot’s commands to
realized thrust force. The magnitudes of reverse thrusts were found to be 94% of the
corresponding forward thrust. The Falcon™ Monitor received the thrust commands,
Fcmd from the ROV telemetry, and provided thruster forces, FThrust , to the measurement
buffer using:
2
FThrust = 0.0059 Fcmd
− 0.022 Fcmd
FThrust
FThrust
FThrust
0%≤ Fcmd ≤ 50% 


2
= 0.040 Fcmd
− 2.8 Fcmd + 53.65 50%≤ Fcmd ≤ 90% 


= 124
90%≤ Fcmd ≤ 100% 
= −0.94 FThrust (− Fcmd )
 Fcmd ≤ 0%

(4.4)
4.3.2 Hydrodynamic Drag Estimation
The hydrodynamic drag model defined in Equation (3.26) was parameterized by linear
and quadratic coefficients in each of the surge, sway, and heave directions. These drag
coefficients were found by piloting the ROV in straight lines with constant force
commands and analysing the steady-state applied thrust and velocity. The DVL was used
to measure the steady-state velocity. The Falcon™ thrust commands were converted into
applied thrusts using Equation (4.4).
Figure 4-12 depicts the ROV accelerating from rest to steady-state velocity as a result
of a 19N surge thrust step input. 10s after the thrust increase, The ROV approached a
steady-state velocity of 0.24m/s. Therefore, the hydrodynamic drag on the ROV was
19N for a surge speed of 0.24m/s.
25
0.5
20
0.4
Thrust
15
0.3
10
0.2
Speed
5
0.1
0
0
-5
125
130
135
140
145
Time (s)
150
155
Surge Speed, u (m/s)
Thrust Force, FDu (N)
105
-0.1
160
Figure 4-12. ROV Velocity Response to a Thrust Force Step Input. The ROV surge speed
(dotted) resulting from a step input of applied thrust (solid) was measured by the DVL. The
19N thrust resulted in a 0.24m/s steady-state speed. The 0.4s delay between thrust step and
velocity change was characteristic of the DVL measurements.
The velocity change measured by the DVL lagged the thrust input by 0.4s. There was
no significant delay in the thruster response, so the entire delay was attributed to the DVL
measurements.
At constant force steady-state, the hydrodynamic drag is the only force opposing the
applied thrust. The steady force acceleration up to steady speed manoeuvre was repeated
for various applied forces. Figure 4-13 shows steady-state speed achieved for each
applied thrust in the surge direction. Similar manoeuvres were performed for each of the
surge, sway, and heave directions.
106
600
Drag Force, FDu (N)
500
400
300
200
Forward
Reverse
Mastless
Fitted
100
0
0
0.25
0.5
0.75
Speed, |u| (m/s)
Figure 4-13. Drag Force as a Function of Speed.
1
1.25
1.5
An origin intersecting quadratic
polynomial was fitted to the data using a least squares method. The relationship for the
surge direction is shown. Note that the drag force was only slightly reduced by removing
the optical marker mast. Drag forces were considered symmetric about the forward and
reverse motions.
The hydrodynamic drag coefficients for surge, sway, and heave motions were found by
fitting Equation (3.26) to the Falcon™ ROV drag data collected from the shallow water
identification maneuver. Table 4-11 lists these drag coefficients and their associated
uncertainty.
Direction
Surge
Sway
Heave
R2
0.98
0.98
0.96
Coefficient
Value
Variance
Du
88.9 N/(m/s)
412 (N/(m/s))2
Duu
183.7 N/(m/s)2
373 (N/(m/s)2)2
Dv
86.5 N/(m/s)
1397 (N/(m/s))2
Dvv
541.9 N/(m/s)2
3920 (N/(m/s)2)2
Dw
173.2 N/(m/s)
2773 (N/(m/s))2
Dww
230.2 N/(m/s)2
16877 (N/(m/s)2)2
Table 4-11. Falcon™ Hydrodynamic Drag Coefficients.
107
4.3.3 Fluid Inertia Estimation
The inertia of water surrounding the ROV increased the effective inertia of the ROV.
The ROV dynamics modeled this phenomenon with the total inertia coefficients:
mu , mv , mw . The total inertias of the system for surge, sway, and heave accelerations
were calculated by analyzing the accelerations resulting from the estimated net forces.
The DVL velocity signal was linearly interpolated to synchronise with the Falcon™
thrust signal. The net force on the ROV was calculated as the total thrust force less the
drag force. The linear acceleration was found by differentiating the velocity signal. A
least squares fit was made to determine the total inertia corresponding to the actuated
DOF. The resulting total inertia coefficients and their estimated uncertainty are listed in
Table 4-12.
This method was sensitive to synchronisation between DVL velocity
measurements and thruster commands, and to errors in the hydrodynamic drag modeling.
Symbol
Value
R2
Variance
Surge
mu
281 kg
0.97
109.5 kg2
Sway
mv
224 kg
0.81
493.6 kg2
Heave
mw
509 kg
0.75
400.5 kg2
Direction
Table 4-12. Falcon™ Inertia – includes the dry mass and the added mass due to the inertia
of surrounding water.
108
4.4 Model Uncertainty Characterization
The last parameters in the EKF that needed to be identified were those that estimated
the confidence in the filter’s process model to accurately propagate the state. Those
parameters formed the entries in the Kalman model error covariance matrix Q.
general, the entries of Q can be nonlinear time varying functions.
In
The entry
corresponding to the tether tension estimate, Q {13,13} , was found to be dependant on
ROV acceleration. The remaining entries of Q were constants.
As in prior work [43, 47], Q was assumed to be diagonal. In other words, the error
accumulated in the propagation of one state was assumed to be independent of the errors
accumulated for all other states. This assumption does not imply that the error in one
state is independent of the other states. In Equation (3.13), off diagonal terms in the state
Jacobian matrix F apply the appropriate state uncertainty to the covariance matrix P
including off diagonal entries in P that capture dependence between any two states.
However, a modeling error in one state’s propagation function was assumed to have
negligible effect on the modeling error of another state’s propagation function.
Unlike the simulation based studies in [16], state values were not exactly known in this
experimentally implemented work.
Earlier works [47, 48] suggested the use of a
sophisticated “truth” model to provide reference state values for estimating the Q entries
of an EKF whose process model needed to be simplified to run in real-time on primitive
computers. However, the ROV model presented in Section 3.4 was deemed to capture
the majority of the actual ROV dynamics, so a more sophisticated “truth” model was not
available to provide reference state values. Instead, the “truth” reference was produced
using the EKF aided by the complete set of instrument measurements.
109
The shallow water identification manoeuvre was used to estimate the values of Q
corresponding to the navigation states.
A reference EKF, whose Q entries were
overestimated, produced “truth” estimates that relied heavily on the measurements. The
accuracy of the EKF process model was identified in stages by hiding select
measurements to create an unaided EKF that relied heavily on the EKF process model.
The accuracy of the unaided EKF estimate was drastically worse than the “truth” estimate
of the fully aided reference EKF. The difference between the estimates of the unaided
EKF and the reference EKF was taken to be the error in the EKF process model. The
following subsections describe the establishment of the “truth” estimate and unaided EKF
for each EKF state.
4.4.1 Constant Rotation Rate Model Uncertainty
First the error variance of the constant rotation rate model was estimated to set the
Q{4,4}, Q{5,5}, and Q{6,6} entries. Underestimating these values would smooth out the
estimated rotation rates, but would also reduce the response of the EKF to changes in
ROV rotation rate. Without rotation rate measurements, the unaided EKF assumed the
rotation rate remained the same as the rotation rate at the last time-step. A change in
rotation rate from one time-step to the next was an error in the constant rotation rate
model. This error is depicted in Figure 4-14. The variance of this error formed the
corresponding entry on the diagonal of the Q matrix.
110
ROV Roll Rate, p (rad/s)
0
True
Measurement
Model Propagation
-0.005
ep
-0.01
-0.015
tk-1 = 630
tk = 630.1
630.2
Time (s)
Figure 4-14. Error in Constant Rotation Model. The EKF process model assumed rotation
rates remained constant, so a change in rotation rate from time-step to time-step was an
error. The variances of these errors for yaw, pitch, and roll formed the corresponding
entries in Q
The Q diagonal values of the reference EKF were initially all set to 1 x 10+2 to heavily
weight the measurements. For the rotation rates p, q, r, this translates to an average
10rad/s change in rotation rate during each 0.1s time-step – much more than anticipated.
The statistics of the variance in rotation rate between each time-step for the test data were
calculated with results shown in Table 4-13.
Axis
Mean error
Variance
Roll, p
1.7x10-7 rad/s
Q {4, 4} = 2.4x10-4 (rad/s)2
Pitch, q
8.2x10-8 rad/s
Q {5,5} = 1.8x10-4 (rad/s)2
Yaw, r
1.1x10-6 rad/s
Q {6, 6} = 5.6x10-4 (rad/s)2
Table 4-13. Constant Rotation Rate Model Errors.
The initial variance settings (1 x 10+2(rad/s)2) in the Q matrix of the reference EKF
were suitably conservative, so the reference EKF estimate was heavily influenced by the
measurements. The accuracy of the gyroscope measurements (Table 4-9) , and therefore
111
of the reference EKF estimate, was one-hundred times better than the rotation model
error variance the reference EKF was used to calculate. Therefore, much confidence can
be put in the rotation rate model error variance estimate. The Q{4,4}, Q{5,5}, and
Q{6,6} entries were updated to reflect the identified rotation rate model error variance
before the reference EKF was used to identify the errors in the Euler angle model.
4.4.2 Euler Angle Model Uncertainty
Next, the uncertainty in the calculation of the Euler angles from the ROV rotation rates
p, q and r was examined to set the Q(10,10), Q(11,11), and Q(12,12) entries. This
uncertainty was due to integration truncation, biases in the rotation rates, and errors in the
Euler angles (contributing to the T2 rotation matrix). Unlike the errors in the rotation rate
model, these errors could not be clearly observed at each time-step because the compass
measurements contained high frequency noise. These errors were observed by filtering
the shallow water identification manoeuvre measurements and hiding the compass
measurements to form the unaided EKF. The drift error incurred due to loss of compass
measurements indicated the uncertainty in the Euler angle propagation model, but only
when the drift error far exceeded the accuracy of the reference EKF’s orientation
estimate.
The reference EKF’s orientation estimate relied heavily on compass
measurements.
Figure 4-15 shows a portion of the test used to identify the errors in the heading
propagation model. The compass measurements were removed from the unaided EKF,
causing the unaided EKF estimate to accumulate error. After a 1s evaluation interval, the
unaided EKF heading estimate was significantly less accurate than the reference EKF’s
estimate of heading. The difference between the estimates of the unaided EKF and the
112
reference EKF was attributed to error in the heading propagation model. The unaided
EKF estimate of Euler angles was reset to the compass measurements on 1s evaluation
intervals, so a large number of drift errors could be observed.
1.58
ROV Heading, ψ (rad)
1.56
1.54
1.52
1.5
1.48
1.46
1.44
1.42
600
601
602
603
604
605
606
Time (s)
607
608
609
610
Figure 4-15. Error Accumulation of Model Propagated ROV Heading. The unaided EKF
heading estimate (solid) diverged from the reference EKF estimate (dashed). The unaided
EKF estimate was reset on 1s evaluation intervals with the reference EKF estimate.
The drift errors resulting from excluding the compass measurements from the EKF
were observed on 1s and 10s evaluation intervals over the test data. The variances of
these errors are shown in Table 4-14. The EKF Q formulation assumed that process error
variances increased at a constant rate with time. The results verified this assumption, as
the error variance calculated using 1s evaluation intervals was observed to be
approximately ten times less than the error variance calculated using 10s evaluation
intervals. Thus the Euler angle model error variance used with the 0.1s time-step EKF
was expected to be ten times less than the error variance calculated using 1s evaluation
intervals, and one-hundred times less than that using 10s evaluation intervals.
113
Axis
Error Variance after 1s
Evaluation Intervals
Error Variance after 10s
Evaluation Intervals
Estimated Model Error
Variance
Roll, φ
4.2x10-3 rad2
1.3x10-2 rad2
Q {10,10} = 2x10-4 rad2
Pitch, θ
3.7x10-3 rad2
1.4x10-2 rad2
Q {11,11} = 2x10-4 rad2
Yaw, ψ
3.1x10-3 rad2
3.0x10-2 rad2
Q {12,12} = 3x10-4 rad2
Table 4-14. Euler Angle Model Errors. As expected, the error variance after 10s evaluation
intervals was approximately ten times that of the 1s evaluation intervals.
The EKF
increments in 0.1s time-steps, so its error variance was estimated to be one-hundredth the
error variance of the 10s evaluation intervals. Notice also that the error variances of each
axis were approximately equal since they used the same type of process and measurements.
The Q(10,10), Q(11,11), and Q(12,12) entries were updated to reflect the identified
Euler angle model error variances before the reference EKF was used to identify the
errors in the velocity model.
4.4.3 Velocity Model Uncertainty
Next, the process noise in the translational velocity model was examined. The model
error was observed by removing the DVL and SBL measurements, so the resulting
unaided EKF velocity estimates were based solely on the model’s processing of applied
thrust, hydrodynamic drag, and tether disturbance.
The resulting velocity estimates
accumulated error with time. The velocity estimates were reset to the reference EKF
velocity estimate on 10s evaluation intervals. Figure 4-16 compares the surge velocity
estimates of the unaided EKF to those of the reference EKF.
114
ROV Surge Speed, u (m/s)
0.8
0.6
0.4
0.2
0
-0.2
-0.4
570
580
590
600
610
620
630
Time (s)
640
650
660
670
Figure 4-16. Body Fixed Velocity Model Errors. Without DVL or SBL measurements, the
unaided EKF estimate (solid) diverged from the reference EKF estimate (dashed). The
unaided EKF estimate was reset to the reference EKF estimate on 10s evaluation intervals.
However, unlike the Euler angle case, damping in the velocity model stopped the error from
growing unbounded.
Since the DVL innovation variance was much larger than the estimated DVL
measurement error variance (Table 4-7), the innovation variance was assumed to be due
to model error. The velocity model error variances, Q{1,1}, Q{2,2}, and Q{3,3}, which
represent the model error accumulation at 10Hz, were set to one-fifth of the innovation
variance which was measured at 2Hz. Whereas the calculation of the Euler angle model
variance required relatively long times to distinguish the model induced error, the
velocity model error variance could be characterized on a short time scale due to accurate
DVL measurements. Also, errors in the model predicted velocity did not accumulate at
constant rates beyond a 2 second evaluation period because extreme estimates in velocity
were damped with hydrodynamic drag. Table 4-15 lists the measurements of model
115
propagated velocity error variances and states the selected model error variance
estimates.
Axis
Innovation
Variance (2Hz)
Error Variance at 10s
Evaluation Intervals
Estimated Model Error
Variance
Surge, u
3.5x10-3 (m/s)2
1.6x10-1 (m/s)2
Q {1,1} = 7x10-4 (m/s)2
Sway, v
4.8x10-3 (m/s)2
1.1x10-1 (m/s)2
Q {2, 2} = 9.6x10-4 (m/s)2
Heave, w
1.8x10-3 (m/s)2
9.0x10-1 (m/s)2
Q {3,3} = 4x10-4 (m/s)2
Table 4-15. Body Fixed Velocity Model Errors.
4.4.4 Position Model Uncertainty
The process noise of the ROV position states was determined with an EKF unaided by
the SBL and depth measurements.
ROV position tracked by the optical motion
measurement system was used instead of the reference EKF to calculate the position
error. After each evaluation period, the difference between the unaided EKF estimate of
position and the optical motion measurement was taken to be the accumulated model
error. The unaided EKF estimate was then reset to the optical motion measurement and
allowed to progress for the next evaluation period. The process was then repeated for the
duration of the shallow water identification manoeuvre. Figure 4-17 shows the resulting
error accumulated in X position after each 10s evaluation interval.
116
9
X Position, X (m)
8
7
6
5
4
3
2
570
580
590
600
610
620
630
Time (s)
640
650
660
670
Figure 4-17. Test of Position Model Uncertainty. Accumulation of error in the unaided
EKF position estimate (continuous line) was evaluated with the more accurate optical
motion measurements (broken line). The drift error was reset every 10s with the optical
data measurement.
The position model uncertainty estimates are listed in Table 4-16. Like the Euler angle
model, position error was observed to accumulate at a constant rate.
Direction
Error Variance at 1s
Evaluation Intervals
Error Variance at 10s
Evaluation Intervals
Estimated model
error variance
North, X
1.3x10-2 m2
1.1x10-1 m2
Q {7, 7} = 1x10-3 m2
West, Y
1.0x10-2 m2
1.3x10-1 m2
Q {8,8} = 1x10-3 m2
Depth, Z
4.6x10-3 m2
5.6x10-2 m2
Q {9,9} = 5x10-4 m2
Table 4-16. Position Model Errors – using optical data for reference.
4.4.5 Tether Disturbance Model Uncertainty
The tether disturbance states ( T , α , β ) were defined in ROV coordinates and modeled
as constant in the earth fixed frame (Equations (3.32) and (3.33)). However, the actual
tether disturbance fluctuated during ROV manoeuvres. The EKF estimate of tether
disturbance did change throughout the manoeuvres, but only as a result of model
117
mismatch in the ROV acceleration. The gross approximations of the tether disturbance
model produced large uncertainties in its estimates, which were reflected in large model
error variance estimates of the tether disturbance states.
Unlike the other states, tether disturbance was not experimentally measured. A “truth”
model [47, 48], in the form of the high fidelity cable and ROV simulation discussed in
Section 1.5, was used to identify errors in the process model for the tether disturbance
states. In the simulation, the ROV manoeuvred at 200m depth through the arbitrary path
shown in Figure 4-18. The surface end of the tether mimicked conventional tether
tending: the top end of the tether was deployed and retrieved to maintain a constant 20N
tension; its location moved to keep the tether near the surface vertical.
80
300s
Y Position, Y (m)
60
1800s
40
100s
20
1000s
0
-20
-60
Start
-40
-20
0
700s
20
40
X Position, X (m)
60
80
100
120
Figure 4-18. Manoeuvre for Tether Disturbance Model Error Identification (plan view). An
1800s manoeuvre was simulated at 200m depth, with the ROV starting at (0,0) and surging,
swaying, and yawing through an arbitrary path.
The simulation recorded the tether force on the ROV, along with ROV position and
velocity.
The time-series for the simulated values of the tether disturbance states
( T , α , β ) were calculated from the simulation data using:
118
T = Tx2 + Ty2 + Tz2
 Ty 

 Tx 



β = tan −1  Tz
2
2 

T
+
T
x
y


α = tan −1 
(4.5)
In Equation (4.5), Tx , Ty and Tz represent the tether disturbance in ROV coordinates.
The EKF tether disturbance model estimates ( Tˆk , αˆ k , βˆk ), were calculated by using
Equation (3.32) and Equation (3.33) to advance the simulated tension states by one
Kalman time-step:
Tˆk = Tk −1
αˆ k = α k −1 + (tk − tk −1 ) ⋅ (− rk −1 )
βˆ = β + (t − t ) ⋅ (− p sin α
k
k −1
k
k −1
k −1
(4.6)
k −1
− qk −1 cos α k −1 )
The error in the EKF tension model was the difference between the estimated values
( Tˆk , αˆ k , βˆk ) and the simulated values ( Tk , α k , β k ). Error in the tension state, T, increased
during maneuver changes. Figure 4-19 compares the tension state error to acceleration of
the ROV.
119
Figure 4-19. Influence of ROV Acceleration on Tether Tension. Tension change between
0.1s time-steps (solid) followed the constant tension model except during manoeuvre
changes (at 600s, 660s, 720s, 750s, and 780s) as indicated by ROV acceleration (dashed).
The large increase in error of the EKF tether tension model during manoeuvre changes
was accounted for by setting the estimated error variance, Q {13,13} according to a time
varying value based on the change in ROV speed between time-steps. A linear function
modeled this relationship:
Q {13,13} = E[(Tˆk − Tk ) 2 ] =ˆ 9 ×10−1 + uk − uk −1 × 103
(4.7)
Propagation errors in the α and β models were more constant over the simulated
manoeuvre, and therefore were estimated directly by taking the variance of the error
observed in the EKF estimates. Table 4-17 lists the estimated error variances of the
tether disturbance model.
120
State
Tether Tension
Tether Bearing
Tether Inclination
Symbol
T
Model Error Variance
Q {13,13} = 9 × 10−1 + uk − uk −1 × 103 N2
α
β
Q {14,14} = 3.0x10-5 rad2
Q {15,15} = 6.0x10-4 rad2
Table 4-17. Tether Disturbance Model Estimated Error Variance.
4.5 Parameter Identification Closing Remarks
The parameters that govern the ROV dynamics and Kalman gain calculations were
quantified through analysis of the shallow water identification manoeuvre. Measurement
error variances were estimated for each sensor used in the EKF. Relationships between
thrust commands and actuated thrust forces were identified with bollard pull tests. ROV
hydrodynamic parameters were identified by comparing the thrust forces with the
resulting ROV velocity. The accuracy of the ROV dynamics in advancing each EKF
state was also estimated. The EKF used these parameters to estimate the ROV position
and velocity during the near surface test manoeuvre presented in Chapter 5 and the
deepwater manoeuvre presented in Chapter 6.
121
Chapter 5. Near Surface Position Tracking Results
The EKF developed in Chapter 3 and Chapter 4 was tested with actual sensor data
collected during a near surface test manoeuvre in the shallow water test facility. The
accuracy of the EKF estimate was evaluated through comparison with the highly accurate
position data provided by the optical motion measurements that were described in
Subsection 4.1.2. The optical motion measurements were much more accurate and were
refreshed at a much higher frequency than GPS which is the conventional reference for
experimentally testing UUV KFs.
This chapter presents the experimental validation of the EKF via a near surface test
manoeuvre in the shallow water test facility. The chapter starts with a description of the
near surface test manoeuvre. Next the EKF position tracking performance is presented
and compared against the conventional SBL performance. In Section 5.5, the merits of
including the relatively expensive DVL are evaluated by examining the EKF
performance with and without DVL measurements.
5.1 The Near Surface Test Manoeuvre
In the near surface manoeuvre, the ROV had to maintain a depth of less than 1m and
stay within the confines of the shallow water test facility as long as the optical motion
122
measurement markers were connected to the ROV to avoid submerging the optical LED
markers. EKF accuracy was directly verified only at times when sufficient markers were
in field of view of the optical motion measurement system to yield a valid optically
measured ROV position. The spatial domain of the test manoeuvre was expanded by: (1)
disconnecting the communication line of the optical motion measurement system from
the ROV mast part way through the test; (2) driving the ROV out into the marina and
back; and (3) reconnecting the communication line before ending the test. Figure 5-1
shows a plan view of the test manoeuvre.
-15
Y Position (m)
-10
-5
0
5
0
5
10
15
X Position (m)
20
Figure 5-1. Plan View of the Near Surface Test Manoeuvre showing the EKF estimated
ROV path (dashed line). Most of the manoeuvre was performed inside the shallow water
test facility (shaded area denotes surrounding dock). When the ROV was within the field of
view of the optical motion measurement system (dotted trapezoid), its position could be
accurately tracked. To expand the test region, the ROV was driven out into the marina half
way through the test.
123
The expansion of the test field into the marina extended the scale on which the EKF
was tested. In addition, reconnecting the communication line of the optical motion
measurement system for the last part of the manoeuvre identified any long term drift in
the EKF position estimate and instability in the error estimate.
5.2 ROV Position Estimation
Tracking the ROV position in the horizontal plane is perhaps the most difficult but
useful part of ROV navigation. The EKF estimated the ROV position based on acoustic
ranging measurements and the estimate of the ROV velocity and orientation. In Figure
5-2, the time-series of the EKF estimate of horizontal position during the shallow water
test is compared to the acoustic and optical position measurements. The EKF estimate of
ROV depth was strongly influenced by the onboard depth sensor and is discussed
separately in the next subsection.
124
ROV X Position, X (m)
30
25
20
8
5
2
1150
1200
15
10
5
0
-20
ROV Y Position, Y (m)
1175
200
600
800
Time (s)
1000
1200
1000
1200
1
-15
2
-10
3
-5
400
1150
1175
1200
0
5
10
200
400
600
800
Time (s)
Figure 5-2. ROV Position during the Shallow Water Test. ROV horizontal position tracked
with optical measurements (dark broken line), EKF estimation (dashed line), and SBL
measurements (stars). The optical measurements were most accurate, but only available
when the ROV mast was within the optical cameras’ field of view. The EKF estimate used
the same range measurements as the SBL algorithm, but also integrated velocity and
orientation estimates to provide enhanced measurement accuracy.
The optical measurements were most accurate and used as a reference to calculate
errors in the EKF estimate and the SBL measurements. The ROV positions based on
optical measurements were linearly interpolated to synchronise with the EKF time-steps
125
within 0.1s of valid optical measurements. The same optical measurements calculated
the SBL target transducer location, and were linearly interpolated to synchronise with
SBL position measurements that were within 0.1s of valid optical measurements. Figure
5-3 shows the errors in the EKF X position estimate and the SBL X position
measurements during the near surface test manoeuvre. Table 5-1 lists the RMS errors of
the SBL measurements and the EKF estimates of both the X and Y positions.
1.5
X Position Error (m)
1
0.5
0
-0.5
-1
-1.5
-2
200
400
600
800
Time (s)
1000
1200
1400
Figure 5-3. Shallow Water Position Error. X Position difference between optical position
measurements and EKF estimate (dots appearing as broken lines) and SBL measurements
(stars).
Coordinate
X
Y
SBL
RMS Error
0.54 (2.2) m
0.82 (0.9) m
EKF Position
RMS Error
0.42 m
0.52 m
Table 5-1. RMS Error of Position Estimates during the Near Surface Test Manoeuvre.
Bracketed quantities are the variance that would have occurred if resampled to match the
EKF rate.
The perils of underwater positioning were reduced with the EKF. The EKF position
estimate was slightly more accurate and at a much higher rate than the standalone SBL
126
measurements. The SBL measurements were observed to drop out (such as between 260s
and 420s) when the acoustic signal did not properly transmit, possibly due to excessive
ambient noise, surfaced transducers, hardware error, or blockage of transmission path.
Even when no acoustic measurements were available, the EKF accurately estimated the
ROV position.
5.3 ROV Depth Estimation
The Falcon™ onboard depth sensor tracked the ROV depth with reasonable accuracy
at nearly the same frequency as the EKF. However, the EKF estimate was more accurate
than the sensor measurements. The estimated depth of the ROV during the near surface
test manoeuvre is shown in Figure 5-4. The sensor’s coarse 0.1 meter resolution and
inclusion of the of DVL measured heave rate in the EKF contributed to the filter having
the more accurate depth readings as shown in Table 5-2.
Coordinate
State
Depth
Z
Depth Sensor
RMS Error
0.13m
EKF Depth
RMS Error
0.086m
Table 5-2. RMS Error of Falcon™ Depth Sensor and the EKF Estimated Depth
127
2.4
2.1
1.8
Depth, Z (m)
1.5
0.9
0.6
0.3
0
620
640
660
680
1.2
0.9
0.6
0.3
0
200
Figure 5-4.
400
600
800
Time (s)
ROV Depth during the Near Surface Test.
1000
1200
Depth was measured by the
onboard depth sensor (star), estimated by the EKF (dashed line), and accurately tracked
with optical measurements (broken line). Notice the 0.1m resolution of the depth sensor.
5.4 Tether Disturbance Estimation
Since no force transducer was available to measure the pull of the tether on the ROV,
the absolute tether disturbance was not known. However, the tether was held slack
throughout the near surface test manoeuvre, so the tether disturbance was assumed to be
zero. The EKF estimate of tether disturbance is shown in Figure 5-5.
128
Figure 5-5. Tracking the Tether Tension. The EKF estimate of the tether tension (dashed
line) is shown with one standard deviation confidence bounds (solid line). Notice the mean
component of tether disturbance over a 10s time window was near zero, as expected because
the tether remained slack in this test. The large estimates of tension (at 530s for example)
occur during rapid manoeuvring when modeling error and measurement errors are large.
The extreme spike in the estimate at 1000s was likely caused by an unmodeled external
force, such as a collision.
The estimated tether disturbance remained less than 220N throughout the near surface
test manoeuvre. Spikes in tether disturbance exceeding 50N were unlikely to occur with
the test conditions, so the spikes larger than 50N were attributed to model mismatch with
the true ROV dynamics. This mismatch could be attributed to coupling of hydrodynamic
terms between DOFs, external forcing such as surface waves, and velocity dependence of
the thruster forcing, which were emulated in the EKF model with the tether disturbance
129
term. The tether disturbance states were not included in the EKF to accurately detect the
disturbance, but merely to approximate it in an effort to improve the kinetic model
embedded in the filter.
5.5 DVL Contribution
The DVL is expensive and relatively large, making it difficult to justify in a budget and
mount to the inspection class ROV. This section investigates the EKF performance
without the aid of DVL measurements.
5.5.1 ROV Positioning without DVL
Figure 5-6 shows the same optical and acoustic position measurements as Figure 5-2,
but now the EKF was not aided by the DVL measurements. The filtered estimate still
accurately tracked ROV position during the acoustic positioning dropout at 250 seconds.
130
30
ROV X Position, X (m)
25
20
8
5
2
1150
1200
10
5
0
-20
ROV Y Position, Y (m)
1175
15
200
600
800
Time (s)
1000
1200
1000
1200
1
-15
2
-10
3
-5
400
1150
1160
1170
1180
1190
1200
0
5
10
200
400
600
800
Time (s)
Figure 5-6. ROV Positioning without DVL. ROV horizontal position was tracked with
optical measurements (broken line), EKF without DVL (dashed line), and SBL
measurements (stars).
Table 5-3 lists the RMS errors of the SBL position measurements, the EKF position
estimate aided by the DVL, and the EKF position estimate unaided by the DVL. Figure
5-7 shows the error time-series of each position tracking method.
131
3
X Position Error (m)
2
1
0
-1
-2
-3
0
200
400
600
800
Time (s)
1000
1200
1400
Figure 5-7. Position Tracking Errors for the full EKF (dot), the EKF un-aided by DVL
(cross), and the SBL measurements (star).
Coordinate
X
Y
Pilot
RMS Error
0.54 (2.2) m
0.82 (0.9) m
Full EKF Position
RMS Error
0.42 m
0.52 m
EKF w/o DVL
RMS Error
0.59 m
0.84 m
Table 5-3. Effect of DVL on Position Estimation Accuracy. Bracketed quantities are the
variance that would have occurred if resampled to match the EKF rate.
Without the DVL measurements, the EKF estimate accuracy was degraded to below
that of the stand alone SBL measurements. However, the filter was still able to provide
greater tracking coverage than the SBL system. If the DVL is removed from the suite of
navigation hardware, it is recommended that the position model uncertainty be reidentified using the method described in Subsection 4.4.4.
5.5.2 Velocity Tracking without DVL
Without the DVL, the EKF relied on the ROV kinetic model and the rate of change of
the SBL position fixes to estimate the ROV velocity. Figure 5-8 shows the ROV surge
velocity tracked by the DVL, the full EKF, and the EKF unaided by the DVL.
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1.5
1
Surge Speed, u (m/s)
0.5
0
-0.5
0.5
-1
-1.5
0
-2
-2.5
-0.5
600
0
610
200
620
400
630
640
600
800
Time (s)
650
1000
1200
Figure 5-8. Surge Velocity Estimated by the EKF Unaided by DVL Measurements (solid
line) compared with the full EKF (dotted line) and DVL measurements (dots).
Measurements of ROV velocity significantly more accurate than the EKF estimates
and DVL measurements were not available for the near surface test manoeuvre. The
RMS errors of the DVL measurements were calculated by assuming the error variances
and biases measured during the stationary test presented in 4.2.3 were representative of
all DVL measurements. The velocity estimate of the EKF aided by the DVL was
expected to be at least as accurate as the DVL measurements. Accuracy of the velocity
estimate of the EKF unaided by the DVL was calculated using the aided EKF as a
reference. Table 5-4 lists the estimates of DVL measurement error and the unaided EKF
velocity error.
133
Coordinate
State
Surge
Sway
Heave
u
v
w
DVL Uncertainty
(Estimated RMS
Error)
6.3 x10-3 m/s
8.9 x10-3 m/s
3.2 x10-3 m/s
Table 5-4. Velocity Tracking Accuracies.
No DVL
Velocity
RMS Error
7.5x10-3 m/s
8.3x10-3 m/s
5.4x10-3 m/s
The DVL accuracy was measured with the
stationary test presented in Subsection 4.2.3.
Error in the EKF unaided by DVL
measurements was calculated using the full EKF as a reference.
The RMS difference between the unaided EKF velocity estimate and the full EKF
velocity estimate was on the order of the estimated DVL RMS errors. Therefore, the full
EKF velocity estimate was not known to be significantly more accurate than the unaided
EKF velocity estimate, and the RMS difference between the two only shows that the
unaided EKF could estimate ROV velocity nearly as accurately as the DVL
measurements.
5.6 Shallow Water Test Remarks
The EKF improved the accuracy of the position and orientation measurements.
Furthermore, the filter provided position measurements at 10Hz, much more frequently
than the SBL 0.5Hz measurements. Inclusion of the DVL measurements was found to be
necessary for significantly improving the position tracking, even though the kinetic
model enabled the EKF to estimate the ROV velocity with reasonable accuracy.
Extrapolation of these near surface results to a full scale ocean manoeuvre is discussed in
the next chapter.
134
Chapter 6. Simulated Deepwater Position Tracking
Most ROV operations occur at depths of 100m or more, beyond the safe working limits
of human divers. While the shallow water test facility provided a unique opportunity to
evaluate the navigation algorithm against the optical motion measurements, actual ROV
operations experience longer SBL ranges and significant tether tensions due to the
hydrodynamic forces that accumulate over the tether scope. The EKF performance at full
ocean scale was evaluated using a numerical simulation that included the ROV, tether
and instrument dynamics.
6.1 Deepwater Manoeuvre
ROV manoeuvres take on a variety of forms. Many missions, such as following a
submerged pipe or documenting a biological monitoring transect, are along a straight
line. Other objectives, such as finding a suitable attachment point for a recovery line,
entail rapid turning and manoeuvring within a small area. To validate the proposed EKF
at the ocean scale, a manoeuvre at 200m depth was simulated. In this manoeuvre the
ROV starts with some rapid turns, proceeds to a 30m depth change, returns to its starting
position before transiting to a waypoint 600m away, and finally holds its position. The
waypoints of this manoeuvre are listed in Table 6-1, a plan view of the ROV path is
135
shown in Figure 6-1, and the tether profiles at notable times are shown in Figure 6-2.
The simulated manoeuvre challenged the EKF to a level expected in typical deployments.
Time
Started
Target
Speed
0s
Waypoint Location
X
Y
Z
0.0m/s
0m
0m
200m
0s
1.5m/s
5m
5m
200m
13.1s
0.3m/s
-10m
10m
230m
99.4s
1.0m/s
0m
0m
240m
148.9s
1.0m/s
0m
0m
200m
246.3s
5.0m/s
600m
0m
200m
1080.7s
0.0m/s
600m
0m
200m
Table 6-1. Waypoints for the Simulated Manoeuvre.
400
10
ROV Y Position, Y (m)
300
100s
14s
5
200
260s
0
100
-5
-10
0s
170s
-5
0
5
10
0
-100
15
1080s
0
100
200
300
400
ROV X Position, X (m)
500
600
Figure 6-1. Plan View of ROV Position during the Deepwater Manoeuvre. The ROV starts
at the origin, proceeds in the Y direction, returns to the origin, and finally proceeds in the X
direction.
136
0
Depth (m)
50
13s
0s
100s
300s
149s
100
150
200
250
-20 0 20
-20 0 20 -20 0 20
-20 0 20
Position (m)
-20 0 20 40 60 80
0
Depth (m)
50
1200s
1081s
100
150 246s
800s
428s
200
250
0
100
Ship
200
300
Position (m)
Tether
ROV
400
500
600
ROV Path
Figure 6-2. Tether Profiles During the Simulated Manoeuvre. 0s: ROV starts from rest.
149s: ROV at maximum manoeuvre depth of 240m. 246s: ROV starts transit. 428s: All
350m of tether is deployed. 1081s: ROV reaches waypoint and stops. 1200s: ROV holds
position while ship approaches overhead.
6.2 Simulation Parameters
Provided the system dynamics were modelled accurately, the numerical simulation
provided a controlled deepwater environment in which to evaluate the EKF.
The
deepwater manoeuvre was simulated with the conventional tether management scheme.
137
The tether properties remained the same as those used in the numerical simulations for
the tether management development presented in Chapter 2.
With the exception of a more accurate tether disturbance model, the simulation’s ROV
model of the surge, sway, and heave DOF matched the translational model employed in
the EKF. To mimic the uncertainty evident in the parameter identification process of
Section 4.3, the ROV dynamic parameters used in the simulation were perturbed from the
parameters values used in the EKF by the estimated standard deviation of each parameter.
Table 6-2 lists the parameter values used in the EKF and the values used in the simulation
that generated the deepwater test manoeuvre. These standard deviations were calculated
by applying the regression method presented in Appendix A to the motion data collected
with the shallow water tests.
Parameter
Surge
Hydrodynamic Drag
Sway
Hydrodynamic Drag
Symbol
Best Estimate
Perturbed Estimate
Kalman Model
Simulation Model
Du
88.9 N/(m/s)
109.2 N/(m/s)
Duu
183.75 N/(m/s)2
169.5 N/(m/s)2
Dv
86.5 N/(m/s)
123.9 N/(m/s)
Dvv
541.9 5 N/(m/s)2
493.1 N/(m/s)2
Heave
Hydrodynamic Drag
Dw
173.2 N/(m/s)
225.9 N/(m/s)
Dww
230.25 N/(m/s)2
140.7 N/(m/s)2
Surge Inertia
mu
281.0 kg
291.5 kg
Sway Inertia
mv
223.8 kg
246.1 kg
Heave Inertia
mw
509.6 kg
529.6 kg
Table 6-2. Simulation Parameters. The least squares fits of the parameter identification
data were used for the kinetic model embedded in the EKF, so the parameters used for the
simulation model were perturbed by one standard deviation.
138
6.3 Instrument Simulation
The deepwater simulation results for ROV position, orientation, and velocity, along
with ship position, were sampled to generate sensor measurements. Random noise with a
Gaussian distribution was added to the exact simulated values.
The following
subsections discuss how deepwater operation was expected to alter the measurement
noise of each sensor from the shallow water operations where the noise properties were
measured.
6.3.1 IMU Measurements
The IMU is a sealed unit which, aside from power and communication lines, does not
interact with the local environment.
The rate gyroscopes, accelerometers, and
digitization hardware are sensitive to changes in temperature, but a thermocouple and
pre-calibration mitigate temperature effects on the measurements. The IMU is expected
to retain its shallow water noise variance and bias since its method of measurement is the
same for deepwater operation.
6.3.2 Compass Measurements
The fluxgate magnetic compasses also have no physical contact with the surrounding
ocean environment. They are sensitive to magnetic field disturbances, such as nearby
thruster operation, or large steel vessels. Once the ROV is near the seafloor, away from
external hard-iron sources, the compass is expected to operate as in the shallow water test
facility, so its noise characteristics were retained.
6.3.3 Depth Sensor Measurements
The Falcon™ depth sensor measures the ambient water pressure to calculate depth in
the range of 0m to 300m. The depth sensor was assumed to retain its noise variance, but
139
a 0.2m bias was added to the simulated measurements to account for errors in water
density calibration.
This bias is equivalent to a 1kg/m3 error in water density
accumulated over the 200m nominal depth of the manoeuvre.
6.3.4 DVL Measurements
The DVL was also expected to retain its noise characteristics, as most operations are
near the seafloor at altitudes less than those in the shallow water test. The 0.4s delay
observed in the shallow water DVL measurements was also introduced in the simulated
DVL measurements.
Often debris suspended in the water limit the visibility of the video camera to several
meters or less. This requires the ROV to be within 1m of the seafloor to maintain site of
it. The DVL only provides velocity measurements at altitudes between 0.5m and 65m.
When the ROV is operating outside of this range, such as near the surface over deepwater
or near the seafloor in poor visibility conditions, DVL measurements won’t be available.
Momentary DVL dropout was not directly simulated in this work, but the EKF was
verified to function both with and without the DVL measurements.
6.3.5 SBL Range Measurements
The ranges reported by the SBL system were based on time of flight, with constant
pulse frequency, so the error accrued in the SBL slant range measurements was not
expected to vary significantly from those observed at the shallow water test facility.
Signal amplitude would be lower for deepwater operations, so sensor dropout may occur
more frequently. Sound speed may vary significantly between the ROV and the surface
listening stations if a strong thermocline was present, which would cause additional error
in range measurements. The reference stations’ absolute locations, which were simulated
140
as mounted to a mobile vessel in deepwater ROV operations, would be less accurately
known, stemming from errors in ship GPS and Motion Reference Unit (MRU)
measurements.
6.3.6 SBL Reference Station Positioning
For ocean deployments, the SBL reference stations would be mounted to a surface
vessel. The vessel position and orientation would be tracked with a GPS and MRU
respectively. This work simulated operation from a 20m vessel with two reference
stations on the corners of the transom, and one on the bow. Reference station locations in
ship fixed coordinates are listed in Table 6-3
Reference Station
Coordinate
Forward
Port Aft
Starboard Aft
Bow
Symbol
Value
0.0 m
Athwartships
xref 1
yref 1
-3.0 m
Depth
zref 1
0.5 m
Forward
0.0 m
Athwartships
xref 2
yref 2
Depth
zref 2
0.5 m
Forward
20.0 m
Athwartships
xref 3
yref 3
Depth
zref 3
0.5 m
3.0 m
0.0 m
Table 6-3. Ship Mounted Reference Station Locations. These locations were converted to
an earth-fixed coordinate system using GPS and MRU measurements.
As listed in Table 6-4, white noise was added to the SBL reference station locations
with a 1.5m standard deviation (based on Kongsberg Seapath™ 100 specifications) to
model uncertainty in the GPS measurements.
Furthermore, the MRU’s orientation
measurement error was assumed to contribute little to the reference station position error.
141
Moreover, since the SBL position measurements were all relative to the ship, any bias in
ship position would directly transfer to bias in estimated ROV position.
Quantity
Symbol
Variance
Ship Position Measurement Noise
σ X2 − Ship , σ Y2− Ship
2.25 m2
Table 6-4. Ship Position Tracking Error Variance - estimated from GPS specifications,
added to all three reference station locations.
6.3.7 Acoustic Position Tracking
For comparison purposes, the SBL measured ROV location was also simulated. The
estimated SBL measurements were calculated by finding the non-linear least-squares fit
to the ROV position based on the same simulated range measurements from each of the
three reference transducers used by the EKF. The acoustically transmitted SBL depth
measurements were also simulated and included in the SBL calculated positions.
6.4 EKF Modifications for Deepwater Applications
Unlike the stationary reference station configuration used in the shallow water test
facility, the deepwater manoeuvre simulated reference stations attached to a moving ship
hull. Reference station locations were calculated based on the ship’s GPS and MRU
measurements.
The reference station position noise necessitated an increase in the
variance parameter RSBL to reflect the larger uncertainty in HSBL. Range is a non-linear
function of ship position.
For small differences between the true reference station
location ( X ref , Yref , Z ref ) and the estimated reference station location ( Xˆ ref , Yˆref , Zˆ ref ) , a
linearized range calculation suitably approximates the length of the displacement vector:
X − X tar
Y − Ytar
Z − Z tar
r ≅ r0 + ( Xˆ ref − X ref ) ref
+ (Yˆref − Yref ) ref
+ ( Zˆ ref − Z ref ) ref
r0
r0
r0
(6.1)
142
In Equation (6.1), r denotes the range from the estimated reference station location to
the target transducer location ( X tar , Ytar , Z tar ) , and r0 denotes the range from the true
reference station location to the target transducer location. The ship position error was
expected to be much smaller than the ROV range to each reference station, so Equation
(6.1) was applied to estimate the influence of ship position error on the range
measurements. The corrected range error variance estimate, denoted σ r2 , is the sum of
the variance of errors in the acoustically measured range, denoted σ r20 , and the error
variance caused by uncertain reference station locations:
σ =σ +
2
r
2
r0
( X Ship − X tar ) 2
r2
σ
2
X − Ship
+
(YShip − Ytar ) 2
r2
σ Y2− Ship
(6.2)
The EKF adjusted to account for the increased range noise was employed to process
the deepwater manoeuvre measurements simulated according to the method described in
Section 6.3. The EKF estimates are compared to the true simulation states in the next
section.
6.5 Deepwater Filter Performance Evaluation
The EKF estimates were compared against the true state values of the simulated
deepwater manoeuvre. The importance of the DVL is again investigated by comparing
the EKF performance with and without the DVL measurements. The RMS errors in the
simulated measurements and the EKF estimates of ROV position and velocity are
presented in the following subsections. The EKF estimate of tether disturbance is also
compared to the tether disturbance calculated by the high fidelity numerical simulation.
143
6.5.1 Position Tracking
The accuracies of the EKF position estimate and of the simulated SBL measurements
were quantified by comparison with the simulated position. Even though the acoustically
measured range was modeled with constant accuracy, the longer acoustic slant ranges
reduced the positioning accuracy. Table 6-5 lists the RMS position errors of the SBL, the
fully aided EKF, and the EKF without DVL measurements.
Coordinate
X
Y
SBL
RMS Error
2.7 m
17.2 m
EKF
RMS Error
1.9 m
3.5 m
EKF w/o DVL
RMS Error
2.2 m
9.2 m
Table 6-5. ROV Position Tracking Accuracy for the Deepwater Manoeuvre.
Both EKF estimates were more accurate than the SBL measurements. The EKF also
provided position updates at 10Hz - much higher than the 0.5Hz nominal SBL rate.
The ROV X position was more accurately tracked than the Y position because the ship
was aligned with X, and thus the SBL system’s reference stations were spaced further
along this direction.
Were the ship to turn 90deg, the error proportions would be
switched.
Figure 6-3 shows the ROV X Position during the deepwater manoeuvre, its estimate
made by the SBL, and its estimate made by the EKF with and without the DVL
measurements.
144
700
10
600
0
ROV X Position, X (m)
500
-10
0
100
200
300
400
300
600
200
590
100
580
1000
1100
1200
0
0
200
400
600
800
1000
1200
Time (s)
Figure 6-3. Simulated ROV X Position (dashed line) estimated with the complete EKF filter
(solid line), EKF filter without DVL (dotted line), and SBL measurements (dots).
The EKF estimate was less accurate at the start of the manoeuvre, due to bias in the
initial range measurements. At the end of the manoeuvre, the EKF closely tracked the
ROV’s true position.
Using the DVL measurements, the EKF placed more confidence in its velocity estimate
and was less influenced by the noisy acoustic range measurements, providing smoother
position estimates.
Even without the DVL, the EKF kinetic model allowed quick
response to velocity changes, such as the abrupt stop at the destination.
145
60
ROV Y Position, Y (m)
40
20
0
-20
-40
-60
100
200
300
400
500
600 700
Time (s)
800
900 1000 1100 1200
Figure 6-4. Simulated ROV Y Position (dashed line) estimated with the complete EKF filter
(solid line), EKF filter without DVL (dotted line), and SBL measurements (dots).
Figure 6-4 shows the ROV Y Position during the deepwater manoeuvre. The SBL Y
position error variance increased as the ROV moved further ahead of the ship. As the
ROV moved horizontally away from the ship, the SBL position calculation increased
reliance on the relative ranges measured by the reference transducers rather than than the
more accurately measured target transducer depth.
The benefit of including the DVL in the EKF was more pronounced in the Y position
estimate. The range measurements provide poor Y position resolution, so the improved
velocity tracking provided by the DVL allowed the EKF to generate a smooth estimate.
6.5.2 Depth Tracking
The RMS errors in the simulated depth sensor measurements and the EKF depth
estimates are shown in Table 6-6.
146
Coordinate
State
Depth
Z
Depth Sensor
RMS Error
0.275 m
EKF
RMS Error
0.215 m
EKF w/o DVL
RMS Error
0.273 m
Table 6-6. Depth Tracking Accuracy during the Deepwater Manoeuvre.
Like in the shallow water tests, the full EKF estimate of depth was slightly better than
the raw depth sensor measurements. Without the DVL, almost no accuracy improvement
was obtained in using the EKF estimate over the raw depth measurements. Most of the
error in all three sets of depth estimates was attributed to the 0.2 meter bias added to the
simulated depth measurements.
6.5.3 ROV Velocity Tracking
The RMS error in the simulated DVL measurements and the EKF velocity
measurements is shown in Table 6-7.
Direction
State
DVL measurements
RMS Error
EKF
RMS Error
EKF w/o DVL
RMS Error
Surge
u
0.08 m/s
0.04 m/s
0.15 m/s
Sway
v
0.11 m/s
0.03 m/s
0.13 m/s
Heave
w
0.023 m/s
0.02 m/s
0.05 m/s
Table 6-7. Velocity Tracking Accuracy during the Deepwater Manoeuvre
Figure 6-5 shows the ROV surge velocity tracked by the DVL and the EKFs.
147
1.5
Surge Velocity, u (m/s)
1
0.5
1.5
0
1
0.5
-0.5
0
-0.5
80
-1
0
200
400
100
120
600
Time (s)
800
140
1000
1200
Figure 6-5. EKF Velocity Tracking Performance. The EKF estimate (solid line) of ROV
surge velocity tracked the true velocity (dashed line) more accurately than the DVL
measurements (dots) throughout the simulated manoeuvre. Notice the significant errors in
the DVL measurements at 105s and 130s due to high ROV yaw rates.
The inclusion of the DVL offset from the ROV reference frame origin in the EKF
allowed unbiased processing of the DVL measurements, even during rapid yawing
activity.
148
6.5.4 Tether Disturbance Estimation
During the simulated manoeuvre, tension in the tether increased as the ROV
accelerated forward. The tension plateaued at 428s when the entire tether was deployed,
and returned to the controlled slack value once the ROV reached its final destination at
1081s.
The EKF indirectly estimated the magnitude and direction of the tether
disturbance. Figure 6-6 compares the EKF estimate of tether tension with the actual
tension calculated with numerical simulation.
450
400
350
100
80
60
Tension, T (N)
300
250
200
150
40
20
0
0
20
40
60
100
50
0
-50
0
200
400
600
800
1000
1200
Figure 6-6. Tether Tension Estimation. The full EKF estimate of tether tension (solid line)
closely tracked the actual tether tension (dashed), but without the DVL measurements, the
EKF estimate exhibited slow response (dotted).
The DVL velocity measurements were used by the EKF to identify force imbalances in
its kinetic model attributed to tether disturbance. Without these measurements, the EKF
relied on SBL range measurements to correct the kinematic model. The high uncertainty
149
in ROV position calculated from range measurements slowed the EKF’s response to
changes in tether disturbance.
The ROV moved mostly in surge during the deepwater manoeuvre, so the tether tended
to be towed out the aft end. Figure 6-7 shows the simulated tether bearing and the
corresponding EKF estimate, α.
Tether Bearing, α (rad)
3Pi/2
Pi
Pi/2
3Pi/2
Pi
0
Pi/2
0
200
-Pi/2
0
200
400
220
600
Time (s)
240
260
800
280
1000
300
1200
Figure 6-7. Tether Bearing Estimation. The EKF estimate (solid line) closely tracked the
simulated (dashed line) tether bearing, α , except during the first 100s when the ROV
performed lateral manoeuvres. Without the DVL measurements, the EKF estimate was
degraded (dotted line).
The tether bearing was most accurately estimated by the full EKF when the tether
tension was high. Apparent forcing caused by modelling inaccuracies, such as ocean
currents and parameter estimation errors was also lumped into the tether disturbance
estimate, so the actual tether disturbance was most accurately characterized by this
estimate when it was large compared to the unmodeled forces.
150
Modeling the tether direction as constant in the earth-fixed reference frame closely
matched the realized dynamics. Even when the ROV was rapidly yawing left and right
from 150s to 250s, the tether bearing was accurately estimated by the EKF.
At the start of the manoeuvre, the tether left the ROV in a near vertical configuration as
shown in Figure 6-2. When the transit manoeuvre started at 248s, the tether trailed out
the aft end of the ROV, inclined slightly above horizontal.
The estimated tether
Tether Inclination, β (rad)
inclination, β, is compared to the simulation result in Figure 6-8.
Pi/2
0
0
200
400
600
Time (s)
800
1000
1200
Figure 6-8. Tether Inclination Estimation. The full EKF (solid line) closely tracked the true
simulated (dashed line) tether inclination, β . Without the DVL measurements, the EKF
estimate exhibited slow dynamic response (dotted line).
The EKF estimate only roughly tracked the true tether inclination angle during the first
250s of the manoeuvre because unmodeled effects, such as heave-added mass error, were
large compared to the tether tension. As with the tension estimate, without the DVL, the
EKF did not have enough feedback to rapidly track changes in inclination angle.
151
The simulated manoeuvre assumed there was no ocean current. If the manoeuvre was
performed in an ocean current, the added hydrodynamic drag on the ROV would bias the
dynamics in a similar manner to tether disturbance.
The EKF estimated tether
disturbance would be tainted with the hydrodynamic disturbance. However, the main
goal of accurately tracking the ROV position would still be obtained, as the unmodeled
disturbances would be lumped into the tether disturbance states.
6.6 Deepwater Performance Remarks
When applied to the deepwater manoeuvres more likely to be performed with the
Falcon™ ROV, the EKF retained the navigation accuracy improvements found in the
shallow water tests. In moving to a ship based mounting configuration, the reference
station spacing was found to impact the SBL measurement accuracy. SBL positioning
RMS errors of 3m were calculated for the X direction and of 17m for the Y direction
(which had a shorter baseline). The EKF provided more accurate position estimates with
RMS errors of 1.9m and 3.5m in the X and Y directions, respectively. As with the
shallow water manoeuvre, the DVL was found to contribute significantly to the EKF
position estimate accuracy.
The EKF estimate of ROV velocity was more accurate than the raw DVL
measurements because it removed the DVL measurement error caused by the instrument
offset during rapid yawing. Even without the DVL, the EKF kinetic model allowed it to
estimate the ROV velocity with accuracy nearly equal to that of the DVL measurements.
152
Chapter 7. Conclusions and Recommendations
7.1 Conclusions
Tether management schemes for the Falcon™ inspection class ROV were developed
and tested with numerical simulation. A navigation suite, including instrumentation
hardware, signal routing, and measurement filtering, was developed and installed on the
Falcon™ and shown to provide position tracking superior to stand-alone SBL systems.
The research objectives set in Section 1.4 have been completed with the results
summarized in the following subsections.
7.1.1 Falcon™ ROV Parameters Identified.
The Falcon™ parameters with strong influence on the EKF model, namely the
translational DOF hydrodynamic coefficients and the thruster mapping parameters were
quantified with a series of shallow water tests. Tether material properties required for
numerical simulation of the system were measured with mechanical tests.
7.1.2 Tether Management Schemes Developed
Driving the ship to lead the ROV was found to reduce tether disturbance for sustained
manoeuvres. For long transects at 200m depth, a ship lead of 26m was found to produce
the smallest tether disturbance. A demonstration transect manoeuvre which experienced
153
tether disturbances as high as 43N using conventional tether management was shown to
experience only 20N of tether disturbance using an advanced tether management scheme.
For transits at 200m, a ship lead of 90m was found to allow the highest sustained transit
speed at slightly over 0.67m/s. Adding a depressor mass to the tether allowed transit
speeds exceeding 1m/s. The tether management schemes were developed and tested on
manoeuvres at 200m depth, but the same methodology is applicable to manoeuvres at
other depths.
7.1.3 The EKF Developed
An EKF was designed and implemented on the Falcon™ ROV. The filter evolves
position and velocity estimates using a kinetic translational model and kinematic
rotational model of the ROV and refines the estimates with feedback from SBL, DVL,
IMU, compass, and depth sensors. The Falcon™ thrust forces were tracked and provided
as an input to the EKF kinetic translational model. The classical formulation of the KF
was extended to account for nonlinearities in the ROV model and range measurement
processing. The filter’s measurement vector was also augmented to handle latency in the
DVL and SBL measurements.
Measurement noise was characterised and model
uncertainty was quantified to determine the entries of the EKF process and measurement
covariance matrices.
7.1.4 Identification of the Tether Disturbance Forces
Tether disturbance was modeled by the EKF as constant in the earth fixed frame. The
EKF initialized and updated changes to the tether disturbance as mismatches between the
model estimated forcing and the forcing that would create the system dynamics measured
by the instruments, primarily the DVL.
154
Even without a load-cell for direct feedback, the EKF estimated tether disturbance with
reasonable accuracy. No direct measure of tether disturbance was made during the
shallow water test, but the EKF estimate of tether disturbance showed good correlation
with simulated tether disturbance during the deepwater manoeuvre. Of all the sensors
used in the EKF, the DVL provided the most useful feedback for resolving tether
disturbance. Without the DVL, the tether disturbance estimate was slow to respond to
changes in actual tether disturbance.
7.1.5 Experimental Testing of the Navigation System
The EKF performance was analysed with actual measurements taken during the
shallow water test. Comparison with the highly accurate and high frequency optical
position measurements allowed quantitative analysis of the EKF position estimate
accuracy. The RMS errors of the EKF position estimate for the shallow water test
manoeuvre were over 20% less than the SBL measurement errors and updated at constant
time intervals at 10Hz. The DVL was an important contributor to the increased accuracy,
and excluding its measurements from the EKF significantly increased the estimate errors.
Table 7-1 summarizes the shallow water position tracking accuracy.
State
X Position
Y Position
Depth
Symbol
X
Y
Z
Instrument
RMS Error
0.54m
0.82m
0.13m
EKF
RMS Error
0.42m
0.52m
0.09m
EKF w/o DVL
RMS Error
0.59m
0.84m
-
Table 7-1. Summary of Shallow Water Navigation Accuracy.
Numerical simulation was used to extend the shallow water results to the deepwater
manoeuvres more commonly performed with the Falcon™ ROV. The increased slant
ranges degraded the SBL positioning accuracy, but the EKF provided position estimates
155
with RMS errors less than 4m. Simulation results were also used to evaluate the accuracy
of the velocity and tether disturbance states. Again, the estimated errors increased when
the DVL was excluded from the EKF. Table 7-2 summarizes the deepwater position and
velocity tracking accuracies.
State
Symbol
X Position
Y Position
Depth
Surge Speed
X
Y
Z
U
Instrument
RMS Error
2.7 m
17.2 m
0.275 m
0.08 m/s
EKF
RMS Error
1.9 m
3.5 m
0.215 m
0.04 m/s
EKF w/o DVL
RMS Error
2.2 m
9.2 m
0.273 m
0.15 m/s
Sway Speed
V
0.11 m/s
0.03 m/s
0.13 m/s
Heave Speed
W
0.023 m/s
0.02 m/s
0.05 m/s
Table 7-2. Summary of the Simulated Deepwater Navigation Accuracy
7.2 Future Work
Tether management and underwater navigation are continuously developing fields of
ROV operation. This work contributes to both fields, but more challenges remain to be
overcome. Several areas for future research to extend the results of this work are listed in
the following subsections.
7.2.1 Tether Disturbance Mapping
This work mapped tether disturbance over ship lead and steady-state transit speed for a
350m tether reaching to 200m depth. The dependence of tether scope and ROV depth on
tether disturbance is needed to quickly extend the tether management schemes to all
possible operating depths. For steady-state transit mapping, many relationships can be
made by shape similarities. For instance, tether disturbance increases linearly with depth
for configurations with the same scope to depth ratio.
156
7.2.2 Model Based Ship Dynamic Positioning
The performance of the PID controllers presented for depressor positioning [21] is
challenged by the depressor depth sensitivity to ship motion and the lack of actuation to
enact rapid horizontal acceleration. A controller embedded with a cable model such as in
[18] may produce better schedules of ship position and winch activity to achieve desired
depressor positioning.
However, depressor position and velocity feedback will still be
necessary to correct controller activity for the inaccuracies that are inevitable in models
of flexible tethers.
7.2.3 ROV Collision Detection
All ROV models used in this work fail to capture the contact forces resulting from
ROV collisions with the seafloor and other objects. A KF model is unlikely to have
sufficient knowledge of objects surrounding the ROV to detect, let alone model
collisions. However, the IMU acceleration measurements, thought to be too noisy to be
of use for translational navigation, may provide clear indication of a collision by sensing
the impact acceleration. Should a collision be detected, the estimated error variance of
the kinetic model could be increased to account for the unmodeled contact forces.
7.2.4 Enhanced Tether Disturbance Estimation
The IMU’s rate gyroscopes provide measurements with such accuracy and frequency
that a kinetic rotational model was deemed unnecessary for the EKF used in this work.
However, while a kinetic model is unlikely to improve ROV rotational rate estimation, it
would improve tether disturbance estimation. The torque caused by tether disturbance
could be inferred from imbalance between the model calculated rotational rates and the
IMU measured rotational rates
157
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163
Appendix A. Parameter Standard Deviations
For independently determined coefficients, such as added mass, the population
standard deviation estimate is the ratio of output standard deviation to the input standard
deviation. Assuming the variance of the data collected for the parameter identification is
equal to the variance of the population of the ROV dynamics, equation (A.1) was used to
calculate the estimate1.
σˆ βˆ =
s
∑ ( xi − x )2
(A.1)
The standard deviation estimate of parameters identified in pairs (such as quadratic
drag) is more complicated, so the Matlab function regstats was used to perform the
calculation.
In this case the uncertainty in one parameter is closely coupled to
uncertainty in the other parameter. Therefore, once one parameter is quantified (i.e. Duu),
regression must be performed again to find the other parameter’s value (i.e. Du) and
standard deviation.
1
J. L. Devore. Probability and Statistics: For Engineering and The Sciences. Brooks/Cole, 2004. pp. 522.
164
Parameter
Surge
Hydrodynamic Drag
Sway
Hydrodynamic Drag
Symbol
Du
Duu
Dv
Dvv
Dw
Best Estimate
Kalman Model
Standard
Deviation
Perturbed
Estimate
Simulation Model
88.9
20.3
109.2 N/(m/s)
183.7
19.3
(164.9)
(4.6)
169.5 N/(m/s)2
86.5
37.4
123.9 N/(m/s)
541.9
62.6
(480.5)
(12.6)
493.1 N/(m/s)2
173.2
52.7
225.9 N/(m/s)
230.2
129.9
(105.2)
(35.4)
140.7 N/(m/s)2
Heave
Hydrodynamic Drag
Dww
Surge Inertia
Mu
281.0
10.5
291.5 kg
Sway Inertia
Mu
223.8
22.2
246.1 kg
Heave Inertia
Mu
509.6
20.0
529.6 kg
Table A-1. Simulation Parameters. The least squares fits of the parameter identification
data were used for the Kalman filter model, so the parameters used for the simulation
model were perturbed by one standard deviation. Bracketed quantities are the unbiased
estimate once the other parameter is perturbed.
165
Appendix B. Tether Material Properties
Material properties of the Falcon™ ROV’s fibre-optic tether were measured with
force-deflection tests. The tether provides power to the ROV through 4 large stranded
copper wires and communication with 2 small fibre-optic lines and two small electrical
signal wires. These wires are wrapped in a VectranTM braided strength lining and two
polyethylene jacket layers. Figure B-1 shows the cross-section of the tether.
Figure B-1. Cross-section of the Falcon™ ROV’s Tether. (Adapted from Seaeye Falcon™
Technical Manual)
B.1 Torsional Stiffness
Torsional stiffness relates how much an object twists to the torque applied. The elastic
equation uses the product of Modulus of Rigidity, G, and the Polar Moment of Inertia of
the cross-section, J, to model this relationship.
φ=
TL
JG
(2.1)
The product JG is the material property needed to model torsional stiffness in the
tether. This property was measured by clamping one end of a 0.545m section of tether
and applying torque to the other end. Torque was applied by applying small weights to a
0.125m lever arm attached to the free end of the tether.
166
Load, F (N)
Deflection, δ (mm)
0
-45
1
-30
2
-5
1
-15
0
-30
1
-7
2
8
3
33
Table B-1. Torsional Deflection Data. Loads were applied to a 0.125m lever arm and the
load deflections were measured.
Angle of twist, φ, is calculated from the ratio of load deflection to lever arm length,
larm.
φ = sin −1
∂
larm
(2.2)
Applied torque was calculated by applying the cross-product of load and lever arm.
T = F ⋅ larm cos(φ )
(2.3)
167
0.4
Torque, T (Nm)
0.3
0.66 Nm/(rad/m)
0.41 Nm/(rad/m)
0.2
0.39Nm/(rad/m)
0.1
0
-0.8
-0.6
-0.4
-0.2
0
0.2
Twist per Length, φ /L (rad/m)
0.4
Figure B-2. Torque-Rotation Test to Identify Tether Torsional Stiffness.
0.6
Notice the
hysteresis present due to strong tether damping. Measured data (dots) is fitted with linear
regression to estimate slope. An average slope of 0.5 Nm/(rad/m) is selected as the torsional
stiffness.
The unbonded nature of the internal wires and plasticity of the polyethylene jackets are
the likely cause of the hysteresis.
Torsional stiffness is approximated as having a
constant value of 0.5 Nm2.
B.2 Bending Stiffness
Bending stiffness denotes the axial deflection of the tether resulting from moments
about a radial direction. The elastic flexure equation uses Modulus of Elasticity, E, and
Moment of Inertia, I, to model the relationship.
∂=
F ⋅ l3
48EI
(2.4)
The product EI was identified through a series of force deflection tests, where a 0.50m
section of tether was supported at both ends and a load was applied at the center. The
defection model equation for this configuration is used to calculate EI from the test data.
168
Deflection, δ (mm)
Load, F (N)
0
-5
2
5
4
15
6
25
8
40
10
60
8
60
6
55
4
50
2
40
0
30
Table B-2. 3-Point Bending Test Data. Loads were applied to the centre of 0.5m span.
10
155N/m
Ramp up
Load, F (N)
8
6
4
259N/m
Ramp Down
2
0
-0.01
0
0.01
0.02
0.03
0.04
Deflection, δ (m)
0.05
0.06
0.07
Figure B-3. 3-Point Bending Test to Identify Bending Stiffness EI.
Isolating EI in Equation reveals the slope of a force vs. deflection plot is related to EI
by a constant factor of L3/48.
169
Quantity
Symbol
Ramp Up
Ramp Down
Average
Force per Deflection
F/δ
155 N/m
259 N/m
207 N/m
2
2
0.54 Nm2
Bending Stiffness
EI
0.40 Nm
0.67 Nm
Table B-3. Bending Stiffness
B.3 Axial Stiffness
Axial stiffness is calculated by assuming the tether stiffness is spatially uniform and
algebraically manipulating the bending stiffness.
EA = EI ⋅
A
4
= EI ⋅ 2
I
r
(2.5)
Quantity
Symbol
Value
Axial Stiffness
EA
4.3 x 104 N
Table B-4. Axial Stiffness
Contrary to the assumption made in this calculation, the tether properties vary over the
cross-section, so the axial stiffness value may contain inaccuracies. However, directly
identifying the axial stiffness with an axial force – deflection test is also poorly
conditioned since the elongations anticipated from typical tether loadings are less than
0.5%.
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