Self-tuning Position and Force Control of a Hydraulic Manipulator Andrew C. Clegg

260 Pages·2000·2.92 MB·English

Self-tuning Position and Force Control
of a Hydraulic Manipulator
Andrew C. Clegg
Thesis submitted
for the
Degree of Doctor of Philosophy
Heriot-Watt University
Department of Computing and Electrical Engineering
November 2000
This copy of the thesis has been supplied on condition that anyone who consults it is
understood to recognise that the copyright rests with its author and that no quotation from
the thesis and no information derived from it may be published without the prior written
consent of the author or the University (as may be appropriate).
Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Principal Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . viii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Chapter 1: Introduction
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Subsea Teleoperated Robots . . . . . . . . . . . . . . . . . . . . . 2
1.3 Robot Teleassistance . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Robot Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Thesis Organisation . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2: Manipulator Control Strategies
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 The Manipulator Control Problem . . . . . . . . . . . . . . . . . . 11
2.3 Manipulator Control Schemes . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Joint Space Control Schemes . . . . . . . . . . . . . . . . 13
2.3.2 Cartesian Space Control Schemes . . . . . . . . . . . . . . 14
2.3.3 Constrained Motion Control Schemes . . . . . . . . . . . . . 16
2.4 Methods for Robot Control . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Model Based Control Techniques . . . . . . . . . . . . . . . 23
2.4.2 Optimal Control Methods . . . . . . . . . . . . . . . . . . 28
2.4.3 Robust Control Strategies . . . . . . . . . . . . . . . . . . 29
2.4.4 Adaptive Controllers . . . . . . . . . . . . . . . . . . . . 31
2.4.5 Other Control Schemes . . . . . . . . . . . . . . . . . . . 35
2.5 Self-tuning Pole Placement Robot Controllers . . . . . . . . . . . . . 36
2.5.1 Selection of Self-tuning Pole Placement for Robot Control . . . . . 37
2.5.2 The Proposed Self-tuning Pole Placement Robot Controllers . . . . 38
2.5.3 Previously Proposed Self-tuning Robot Controllers . . . . . . . . 39
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 3: Manipulator, Actuator and Contact Modelling
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Experimental Manipulator . . . . . . . . . . . . . . . . . . . . . 47
3.3 Kinematic Manipulator Model . . . . . . . . . . . . . . . . . . . . 48
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3.4 Dynamic Manipulator Model . . . . . . . . . . . . . . . . . . . . 51
3.4.1 Modelling of Electrohydraulic Servovalves . . . . . . . . . . . 52
3.4.2 Linear Hydraulic Actuators for Robots . . . . . . . . . . . . . 54
3.4.3 Linear Hydraulic Actuators Acting About a Pivot . . . . . . . . 58
3.4.4 Static Characteristics of Linear Hydraulic Actuators . . . . . . . 60
3.4.5 Hydraulically Actuated Robot Model . . . . . . . . . . . . . 62
3.5 Environment Model . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6 Hydraulic Manipulator Model Realisation . . . . . . . . . . . . . . . 64
3.6.1 Model Initial Conditions . . . . . . . . . . . . . . . . . . 65
3.6.2 Controller Model Realisation . . . . . . . . . . . . . . . . 66
3.6.3 Model Integration Algorithm . . . . . . . . . . . . . . . . 66
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Chapter 4: Self-tuning Controller Theory for Robot Applications
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Self-tuning Pole Placement Controllers . . . . . . . . . . . . . . . . 70
4.2.1 The SISO Process Model . . . . . . . . . . . . . . . . . . 71
4.2.2 SISO System Identification . . . . . . . . . . . . . . . . . 72
4.2.3 SISO Pole Placement Controller . . . . . . . . . . . . . . . 76
4.2.4 Operational Issues of Self-tuning Controllers . . . . . . . . . . 80
4.3 Application of SISO Self-tuning Controllers to Robot Control . . . . . . . 83
4.4 Multivariable Self-tuning Control . . . . . . . . . . . . . . . . . . 86
4.4.1 The MIMO Process Model . . . . . . . . . . . . . . . . . 88
4.4.2 MIMO System Identification . . . . . . . . . . . . . . . . 89
4.4.3 MIMO Pole Placement Controller . . . . . . . . . . . . . . 91
4.5 MIMO Self-tuning Control of Robots . . . . . . . . . . . . . . . . . 93
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Chapter 5: SISO Self-tuning Pole Placement Joint Angle Control
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3 Practical SISO System Identification . . . . . . . . . . . . . . . . . 101
5.3.1 Operational Issues for Practical System Identification . . . . . . . 106
5.3.2 Effect of Different Identification Algorithms . . . . . . . . . . 108
5.3.3 Effect of Different Model Orders . . . . . . . . . . . . . . . 110
5.4 Off-line PID Tuning . . . . . . . . . . . . . . . . . . . . . . . . 111
5.5 SISO Self-tuning Pole Placement Join Angle Control. . . . . . . . . . . 114
5.5.1 Effect of Different Model Orders . . . . . . . . . . . . . . . 116
5.5.2 Effect of Different Identification Algorithms . . . . . . . . . . 118
5.5.3 Effect of Different Operating Conditions . . . . . . . . . . . . 120
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5.5.4 Static Accuracy of Self-tuning Controllers . . . . . . . . . . . 123
5.5.5 Effect of Coupling Between Joints . . . . . . . . . . . . . . 124
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Chapter 6: Fixed Gain Hybrid Position/Force Control
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Practical Fixed Gain Hybrid Position/Force Control . . . . . . . . . . . 128
6.3 Hybrid Position/Force Control Applied to the Restricted TA9 . . . . . . . 130
6.3.1 Coordinate Systems and Transformations Used . . . . . . . . . 131
6.3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . 132
6.3.3 Controller Implementation . . . . . . . . . . . . . . . . . 135
6.3.4 Operation of Experimental Hybrid Position/Force Controller . . . . 137
6.3.5 Development Process for the Hybrid Position/Force Controller . . . 138
6.4 Experimental Hybrid Position/Force Control Results . . . . . . . . . . . 140
6.4.1 Experimental Tests Performed . . . . . . . . . . . . . . . . 141
6.4.2 Principal Results at Nominal Conditions . . . . . . . . . . . . 142
6.4.3 Effect of Different Contact Positions . . . . . . . . . . . . . 145
6.4.4 Effect of Using a Modified Position Reference Trajectory . . . . . 148
6.4.5 Effect of Different Levels of Commanded Force . . . . . . . . . 149
6.4.6 Effect of Different Sampling Rates . . . . . . . . . . . . . . 150
6.5 Practical Manipulation Tasks . . . . . . . . . . . . . . . . . . . . 150
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Chapter 7: Self-tuning Hybrid Position/Force Control
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.2 Self-tuning Pole Placement Hybrid Position/Force Control . . . . . . . . 158
7.3 Utilisation of Simulations . . . . . . . . . . . . . . . . . . . . . 161
7.3.1 Simulation Model Validation . . . . . . . . . . . . . . . . 162
7.4 Self-tuning Hybrid Position/Force Control Development . . . . . . . . . 165
7.4.1 MIMO System Identification Operation . . . . . . . . . . . . 165
7.4.2 MIMO Model Order and Structure Selection . . . . . . . . . . 166
7.4.3 Self-tuning Hybrid Position/Force Control Operation . . . . . . . 168
7.5 Self-tuning Hybrid Position/Force Control Results . . . . . . . . . . . . 169
7.5.1 Simulation Tests Performed . . . . . . . . . . . . . . . . . 170
7.5.2 Principal Results at Nominal Conditions . . . . . . . . . . . . 171
7.5.3 Effect of Different Environmental Stiffnesses . . . . . . . . . . 174
7.5.4 Effect of Different Contact Positions . . . . . . . . . . . . . 179
7.5.5 Effect of Different Levels of Commanded Force . . . . . . . . . 183
7.5.6 Effect of Different Hydraulic Fluid Compressibility . . . . . . . 185
7.5.7 Effect of Using a Modified Reference Trajectories . . . . . . . . 186
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7.6 Comparison Between Self-tuning and Robust Control Schemes. . . . . . . 187
7.6.1 Description of VSC-HF Controller . . . . . . . . . . . . . . 187
7.6.2 Comparison of Results . . . . . . . . . . . . . . . . . . . 188
7.7 Experimental Self-tuning Hybrid Position/Force Control . . . . . . . . . 190
7.7.1 Practical MIMO System Identification . . . . . . . . . . . . . 191
7.7.2 Development of the Self-tuning Hybrid Position/Force Controller . . 193
7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Chapter 8: Conclusions
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.2 Author's Contributions . . . . . . . . . . . . . . . . . . . . . . . 198
8.3 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . 198
Appendix A: TA9 Manipulator Model Parameters and Simulation Files
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
A.2 TA9 Model Parameters . . . . . . . . . . . . . . . . . . . . . . 202
A.3 Useful Conversions . . . . . . . . . . . . . . . . . . . . . . . . 206
A.4 TA9 Dynamic and Kinematic Model Matrices . . . . . . . . . . . . . 206
A.5 MATLAB/SIMULINK Simulation and Modelling Files . . . . . . . . . 208
Appendix B: Bierman U/D Factorisation Algorithm
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
B.2 BUD-RLS Algorithm . . . . . . . . . . . . . . . . . . . . . . . 217
Appendix C: Explicit Solutions for Self-tuning Pole Placement Controllers
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
C.2 Self-tuning PID Controller Design . . . . . . . . . . . . . . . . . . 220
C.3 Self-tuning Controller Design for n = 3, n = 2 . . . . . . . . . . . . . 222
a b
C.4 MIMO Self-tuning PID Controller Design . . . . . . . . . . . . . . . 224
C.5 MIMO Self-tuning Controller Design for n = 3, n = 2 . . . . . . . . . . 225
a b
C.6 Pseudo-Commutivity Transformation . . . . . . . . . . . . . . . . . 226
List of References . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
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List of Figures
1.1 Teleassistance Functional Architecture . . . . . . . . . . . . . . . . . 4
2.1 Joint Space and Cartesian Space Control Schemes . . . . . . . . . . . . 15
2.2 Explicit and Implicit Force Control Schemes . . . . . . . . . . . . . . 18
2.3 Hybrid Position/Force Control . . . . . . . . . . . . . . . . . . . . 21
2.4 Model Based Controllers . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Variable Structure Control . . . . . . . . . . . . . . . . . . . . . 30
2.6 Generalised Adaptive Controller . . . . . . . . . . . . . . . . . . . 32
3.1 Slingsby TA9 Underwater Manipulator . . . . . . . . . . . . . . . . 48
3.2 Plan View of Restricted TA9 Configuration . . . . . . . . . . . . . . 49
3.3 Servovalve Schematic Diagram . . . . . . . . . . . . . . . . . . . 53
3.4 Linear Hydraulic Actuator . . . . . . . . . . . . . . . . . . . . . 55
3.5 Linear Hydraulic Actuator acting about a Pivot . . . . . . . . . . . . . 58
3.6 Static Characteristics for Hydraulic and Ideal Actuators . . . . . . . . . . 61
3.7 SIMULINK Graphical Model of a Hydraulic Actuator . . . . . . . . . . 65
4.1 Self-tuning Controller Functional Structure . . . . . . . . . . . . . . 70
4.2 Incremental Self-tuning Controller Structure . . . . . . . . . . . . . . 77
4.3 Alternative Incremental Self-tuning Controller Structure . . . . . . . . . 79
5.1 Response of Forearm Rotate Joint under Fixed Gain PI Control . . . . . . 102
5.2 Fixed Gain PI Controller Output . . . . . . . . . . . . . . . . . . . 102
5.3 RLS Parameter Estimates for Forearm Rotate Joint . . . . . . . . . . . 103
5.4 RLS Estimates of Poles, Zeros and Gain for Forearm Rotate Joint . . . . . . 104
5.5 Prediction Error for RLS System Identification . . . . . . . . . . . . . 105
5.6 Effect of using Different (cid:1)(0) on the a Parameter Estimate . . . . . . . . 107
1
5.7 Effect of using Different (cid:2) on the a Parameter Estimate . . . . . . . . . 107
1
5.8 Effect of using a priori Parameter Estimates . . . . . . . . . . . . . . 108
5.9 Effect of model order on Prediction Error . . . . . . . . . . . . . . . 111
5.10 Estimated Proportional Gains for PI and PID Controllers . . . . . . . . . 112
5.11 Response of Fixed Gain PI and PID Controllers . . . . . . . . . . . . 113
5.12 Response of Self-tuning Controller . . . . . . . . . . . . . . . . . 115
5.13 Self-tuning Controller Output . . . . . . . . . . . . . . . . . . . 115
5.14 Response for Different Desired Polynomials . . . . . . . . . . . . . . 116
5.15 Effect of using Different Estimation Algorithms . . . . . . . . . . . . 119
5.16 Response of Self-tuning Controller (n = 3, n = 2, n = 1) under
a b d
Conditions a) to d) . . . . . . . . . . . . . . . . . . . . . . . 122
5.17 Response of Self-tuning PID Controller under Conditions a) to d) . . . . . 122
5.18 Response of Fixed Gain PI Controller under Conditions a) to d) . . . . . . 122
5.19 Static Response of Elbow Joint under Fixed Gain and Self-tuning Control . . 124
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6.1 Fixed Gain Hybrid Position/Force Control using Joint Space PID Controllers 129
6.2 TA9 Manipulator Performing Hybrid Position/Force Task . . . . . . . . . 133
6.3 Experimental 2 DOF Fixed Gain Hybrid Position/Force Control . . . . . . 135
6.4 Hybrid Position/Force Control Results at Nominal Conditions . . . . . . . 143
6.5 Orthogonal Position and Force Measurements . . . . . . . . . . . . . 143
6.6 Control Signals for Hybrid Position/Force Control Task . . . . . . . . . 145
6.7 RMS Position and Force Errors for Different Contact Positions . . . . . . . 146
6.8 Elements of the J T((cid:3)) Matrix . . . . . . . . . . . . . . . . . . . . 146
6.9 Elements of the J -1((cid:3)) Matrix . . . . . . . . . . . . . . . . . . . . 147
6.10 Variation of Position Control Loop Response for 2 DOF Cartesian Controller 147
6.11 Hybrid Position/Force Control Results with Ramped Position Reference . . 149
6.12 Automated Insertion of a Subsea Connector . . . . . . . . . . . . . . 151
6.13 Forces and Torques During a Teleoperated Insertion . . . . . . . . . . 152
6.14 Controller Structure for Insertion Task . . . . . . . . . . . . . . . . 153
6.15 Forces and Torques During an Automatic Insertion . . . . . . . . . . . 154
7.1 Self-tuning Pole Placement Hybrid Position/Force Controller . . . . . . . 159
7.2 MIMO Self-tuning Controller Configuration . . . . . . . . . . . . . . 160
7.3 Experimental Determination of k . . . . . . . . . . . . . . . . . . 163
leak
7.4 Simulated Fixed Gain Hybrid Position/Force Control Results . . . . . . . 164
7.5 Self-tuning Hybrid Position/Force Control Results at Nominal Conditions . . 172
7.6 Control Signals for Self-tuning Hybrid Position/Force Controller . . . . . . 172
7.7 Fixed Gain PID Hybrid Position/Force Control Results at Nominal Conditions 173
7.8 Fixed Gain PP Hybrid Position/Force Control Results at Nominal Conditions 174
7.9 Self-tuning Hybrid Position/Force Control Results for Different Stiffnesses . . 175
7.10 Fixed Gain PP Hybrid Position/Force Control Results for Different Stiffnesses 176
7.11 Hybrid Position/Force Control Results for Increasing Stiffnesses . . . . . . 178
7.12 Hybrid Position/Force Control Results for Decreasing Stiffnesses . . . . . 178
7.13 Self-tuning Controller Results for Different Contact Positions . . . . . . . 180
7.14 Fixed Gain PP Controller Results for Different Contact Positions . . . . . 181
7.15 Hybrid Position/Force Control Results for Increasing Contact Positions . . . 182
7.16 Self-tuning Controller Results for Decreasing Contact Positions . . . . . . 184
7.17 Fixed Gain PP Controller Results for Decreasing Contact Positions . . . . 184
7.18 Hybrid Position/Force Control Results for Increasing Applied Force . . . . 185
7.19 Effect of Different Stiffnesses on Self-tuning and VSC-HF Controllers . . . 189
7.20 Effect of Oil Compressibility on Self-tuning and VSC-HF Controllers . . . 189
7.21 Effect of Different (cid:2) on the a Parameter Estimate . . . . . . . . . . . 192
111
7.22 Response of Different Experimental Controller Structures . . . . . . . . 194
A.1 SIMULINK Diagram for Self-tuning Hybrid Position/Force Controller . . . 209
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List of Tables
2.1 Different SISO Self-tuning Controllers used for Robot Control . . . . . . . 41
2.2 Different MIMO Self-tuning Controllers used for Robot Control . . . . . . 43
3.1 Variation of Bulk Modulus with Fluid Temperature . . . . . . . . . . . 57
4.1 Different Model Orders and Structures used for SISO Self-tuning Control of
Manipulator Joints . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Different Model Orders and Structures used for MIMO Self-tuning Control of
Manipulators . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1 System Identification Computational Requirements . . . . . . . . . . . 109
5.2 Controller Gains Obtained by System Identification . . . . . . . . . . . 113
5.3 Self-tuning Controller Errors for Different Model Orders . . . . . . . . . 117
5.4 Self-tuning Controller Computational Requirements . . . . . . . . . . . 118
5.5 Controller Errors for Different RLS Algorithms . . . . . . . . . . . . . 120
7.1 RMS A Priori Prediction Errors for Different Model Orders . . . . . . . . 167
7.2 RMS Force and Position Errors for Different Stiffnesses . . . . . . . . . 177
7.3 RMS Force and Position Errors for Different Contact Positions . . . . . . . 182
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Principal Abbreviations
ADC Analogue to Digital Convertor
ARMAX AutoRegressive Moving Average Exogenous
ATI Assurance Technologies Inc.
BUD-RLS Bierman U-D Factorisation Recursive Least Squares
DAC Digital to Analogue Convertor
DOF Degrees Of Freedom
DSP Digital Signal Processor
EASY-RLS Simplified Matrix Inversion Lemma Recursive Least Squares
flops floating point operations
GPP Generalised Pole Placement
GUI Graphical User Interface
LIRMM Laboratoire d'Informatique, de Robotique et de Microélectric de
Montpellier
LQG Linear Quadratic Gaussian
LSI Loughborough Sound Images
MIL-RLS Matrix Inversion Lemma Recursive Least Squares
MIMO Multi-Input Multi-Output
MRAC Model Reference Adaptive Controller
MV Minimum Variance
PP Pole Placement
RLS Recursive Least Squares
RMS Root Mean Square
ROV Remotely Operated Vehicle
SEL Slingsby Engineering Limited
SISO Single-Input Single-Output
VSC Variable Structure Control
VSC-HF Variable Structure Control - High Frequency
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Acknowledgements
Firstly, I would like to thank my supervisors Dr. Matt Dunnigan and Prof. Dave
Lane for their support and enthusiasm throughout the years. I would particularly like to
thank Dave for establishing (and continuing long past my departure) an excellent research
environment in the Ocean Systems Laboratory, which provided the motivation and
emphasis for my work. From Matt I gained an excellent understanding of control
engineering, a subject that I now feel at least competent in. I am indebted to both of them
for their many suggestions and corrections to this thesis.
I would also like to thank all of those people I worked with during the course of this
research, in particular Andrew Quinn, Phil Knightbridge, Alistair Houstin, and the staff of
the Mechanical Workshop who helped keep the robots going. This work was undertaken
under several research projects, namely TUUV (Technology for Unmanned Underwater
Vehicles) and UNION (Underwater Intelligent Operation and Navigation). I must extend
my gratitude to those companies that sponsored this research work. I hope you found it
worthwhile.
Thanks go to all of my family, friends and colleagues (both past and present).
Finally, I will be forever grateful to Lorna without whose love and support this work would
still only be "nearly there". Thank you.
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