Table of Contents
Preface vii
1 Introduction 1
2 Preliminaries 11
2.1 Introduction 11
2.2 Vector Spaces 11
2.2.1 Metric space 13
2.2.2 Normed vector space 14
2.3 Best Approximation Problem in Hilbert Space 15
2.4 Orthogonal Functions 17
2.5 Vector and Matrix Analysis 24
2.5.1 Properties of matrices 24
2.5.2 Differential calculus of vectors and matrices 26
2.6 Various Norms 28
2.6.1 Vector norms 28
2.6.2 Matrix norms 29
2.6.3 Function norms and normed function spaces 30
2.7 Representations for Approximation 31
2.8 Lyapunov Stability Theory 35
2.8.1 Concepts of stability 35
2.8.2 Lyapunov stability theorem 37
2.9 Sliding Control 39
2.10 Model Reference Adaptive Control 45
2.10.1 MRAC of LTI scalar systems 45
2.10.2 MRAC of LTI systems: vector case 48
2.10.3 Persistent excitation 50
2.10.4 Robust adaptive control 54
2.11 General Uncertainties 57
2.11.1 MRAC of LTV systems 58
2.11.2 Sliding control for systems with unknown variation bounds 59
2.12 FAT-Based Adaptive Controller Design 61
3 Dynamic Equations for Robot Manipulators 71
3.1 Introduction 71
3.2 Rigid Robot 71
3.3 Rigid Robot Interacting with Environment 73
3.4 Electrically-Driven Rigid Robot 75
3.5 Electrically-Driven Rigid Robot Interacting with Environment 76
3.6 Flexible Joint Robot 77
3.7 Flexible Joint Robot Interacting with Environment 78
3.8 Electrically-Driven Flexible Joint Robot 79
3.9 Electrically-Driven Flexible Joint Robot Interacting with Environment 80
4 Adaptive Control of Rigid Robots 83
4.1 Introduction 83
4.2 Review of Conventional Adaptive Control for Rigid Robots 85
4.3 Slotine and Li's Approach 87
4.4 The Regressor Matrix 89
4.5 FAT-Based Adaptive Controller Design 91
4.6 Consideration of Actuator Dynamics 101
4.6.1 Regressor-based adaptive control 103
4.6.2 Regressor-free adaptive control 105
5 Adaptive Impedance Control of Rigid Robots 129
5.1 Introduction 129
5.2 Impedance Control and Adaptive Impedance Control 130
5.3 Regressor-Based Adaptive Impedance Controller Design 134
5.4 FAT-Based Adaptive Impedance Controller Design 136
5.5 Consideration of Actuator Dynamics 146
5.5.1 Regressor-based adaptive controller 147
5.5.2 Regressor-free adaptive controller 148
6 Adaptive Control of Flexible Joint Robots 163
6.1 Introduction 163
6.2 Control of Known Flexible Joint Robots 164
6.3 Regressor-Based Adaptive Control of Flexible Joint Robots 167
6.4 FAT-Based Adaptive Control of Flexible Joint Robots 168
6.5 Consideration of Actuator Dynamics 181
6.5.1 Regressor-based adaptive controller design 184
6.5.2 Regressor-free adaptive controller design 186
7 Adaptive Impedance Control of Flexible Joint Robots 201
7.1 Introduction 201
7.2 Impedance Control of Known Flexible Joint Robots 202
7.3 Regressor-Based Adaptive Impedance Control of Flexible Joint Robots 205
7.4 Regressor-Free Adaptive Impedance Control of Flexible Joint Robots 207
7.5 Consideration of Actuator Dynamics 220
7.5.1 Regressor-based adaptive controller design 223
7.5.2 Regressor-free adaptive controller design 224
Appendix 241
References 247
Symbols, Definitions and Abbreviations 257
Index 261
