Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach

Contents......Page 10
Preface......Page 8
1 Introduction......Page 13
Free space tracking of a rigid robot......Page 14
Compliant motion control of a rigid robot......Page 15
Consideration of the actuator dynamics......Page 16
The regressor-free adaptive controller design......Page 17
The FAT-based design......Page 18
Organization of the book......Page 19
2.2 Vector Spaces......Page 23
2.2.1 Metric space......Page 25
2.2.2 Normed vector space......Page 26
2.3 Best Approximation Problem in Hilbert Space......Page 27
2.4 Orthogonal Functions......Page 29
Examples of orthonormal functions......Page 30
2. Chebyshev polynomials......Page 31
4. Hermite polynomials......Page 32
5. Laguerre polynomials......Page 33
6. Bessel polynomials......Page 34
7. Fourier series......Page 35
2.5.1 Properties of matrices......Page 36
2.5.2 Differential calculus of vectors and matrices......Page 38
2.6.1 Vector norms......Page 40
2.6.2 Matrix norms......Page 41
2.6.3 Function norms and normed function spaces......Page 42
2.7 Representations for Approximation......Page 43
2.8.1 Concepts of stability......Page 47
Lyapunov stability theorem for non-autonomous systems......Page 49
Barbalat’s lemma......Page 50
2.9 Sliding Control......Page 51
Smoothed sliding control law......Page 54
2.10.1 MRAC of LTI scalar systems......Page 57
2.10.2 MRAC of LTI systems: vector case......Page 60
2.10.3 Persistent excitation......Page 62
2.10.4 Robust adaptive control......Page 66
Dead-Zone......Page 67
s-modification......Page 68
2.11 General Uncertainties......Page 69
2.11.1 MRAC of LTV systems......Page 70
2.11.2 Sliding control for systems with unknown variation bounds......Page 71
Bound estimation for uncertain parameter......Page 72
2.12 FAT-Based Adaptive Controller Design......Page 73
FAT-based MRAC for LTV systems......Page 74
Consideration of approximation error......Page 75
The case when the bound for the approximation error is known......Page 81
3.2 Rigid Robot......Page 83
3.3 Rigid Robot Interacting with Environment......Page 85
3.4 Electrically-Driven Rigid Robot......Page 87
3.5 Electrically-Driven Rigid Robot Interacting with Environment......Page 88
3.6 Flexible Joint Robot......Page 89
3.7 Flexible Joint Robot Interacting with Environment......Page 90
3.8 Electrically-Driven Flexible Joint Robot......Page 91
3.10 Conclusions......Page 92
4.1 Introduction......Page 95
4.2 Review of Conventional Adaptive Control for Rigid Robots......Page 97
4.3 Slotine and Li’s Approach......Page 99
4.4 The Regressor Matrix......Page 101
4.5 FAT-Based Adaptive Controller Design......Page 103
4.6 Consideration of Actuator Dynamics......Page 113
4.6.1 Regressor-based adaptive control......Page 115
4.6.2 Regressor-free adaptive control......Page 117
4.7 Conclusions......Page 140
5.1 Introduction......Page 141
5.2 Impedance Control and Adaptive Impedance Control......Page 142
5.3 Regressor-Based Adaptive Impedance Controller Design......Page 146
5.4 FAT-Based Adaptive Impedance Controller Design......Page 148
5.5 Consideration of Actuator Dynamics......Page 158
5.5.1 Regressor-based adaptive controller......Page 159
5.5.2 Regressor-free adaptive controller......Page 160
5.6 Conclusions......Page 174
6.1 Introduction......Page 175
6.2 Control of Known Flexible Joint Robots......Page 176
6.3 Regressor-Based Adaptive Control of Flexible Joint Robots......Page 179
6.4 FAT-Based Adaptive Control of Flexible Joint Robots......Page 180
6.5 Consideration of Actuator Dynamics......Page 193
6.5.1 Regressor-based adaptive controller design......Page 196
6.5.2 Regressor-free adaptive controller design......Page 198
6.6 Conclusions......Page 212
7.1 Introduction......Page 213
7.2 Impedance Control of Known Flexible Joint Robots......Page 214
7.3 Regressor-Based Adaptive Impedance Control of Flexible Joint Robots......Page 217
7.4 Regressor-Free Adaptive Impedance Control of Flexible Joint Robots......Page 219
7.5 Consideration of Actuator Dynamics......Page 232
7.5.1 Regressor-based adaptive controller design......Page 235
7.5.2 Regressor-free adaptive controller design......Page 236
7.6 Conclusions......Page 251
Appendix......Page 253
References......Page 259
Symbols, Definitions and Abbreviations......Page 269
Index......Page 273