 | Lyapunov-based control of robotic systems / A.Behal, W.Dixon, D.M.Dawson, B.Xian. - Boca Raton: CRC Press, 2010. - xiv, 375 p. - (Automation and control engineering). - Incl. bibl. ref. - Ind.: p.373-375. - ISBN 978-0-8493-7025-0
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Preface ........................................................ xi
1 Introduction ................................................. 1
1.1 History of Robotics ..................................... 1
1.2 Lyapunov-Based Control Philosophy ....................... 3
1.3 The Real-Time Computer Revolution ....................... 5
References ................................................... 7
2 Robot Control ................................................ 9
2.1 Introduction ............................................ 9
2.2 Modeling and Control Objective ......................... 10
2.2.1 Robot Manipulator Model and Properties .......... 10
2.2.2 Control Objective ............................... 12
2.3 Computed Torque Control Approaches ..................... 12
2.3.1 PD Control ...................................... 12
2.3.2 Robust Control .................................. 15
2.3.3 Sliding Mode Control ............................ 16
2.4 Adaptive Control Design ................................ 17
2.4.1 Direct Adaptive Control ......................... 18
2.4.2 Neural Network-Based Control .................... 24
2.5 Task-Space Control and Redundancy ...................... 28
2.5.1 Kinematic Model ................................. 29
2.5.2 Control Objective and Error System
Formulation ..................................... 30
2.5.3 Computed Torque Control Development and Stabil
ity Analysis .................................... 32
2.5.4 Adaptive Control Extension ...................... 33
References .................................................. 34
3 Vision-Based Systems ........................................ 37
3.1 Introduction ........................................... 37
3.2 Monocular Image-Based Geometry ......................... 41
3.2.1 Fixed-Camera Geometry ........................... 41
3.2.2 Euclidean Reconstruction ........................ 44
3.2.3 Camera-in-Hand Geometry ......................... 46
3.2.4 Homography Calculation .......................... 47
3.2.5 Virtual Parallax Method ......................... 50
3.3 Visual Servo Tracking .................................. 51
3.3.1 Control Objective ............................... 51
3.3.2 Control Formulation ............................. 54
3.3.3 Stability Analysis .............................. 56
3.3.4 Camera-in-Hand Extension ........................ 57
3.3.5 Simulation Results .............................. 58
3.4 Continuum Robots ....................................... 65
3.4.1 Continuum Robot Kinematics ...................... 69
3.4.2 Joint Variables Extraction ...................... 72
3.4.3 Task-Space Kinematic Controller ................. 74
3.4.4 Simulations and Discussion ...................... 76
3.5 Mobile Robot Regulation and Tracking ................... 78
3.5.1 Regulation Control .............................. 79
3.5.2 Tracking Control ................................ 93
3.6 Structure from Motion ................................. 107
3.6.1 Object Kinematics .............................. 107
3.6.2 Identification of Velocity ..................... 108
3.6.3 Camera-in-Hand Extension ....................... 113
3.6.4 Simulations and Experimental Results ........... 119
3.7 Notes ................................................. 125
References ................................................. 129
4 Path Planning and Control .................................. 141
4.1 Introduction .......................................... 141
4.2 Velocity Field and Navigation Function Control for
Manipulators .......................................... 144
4.2.1 System Model ................................... 145
4.2.2 Adaptive VFC Control Objective ................. 146
4.2.3 Navigation Function Control Extension .......... 150
4.2.4 Experimental Verification ...................... 154
4.3 Velocity Field and Navigation Function Control for
WMRs .................................................. 163
4.3.1 Kinematic Model ................................ 163
4.3.2 WMR Velocity Field Control ..................... 164
4.3.3 WMR Navigation Function Control Objective ...... 174
4.4 Vision Navigation ..................................... 181
4.4.1 Geometric Modeling ............................. 184
4.4.2 Image-Based Path Planning ...................... 187
4.4.3 Tracking Control Development ................... 191
4.4.4 Simulation Results ............................. 194
4.5 Optimal Navigation and Obstacle Avoidance ............. 209
4.5.1 Illustrative Example: Planar PBVS .............. 213
4.5.2 6D Visual Servoing: Camera-in-Hand ............. 218
4.6 Background and Notes .................................. 222
References ................................................. 225
5 Human Machine Interaction .................................. 233
5.1 Introduction .......................................... 233
5.2 Exercise Machine ...................................... 235
5.2.1 Exercise Machine Dynamics ...................... 236
5.2.2 Control Design with Measurable User Input ...... 237
5.2.3 Desired Trajectory Generator ................... 239
5.2.4 Control Design without Measurable User Input ... 241
5.2.5 Desired Trajectory Generator ................... 246
5.2.6 Experimental Results and Discussion ............ 247
5.3 Steer-by-Wire ......................................... 249
5.3.1 Control Problem Statement ...................... 254
5.3.2 Dynamic Model Development ...................... 255
5.3.3 Control Development ............................ 258
5.3.4 Stability Analysis ............................. 259
5.3.5 Elimination of Torque Measurements:
Extension ...................................... 260
5.3.6 Numerical Simulation Results ................... 265
5.3.7 Experimental Results ........................... 271
5.4 Robot Teleoperation ................................... 274
5.4.1 System Model ................................... 277
5.4.2 MIF Control Development ........................ 278
5.4.3 UMIF Control Development ....................... 284
5.5 Rehabilitation Robot .................................. 295
5.5.1 Robot Dynamics ................................. 296
5.5.2 Path Planning and Desired Trajectory
Generator ...................................... 297
5.5.3 Control Problem Formulation .................... 302
5.5.4 Simulation Results ............................. 307
5.6 Background and Notes .................................. 317
References ................................................. 318
Appendices .................................................... 326
A Mathematical Background .................................... 327
References ................................................. 334
В Supplementary Lemmas and Expressions ....................... 335
B.1 Chapter 3 Lemmas ...................................... 335
B.1.1 Open-Loop Rotation Error System ................ 335
B.1.2 Open-Loop Translation Error System ............. 337
B.1.3 Persistence of Excitation Proof ................ 337
B.2 Chapter 4 Lemmas and Auxiliary Expressions ............ 339
B.2.1 Experimental Velocity Field Selection .......... 339
B.2.2 GUB Lemma ...................................... 340
B.2.3 Boundedness of θd(t) ........................... 342
B.2.4 Open-Loop Dynamics for ϒ(t) .................... 344
B.2.5 Measurable Expression for Lϒd(t) ............... 344
B.2.6 Development of an Image Space NF and Its
Gradient ....................................... 345
B.2.7 Global Minimum ................................. 347
B.3 Chapter 5 Lemmas and Auxiliary Expressions ............ 347
B.3.1 Numerical Extremum Generation .................. 347
B.3.2 Proof of Lemma 5.1 ............................. 349
B.3.3 Definitions from Section 5.3.2 ................. 350
B.3.4 Upperbound for Val(t) .......................... 350
B.3.5 Upper Bound Development for MIF Analysis ....... 351
B.3.6 Teleoperator - Proof of MIF Controller
Stability ...................................... 354
B.3.7 Teleoperator - Proof of MIF Passivity .......... 358
B.3.8 Teleoperator - Proof of UMIF Desired
Trajectory Boundedness ......................... 359
B.3.9 Teleoperator - Proof of UMIF Controller
Stability ...................................... 363
B.3.10 Teleoperator-Proof of UMIF Passivity ........... 366
B.3.11 Proof of Bound on Ñ ............................ 367
B.3.12 Calculation of Region of Attraction ............ 369
References ................................................. 370
Index ......................................................... 373
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