Lyapunov-Based Control of Robotic Systems describes nonlinear control design solutions for problems that arise from robots required to interact with and manipulate their environments. Since most practical scenarios require the design of nonlinear controllers to work around uncertainty and measurement-related issues, the authors use Lyapunov’s direct method as an effective tool to design and analyze controllers for robotic systems. After describing the evolution of real-time control design systems and the associated operating environments and hardware platforms, the book presents a host of standard control design tools for robotic systems using a common Lyapunov-based framework. It then discusses several problems in visual servoing control, including the design of homography-based visual servo control methods and the classic structure from motion problem. The book also deals with the issues of path planning and control for manipulator arms and wheeled mobile robots. With a focus on the emerging research area of human machine interaction, the final chapter illustrates the design of control schemes based on passivity such that the machine is a net energy sink. Including much of the authors’ own research work in controls and robotics, this book facilitates an understanding of the application of Lyapunov-based control design techniques to up-and-coming problems in robotics.
Author(s): Aman Behal, Warren Dixon, Darren M. Dawson, Bin Xian
Series: Automation and Control Engineering
Publisher: CRC Press
Year: 2009
Language: English
Pages: 389
Lyapunov-Based Control of Robotic Systems......Page 4
Contents......Page 7
Preface......Page 11
1.1 History of Robotics......Page 15
1.2 Lyapunov-Based Control Philosophy......Page 17
1.3 The Real-Time Computer Revolution......Page 19
References......Page 21
2.1 Introduction......Page 23
2.2.1 Robot Manipulator Model and Properties......Page 24
Control Development......Page 26
Alternative Control Development and Analysis......Page 27
Control Development......Page 29
Control Development......Page 30
2.4 Adaptive Control Design......Page 31
Control Development......Page 32
Stability Analysis......Page 33
DCAL Extension......Page 34
Stability Analysis......Page 36
Function Approximation......Page 38
Closed-Loop Error System......Page 40
Stability Analysis......Page 41
2.5 Task-Space Control and Redundancy......Page 42
2.5.1 Kinematic Model......Page 43
2.5.2 Control Objective and Error System Formulation......Page 44
2.5.3 Computed Torque Control Development and Stability Analysis......Page 46
2.5.4 Adaptive Control Extension......Page 47
References......Page 48
3.1 Introduction......Page 51
3.2.1 Fixed-Camera Geometry......Page 55
3.2.2 Euclidean Reconstruction......Page 58
3.2.3 Camera-in-Hand Geometry......Page 60
3.2.4 Homography Calculation......Page 61
3.2.5 Virtual Parallax Method......Page 64
3.3.1 Control Objective......Page 65
3.3.2 Control Formulation......Page 68
3.3.3 Stability Analysis......Page 70
3.3.4 Camera-in-Hand Extension......Page 71
3.3.5 Simulation Results......Page 72
3.4 Continuum Robots......Page 79
3.4.1 Continuum Robot Kinematics......Page 83
3.4.2 Joint Variables Extraction......Page 86
3.4.3 Task-Space Kinematic Controller......Page 88
3.4.4 Simulations and Discussion......Page 90
3.5 Mobile Robot Regulation and Tracking......Page 92
Camera Model......Page 93
Problem Formulation......Page 96
Control Development......Page 97
Stability Analysis......Page 99
3.5.2 Tracking Control......Page 107
Geometric Model......Page 108
Euclidean Reconstruction......Page 109
Control Development......Page 111
Open-loop Error System......Page 112
Closed-Loop Error System......Page 113
Stability Analysis......Page 114
Experimental Results......Page 115
3.6.1 Object Kinematics......Page 121
3.6.2 Identification of Velocity......Page 122
Euclidean Reconstruction of Feature Points......Page 123
Analysis......Page 125
3.6.3 Camera-in-Hand Extension......Page 127
3.6.4 Simulations and Experimental Results......Page 133
3.7 Notes......Page 139
References......Page 143
4.1 Introduction......Page 154
4.2 Velocity Field and Navigation Function Control for Manipulators......Page 157
4.2.1 System Model......Page 158
Benchmark Control Modification......Page 159
Stability Analysis......Page 161
Control Objective......Page 163
Benchmark Control Modification......Page 164
Stability Analysis......Page 165
Experimental Setup......Page 167
Adaptive VFC Experiment......Page 169
Adaptive Navigation Function Control Experiment......Page 170
4.3.1 Kinematic Model......Page 176
4.3.2 WMR Velocity Field Control......Page 177
Kinematic Transformation......Page 178
Dynamic Model......Page 180
Control Objective......Page 181
Control Formulation......Page 182
Closed-Loop Error System......Page 183
Stability Analysis......Page 184
Trajectory Planning......Page 187
Model Transformation......Page 188
Control Development......Page 189
Trajectory Planning......Page 190
Control Development......Page 191
Stability Analysis......Page 192
Simulation Results......Page 193
4.4 Vision Navigation......Page 194
Euclidean Homography......Page 197
Projective Homography......Page 198
Kinematic Model of Vision System......Page 199
4.4.2 Image-Based Path Planning......Page 200
Pose Space to Image Space Relationship......Page 201
Desired Image Trajectory Planning......Page 202
Path Planner Analysis......Page 203
4.4.3 Tracking Control Development......Page 204
Controller Analysis......Page 205
4.4.4 Simulation Results......Page 207
Simulation Results: Optical axis rotation......Page 208
Simulation Results: Camera y-axis rotation......Page 213
Simulation Results: General Camera Motion......Page 221
4.5 Optimal Navigation and Obstacle Avoidance......Page 222
Camera Model......Page 226
Closed-Loop Error System Development......Page 228
Image-Based Extremum Seeking Path Planner......Page 229
Geometric Model......Page 231
Camera Model......Page 232
Closed-Loop Error System Development......Page 234
4.6 Background and Notes......Page 235
References......Page 238
5.1 Introduction......Page 246
5.2 Exercise Machine......Page 248
5.2.1 Exercise Machine Dynamics......Page 249
Control Objectives......Page 250
Control Development and Analysis......Page 251
5.2.3 Desired Trajectory Generator......Page 252
Numerically-Based Extremum Generation......Page 253
Open-Loop Error System......Page 254
Closed-Loop Error System......Page 255
Stability Analysis......Page 256
5.2.5 Desired Trajectory Generator......Page 259
5.2.6 Experimental Results and Discussion......Page 260
5.3 Steer-by-Wire......Page 262
5.3.1 Control Problem Statement......Page 267
5.3.2 Dynamic Model Development......Page 268
Steering System Model Formulation......Page 269
Open-Loop Error System Development......Page 270
Control Formulation......Page 271
5.3.4 Stability Analysis......Page 272
5.3.5 Elimination of Torque Measurements: Extension......Page 273
Control Development......Page 274
Closed-Loop Error System Development......Page 275
Stability Proof......Page 276
5.3.6 Numerical Simulation Results......Page 278
Experimental Setup......Page 284
Tests and Results......Page 286
5.4 Robot Teleoperation......Page 287
5.4.1 System Model......Page 290
Objective and Model Transformation......Page 291
Closed-Loop Error System......Page 293
Simulation Results......Page 295
5.4.3 UMIF Control Development......Page 297
Objective and Model Transformation......Page 300
Closed Loop Error System......Page 301
Stability Analysis......Page 303
Simulation Results......Page 304
5.5 Rehabilitation Robot......Page 308
5.5.1 Robot Dynamics......Page 309
Path Planning: Tier 1......Page 310
Time Parameterization of Contour rd (s): Tier 2......Page 312
Proof of Passivity......Page 314
5.5.3 Control Problem Formulation......Page 315
Control Design: Tier 3......Page 316
Stability Analysis......Page 318
5.5.4 Simulation Results......Page 320
5.6 Background and Notes......Page 330
References......Page 331
Appendix A: Mathematical Background......Page 339
References......Page 346
B.1.1 Open-Loop Rotation Error System......Page 347
B.1.3 Persistence of Excitation Proof......Page 349
B.2.1 Experimental Velocity Field Selection......Page 351
B.2.2 GUB Lemma......Page 352
B.2.3 Boundedness of thetad (t)......Page 354
B.2.5 Measurable Expression for LΥd (t)......Page 356
B.2.6 Development of an Image Space NF and Its Gradient......Page 357
B.3.1 Numerical Extremum Generation......Page 359
B.3.2 Proof of Lemma 5.1......Page 361
B.3.4 Upperbound for Va1 (t)......Page 362
B.3.5 Upper Bound Development for MIF Analysis......Page 363
B.3.6 Teleoperator — Proof of MIF Controller Stability......Page 366
B.3.7 Teleoperator — Proof of MIF Passivity......Page 370
B.3.8 Teleoperator — Proof of UMIF Desired Trajectory Boundedness......Page 371
B.3.9 Teleoperator — Proof of UMIF Controller Stability......Page 375
B.3.10 Teleoperator — Proof of UMIF Passivity......Page 378
B.3.11 Proof of Bound on Ñ......Page 379
B.3.12 Calculation of Region of Attraction......Page 381
References......Page 382
