Nonlinear Control of Vehicles and Robots (eBook)

Nonlinear Control of Vehicles and Robots (eBook)

Tracking of autonomous vehicles and the high-precision positioning of robotic manipulators require advanced modeling techniques and control algorithms. Controller design should take into account any model nonlinearities. Nonlinear Control of Vehicles and Robots develops a unified approach to the dynamic modeling of robots in terrestrial, aerial and marine environments. To begin with, the main classes of nonlinear systems and stability methods are summarized. Basic nonlinear control methods useful in manipulator and vehicle control - linearization, backstepping, sliding-mode and receding-horizon control - are presented. Formation control of ground robots and ships is discussed. The second part of the book deals with the modeling and control of robotic systems in the presence of non-smooth nonlinearities including analysis of their influence on the performance of motion control systems. Robust adaptive tracking control of robotic systems with unknown payload and friction in the presence of uncertainties is treated. Theoretical (guaranteed stability, guaranteed tracking precision, boundedness of all signals in the control loop) and practical (implementability) aspects of the control algorithms under discussion are detailed. Examples are included throughout the book allowing the reader to apply the control and modeling techniques in their own research and development work. Some of these examples demonstrate state estimation based on the use of advanced sensors such as Inertial Measurement System, Global Positioning System and vision systems as part of the control system. Nonlinear Control of Vehicles and Robots will interest academic researchers studying the control of robots and industrial research and development engineers and graduate students wishing to become familiar with modern control algorithms and modeling techniques for the most common mechatronics systems: vehicles and robot manipulators.

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Professor Béla Lantos is based at Budapest University of Technology and Economics, and is lead researcher for leads many scientific grants related to robot and vehicle control. Currently, He leads the 'Advanced Control Theory and Artificial Intelligence Techniques of Autonomous Ground, Aerial, and Marine Robots' research group, financed by Hungarian National Research program under grant No. OTKA K 71762. Lorinc Márton is an assistant lecturer at Sapientia Hungarian University of Transylvania and is a grantee of Janos Bolyai postdoctoral scholarship, financed by the Hungarian Academy of Sciences. He is also a senior researcher in the OTKA K 71762 research program.

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Inhaltsangabe

Series Editors' Foreword ... 8
Preface ... 11
Acknowledgements ... 13
Contents ... 14
Nomenclature ... 20
Introduction ... 26
Overview ... 26
Basic Notions, Background ... 26
A Short History ... 28
Control Systems for Vehicles and Robots, Research Motivation ... 30
Outline of the Following Chapters ... 32
Basic Nonlinear Control Methods ... 35
Overview ... 35
Nonlinear System Classes ... 35
State Equation of Nonlinear Systems ... 36
Holonomic and Nonholonomic Systems ... 39
Holonomic Constraints ... 39
Nonholonomic Constraints ... 41
Lagrange-d'Alambert Equations ... 42
Dynamics of Rolling Disk ... 42
Holonomic Property Related to Frobenius Theorem ... 44
Motion Equation in Hamiltonian Form ... 44
Coordinate Transformation of Constrained Motion Equations ... 46
Differentially Flat Systems ... 48
Prolongation of Vector Fields, the Cartan Fields ... 49
Lie-Bäcklund Transformation ... 50
Endogenous State Feedback ... 52
Flat Output Variable ... 52
Path Design for Differentially Flat Systems ... 53
Application Possibilities for Different System Classes ... 54
Dynamic Model of Simple Systems ... 54
Dynamic Model of Inverted Pendulum ... 54
Car Active Suspension Model ... 57
The Model of the 2 DOF Robot Arm ... 59
Stability of Nonlinear Systems ... 62
Stability Definitions ... 63
Lyapunov Stability Theorems ... 64
Lyapunov's Direct Method ... 65
Lyapunov's Indirect Method ... 66
LaSalle's Method for Time Invariant Systems ... 68
K and KL Comparison Functions for Stability Investigations ... 69
Input-to-State Stability (ISS) ... 70
Barbalat Lemmas ... 71
Stability of Interconnected Passive Systems ... 73
Lp-Stable Nonlinear Systems ... 73
Passive Systems ... 74
Dissipative Systems ... 75
Input-Output Linearization ... 78
Flatness Control ... 81
Backstepping ... 84
Sliding Control ... 88
Sliding Control of Second Order Systems ... 89
Proportional Control ... 89
Integral Control ... 90
Proportional Control in Case of Variable Gain ... 90
Control Chattering ... 91
Compensation of Control Chattering Using Boundary Layer ... 92
Boundary Layer and Time Varying Filter for Second Order System ... 93
Sliding Control of Robot ... 94
Receding Horizon Control ... 95
Nonlinear Receding Horizon Control ... 96
Nonlinear RHC Control of 2D Crane ... 98
RHC Based on Linearization at Each Horizon ... 100
Closing Remarks ... 100
Dynamic Models of Ground, Aerial and Marine Robots ... 105
Overview ... 105
Dynamic Model of Rigid Body ... 105
Dynamic Model Based on Newton-Euler Equations ... 106
Kinematic Model Using Euler (RPY) Angles ... 108
Kinematic Model Using Quaternion ... 109
Dynamic Model of Industrial Robot ... 110
Recursive Computation of the Kinematic Quantities ... 111
Robot Dynamic Model Based on Appell's Equation ... 113
Robot Dynamic Model Based on Lagrange's Equation ... 116
Dynamic Model of SCARA Robot ... 118
Dynamic Model of Car ... 122
Nonlinear Model of Car ... 123
Input Affine Approximation of the Dynamic Model ... 126
Linearized Model for Constant Velocity ... 127
Dynamic Model of Airplane ... 128
Coordinate Systems for Navigation ... 128
Earth Centered Inertial Frame ... 128
Earth Centered Earth Fixed Frame ... 129
North-East-Down Coordinate System ... 131
Aircraft-Body Coordinate System ... 132
Airplane Kinematics ... 132
Airplane Dynamics ... 133
Wind-Axes Coordinate System ... 135
Gravity Effect ... 136
Aerodynamic Forces and Torques ... 137
Gyroscopic Effect of Rotary Engine ... 140
State Equations of Airplane ... 140
Linearization of the Nonlinear Airplane Model ... 142
Parametrization of Aerodynamic and Trust Forces and Moments ... 143
Dynamic Model of Surface and Underwater Ships ... 145
Rigid Body Equation of Ship ... 145
Hydrodynamic Forces and Moments ... 147
Restoring Forces and Moments ... 148
Ballast Systems ... 150
Wind, Wave and Current Models ... 150
Wind Models ... 150
Wind Generated Waves ... 151
Ocean Current ... 153
Kinematic Model ... 154
Dynamic Model in Body Frame ... 154
Dynamic Model in NED Frame ... 155
Closing Remarks ... 156
Nonlinear Control of Industrial Robots ... 158
Overview ... 158
Decentralized Three-Loop Cascade Control ... 158
Dynamic Model of DC Motor ... 158
Design of Three-Loop Cascade Controller ... 161
Design of Internal Current Loop ... 162
Design of Intermediate Velocity Loop ... 164
Design of External Position Control Loop ... 164
Approximation of Load Inertia and Disturbance Torque ... 166
Computed Torque Technique ... 167
Nonlinear Decoupling in Cartesian Space ... 168
Computation of Equivalent Forces and Torques ... 169
Computation of Equivalent Joint Torques ... 170
Robot Dynamic Model in Cartesian Space ... 170
Nonlinear Decoupling of the Free Motion ... 171
Hybrid Position and Force Control ... 172
Generalized Task Specification Matrices ... 173
Hybrid Position/Force Control Law ... 174
Self-Tuning Adaptive Control ... 175
Independent Parameters of Robot Dynamic Model ... 175
Control and Adaptation Laws ... 177
Simulation Results for 2-DOF Robot ... 179
Identification Strategy ... 179
Robust Backstepping Control in Case of Nonsmooth Path ... 181
Gradient Update Laws for Speed Error ... 182
Control of 2-DOF Robot Arm Along Rectangle Path ... 183
Path and Speed Design ... 184
Inverse Kinematics ... 185
Robot Dynamic Model for Backstepping ... 186
Backstepping Control with Filtered-Gradient Update Law ... 187
Simulation Experiment ... 187
Closing Remarks ... 189
Nonlinear Control of Cars ... 192
Overview ... 192
Control Concept of Collision Avoidance System (CAS) ... 192
Path Design Using Elastic Band ... 193
Reference Signal Design for Control ... 195
Nonlinear Dynamic Model ... 197
Differential Geometry Based Control Algorithm ... 198
External State Feedback Design ... 199
Stability Proof of Zero Dynamics ... 201
Simulation Results Using DGA Method ... 204
Receding Horizon Control ... 205
Nominal Values and Perturbations ... 207
RHC Optimization Using End Constraint ... 209
State Estimation Using GPS and IMU ... 212
Simulation Results with RHC Control and State Estimation ... 215
Software Implementations ... 215
Standalone Programs ... 216
Quick Prototype Design for Target Processors ... 218
Closing Remarks ... 218
Nonlinear Control of Airplanes and Helicopters ... 221
Overview ... 221
Receding Horizon Control of the Longitudinal Motion of an Airplane ... 221
Robust Internal Stabilization Using Disturbance Observer ... 223
High Level Receding Horizon Control ... 225
Simulation Results with External RHC and Internal Disturbance Observer ... 230
Control with Disturbance Observer Alone ... 230
Control with High Level RHC and Low Level Disturbance Observer ... 232
Backstepping Control of an Indoor Quadrotor Helicopter ... 235
Dynamic Model of the Quadrotor Helicopter ... 237
Sensor System of the Helicopter ... 239
Inertial Measurement Unit ... 241
Vision System ... 245
State Estimation Using Vision and Inertial Measurements ... 248
Backstepping Control Algorithm ... 252
Embedded Control Realization ... 258
Closing Remarks ... 263
Nonlinear Control of Surface Ships ... 266
Overview ... 266
Control System Structure ... 266
Reference Path Design ... 268
Line-of-Sight Guidance ... 268
Filtering Wave Disturbances ... 269
State Estimation Using IMU and GPS ... 270
Integration of IMU and GPS Position ... 271
Attitude Observer Using Quaternion ... 273
Acceleration Feedback and Nonlinear PD ... 275
Nonlinear Decoupling ... 276
Nonlinear Decoupling in Body Frame ... 276
Nonlinear Decoupling in NED Frame ... 277
Adaptive Feedback Linearization ... 278
MIMO Backstepping in 6 DOF ... 280
Constrained Control Allocation ... 283
Simulation Results ... 284
Closing Remarks ... 288
Formation Control of Vehicles ... 290
Overview ... 290
Selected Approaches in Formation Control of Vehicles ... 290
Stabilization of Ground Vehicles Using Potential Field Method ... 291
Low Level Linearizing Controller ... 291
High Level Formation Controller ... 293
Passivity Based Formation Stabilization ... 296
Simulation Results for UGVs ... 297
Stabilization of Marine Vehicles Using Passivity Theory ... 298
Problem Formulation for Synchronized Path Following ... 299
Control Structure ... 300
Stability Proof Based on Passivity Theory ... 301
Simulation Results for UMVs ... 304
Closing Remarks ... 308
Modeling Nonsmooth Nonlinearities in Mechanical Systems ... 312
Overview ... 312
Modeling and Stability of Nonsmooth Systems ... 312
Modeling and Stability of Switched Systems ... 313
Modeling, Solution and Stability of Differential Inclusions ... 316
Filippov Solution ... 317
Stability ... 317
Global Asymptotic Stability ... 317
Clarke Generalized Gradient ... 318
Static Friction Models ... 319
Coulomb Friction Model ... 319
Coulomb + Viscous Friction Model ... 319
Stribeck Friction Models ... 320
Stick-Slip Motion ... 322
Friction-Induced Dead Zone ... 324
Dynamic Friction Models ... 325
Classic Dynamic Friction Models ... 325
Dahl Model ... 325
LuGre Model ... 326
Modified and Advanced Dynamic Friction Models ... 329
Elastoplastic Model ... 329
Leuven Friction with Maxwell-slip Elements ... 329
Generalized Maxwell Slip Model (GMS) ... 331
Piecewise Linearly Parameterized Friction Model ... 331
Parameter Equivalence with the Tustin Model ... 333
Modeling Errors ... 334
Incorporating the Dynamic Effects ... 334
Backlash in Mechanical Systems ... 335
Closing Remarks ... 338
Mechanical Control Systems with Nonsmooth Nonlinearities ... 340
Overview ... 340
Switched System Model of Mechanical Systems with Stribeck Friction and Backlash ... 340
Motion Control ... 342
Stabilizing Control ... 343
Case Study ... 345
Extension of the Control Law for Tracking ... 347
Simulation Results ... 348
Friction and Backlash Induced Limit Cycle Around Zero Velocity ... 351
Chaotic Measures for Nonlinear Analysis ... 354
Simulation Measurements ... 355
Friction Generated Limit Cycle Around Stribeck Velocities ... 357
Case Study-PD Control ... 359
Simulation Results ... 360
Experimental Measurements ... 360
Closing Remarks ... 362
Model Based Identification and Adaptive Compensation of Nonsmooth Nonlinearities ... 364
Overview ... 364
Friction and Backlash Measurement and Identification in Robotic Manipulators ... 364
Friction Measurement and Identification ... 366
Backlash Measurement ... 367
Velocity Control for Measurements ... 368
Experimental Measurements ... 370
Experimental Setup ... 370
Experimental Results ... 373
Friction Measurement and Identification in Hydraulic Actuators ... 376
Mathematical Model of Hydraulic Actuators ... 377
Friction Measurement and Identification ... 379
Experimental Measurements ... 380
Nonlinear Control of a Ball and Beam System Using Coulomb Friction Compensation ... 384
Adaptive Friction Identification ... 387
Nonlinear Control Algorithm for the Ball and Beam System ... 388
Experimental Evaluations ... 389
Experimental Setup ... 389
Experimental Measurements: Friction Estimation ... 390
Experimental Measurements: LQ Control ... 391
Experimental Measurements: Nonlinear Combined Error Metric Control ... 391
Adaptive Payload and Friction Compensation in Robotic Manipulators ... 392
Control Law ... 396
Lyapunov Analysis of the Control ... 397
Simulation Results-Adaptive Friction Compensation in the Presence of Backlash ... 398
Experimental Measurements ... 400
Closing Remarks ... 403
Conclusions and Future Research Directions ... 405
Overview ... 405
Summary ... 405
Future Research Directions ... 407
Appendix A Kinematic and Dynamic Foundations of Physical Systems ... 409
Overview ... 409
Orientation Description Using Rotations and Quaternion ... 409
Homogeneous Transformations ... 409
Orientation Description Using Rotations ... 411
Orientation Description Using Quaternion ... 413
Solution of the Inverse Orientation Problem ... 414
Differentiation Rule in Moving Coordinate System ... 416
Inertia Parameters of Rigid Objects ... 418
Lagrange, Appell and Newton-Euler Equations ... 420
Lagrange Equation ... 422
Appell Equation ... 423
Newton-Euler Equations ... 424
Robot Kinematics ... 426
Denavit-Hartenberg Form ... 426
Direct Kinematic Problem ... 428
Inverse Kinematic Problem ... 430
Robot Jacobian ... 431
Appendix B Basis of Differential Geometry for Control Problems ... 436
Overview ... 436
Lie Derivatives, Submanifold, Tangent Space ... 436
Frobenius Theorem ... 441
Local Reachability and Observability ... 447
Input/Output Linearization, Zero Dynamics ... 458
References ... 465
Index ... 472

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Inhaltsangabe

Introduction.- Basic Nonlinear Control Methods.- Dynamic Models of Ground, Aerial and Marine Robots.- Nonlinear Control of Industrial Robots.- Nonlinear Control of Cars.- Nonlinear Control of Airplanes and Helicopters.- Nonlinear Control of Surface Ships.- Formation Control of Vehicles.- Modeling Mechanical Systems with Non-smooth Nonlinearities.- Mechanical Control Systems with Non-smooth Nonlinearities.- Model-based Identification and Adaptive Compensation of Non-smooth Nonlinearities.- Conclusions and Future Research Directions.- Appendices.