Robot manipulator control : theory and practice

Robot Manipulator Control offers a complete survey of control systems for serial-link robot arms and acknowledges how robotic device performance hinges upon a well-developed control system. Containing over 750 essential equations, this thoroughly up-to-date Second Edition, the book explicates theoretical and mathematical requisites for controls design and summarizes current techniques in computer simulation and implementation of controllers. It also addresses procedures and issues in computed-torque, robust, adaptive, neural network, and force control. New chapters relay practical information on commercial robot manipulators and devices and cutting-edge methods in neural network control.

Author Notes

Chaouki T. Abdallah is Gardner-Zemke Professor and Associate Chair of Electrical and Computer Engineering at the University of New Mexico, Albuquerque.

Series Introduction	p. v
Preface	p. vii
1 Commercial Robot Manipulators	p. 1
1.1 Introduction	p. 1
Flexible Robotic Workcells	p. 2
1.2 Commercial Robot Configurations and Types	p. 3
Manipulator Performance	p. 3
Common Kinematic Configurations	p. 4
Drive Types of Commercial Robots	p. 9
1.3 Commercial Robot Controllers	p. 10
1.4 Sensors	p. 12
Types of Sensors	p. 13
Sensor Data Processing	p. 16
References	p. 19
2 Introduction to Control Theory	p. 21
2.1 Introduction	p. 21
2.2 Linear State-Variable Systems	p. 22
Continuous-Time Systems	p. 22
Discrete-Time Systems	p. 28
2.3 Nonlinear State-Variable Systems	p. 31
Continuous-Time Systems	p. 31
Discrete-Time Systems	p. 35
2.4 Nonlinear Systems and Equilibrium Points	p. 36
2.5 Vector Spaces, Norms, and Inner Products	p. 39
Linear Vector Spaces	p. 39
Norms of Signals and Systems	p. 40
Inner Products	p. 48
Matrix Properties	p. 48
2.6 Stability Theory	p. 51
2.7 Lyapunov Stability Theorems	p. 67
Functions Of Class K	p. 67
Lyapunov Theorems	p. 69
The Autonomous Case	p. 72
2.8 Input/Output Stability	p. 80
2.9 Advanced Stability Results	p. 82
Passive Systems	p. 82
Positive-Real Systems	p. 84
Lure's Problem	p. 85
The MKY Lemma	p. 86
2.10 Useful Theorems and Lemmas	p. 88
Small-Gain Theorem	p. 88
Total Stability Theorem	p. 89
2.11 Linear Controller Design	p. 93
2.12 Summary and Notes	p. 101
References	p. 103
3 Robot Dynamics	p. 107
3.1 Introduction	p. 107
3.2 Lagrange-Euler Dynamics	p. 108
Force, Inertia, and Energy	p. 108
Lagrange's Equations of Motion	p. 111
Derivation of Manipulator Dynamics	p. 119
3.3 Structure and Properties of the Robot Equation	p. 125
Properties of the Inertia Matrix	p. 126
Properties of the Coriolis/Centripetal Term	p. 127
Properties of the Gravity, Friction, and Disturbance	p. 134
Linearity in the Parameters	p. 136
Passivity and Conservation of Energy	p. 141
3.4 State-Variable Representations and Feedback Linearization	p. 142
Hamiltonian Formulation	p. 143
Position/Velocity Formulations	p. 145
Feedback Linearization	p. 145
3.5 Cartesian and Other Dynamics	p. 148
Cartesian Arm Dynamics	p. 148
Structure and Properties of the Cartesian Dynamics	p. 150
3.6 Actuator Dynamics	p. 152
Dynamics of a Robot Arm with Actuators	p. 152
Third-Order Arm-Plus-Actuator Dynamics	p. 154
Dynamics with Joint Flexibility	p. 155
3.7 Summary	p. 161
References	p. 163
Problems	p. 166
4 Computed-Torque Control	p. 169
4.1 Introduction	p. 169
4.2 Path Generation	p. 170
Converting Cartesian Trajectories to Joint Space	p. 171
Polynomial Path Interpolation	p. 173
Linear Function with Parabolic Blends	p. 176
Minimum-Time Trajectories	p. 178
4.3 Computer Simulation of Robotic Systems	p. 181
Simulation of Robot Dynamics	p. 181
Simulation of Digital Robot Controllers	p. 182
4.4 Computed-Torque Control	p. 185
Derivation of Inner Feedforward Loop	p. 185
PD Outer-Loop Design	p. 188
PID Outer-Loop Design	p. 197
Class of Computed-Torque-Like Controllers	p. 202
PD-Plus-Gravity Controller	p. 205
Classical Joint Control	p. 208
4.5 Digital Robot Control	p. 222
Guaranteed Performance on Sampling	p. 224
Discretization of Inner Nonlinear Loop	p. 225
Joint Velocity Estimates from Position Measurements	p. 226
Discretization of Outer PD/PID Control Loop	p. 226
Actuator Saturation and Integrator Antiwindup Compensation	p. 228
4.6 Optimal Outer-Loop Design	p. 243
Linear Quadratic Optimal Control	p. 243
Linear Quadratic Computed-Torque Design	p. 246
4.7 Cartesian Control	p. 248
Cartesian Computed-Torque Control	p. 248
Cartesian Error Computation	p. 250
4.8 Summary	p. 251
References	p. 253
Problems	p. 257
5 Robust Control of Robotic Manipulators	p. 263
5.1 Introduction	p. 263
5.2 Feedback-Linearization Controllers	p. 265
Lyapunov Designs	p. 268
Input-Output Designs	p. 273
5.3 Nonlinear Controllers	p. 293
Direct Passive Controllers	p. 293
Variable-Structure Controllers	p. 297
Saturation-Type Controllers	p. 306
5.4 Dynamics Redesign	p. 316
Decoupled Designs	p. 316
Imaginary Robot Concept	p. 318
5.5 Summary	p. 320
References	p. 321
Problems	p. 324
6 Adaptive Control of Robotic Manipulators	p. 329
6.1 Introduction	p. 329
6.2 Adaptive Control by a Computed-Torque Approach	p. 330
Approximate Computed-Torque Controller	p. 330
Adaptive Computed-Torque Controller	p. 333
6.3 Adaptive Control by an Inertia-Related Approach	p. 341
Examination of a PD Plus Gravity Controller	p. 343
Adaptive Inertia-Related Controller	p. 344
6.4 Adaptive Controllers Based on Passivity	p. 349
Passive Adaptive Controller	p. 349
General Adaptive Update Rule	p. 356
6.5 Persistency of Excitation	p. 357
6.6 Composite Adaptive Controller	p. 361
Torque Filtering	p. 362
Least-Squares Estimation	p. 365
Composite Adaptive Controller	p. 368
6.7 Robustness of Adaptive Controllers	p. 371
Torque-Based Disturbance Rejection Method	p. 372
Estimator-Based Disturbance Rejection Method	p. 375
6.8 Summary	p. 377
References	p. 379
Problems	p. 381
7 Advanced Control Techniques	p. 383
7.1 Introduction	p. 383
7.2 Robot Controllers with Reduced On-Line Computation	p. 384
Desired Compensation Adaptation Law	p. 384
Repetitive Control Law	p. 392
7.3 Adaptive Robust Control	p. 399
7.4 Compensation for Actuator Dynamics	p. 407
Electrical Dynamics	p. 408
Joint Flexibilities	p. 416
7.5 Summary	p. 426
References	p. 427
Problems	p. 429
8 Neural Network Control of Robots	p. 431
8.1 Introduction	p. 431
8.2 Background in Neural Networks	p. 433
Multilayer Neural Networks	p. 433
Linear-in-the-parameter neural nets	p. 437
8.3 Tracking Control Using Static Neural Networks	p. 440
Robot Arm Dynamics and Error System	p. 440
Adaptive Control	p. 442
Neural Net Feedback Tracking Controller	p. 443
8.4 Tuning Algorithms for Linear-in-the-Parameters NN	p. 445
8.5 Tuning Algorithms for Nonlinear-in-the-Parameters NN	p. 449
Passivity Properties of NN Controllers	p. 453
Passivity of the Robot Tracking Error Dynamics	p. 453
Passivity Properties of 2-layer NN Controllers	p. 455
Passivity Properties of 1-Layer NN Controllers	p. 458
8.6 Summary	p. 458
References	p. 459
9 Force Control	p. 463
9.1 Introduction	p. 463
9.2 Stiffness Control	p. 464
Stiffness Control of a Single-Degree-of-Freedom Manipulator	p. 464
The Jacobian Matrix and Environmental Forces	p. 467
Stiffness Control of an N-Link Manipulator	p. 474
9.3 Hybrid Position/Force Control	p. 478
Hybrid Position/Force Control of a Cartesian Two-Link Arm	p. 479
Hybrid Position/Force Control of an N-Link Manipulator	p. 482
Implementation Issues	p. 487
9.4 Hybrid Impedance Control	p. 489
Modeling the Environment	p. 490
Position and Force Control Models	p. 492
Impedance Control Formulation	p. 494
Implementation Issues	p. 499
9.5 Reduced State Position/Force Control	p. 501
Effects of Holonomic Constraints on the Manipulator Dynamics	p. 501
Reduced State Modeling and Control	p. 504
Implementation Issues	p. 509
9.6 Summary	p. 510
References	p. 513
Problems	p. 514
10 Robot Control Implementation and Software	p. 517
10.1 Introduction	p. 518
10.2 Tools and Technologies	p. 520
10.3 Design of the Robotic Platform	p. 523
Overview	p. 523
Core Classes	p. 526
Robot Control Classes	p. 527
External Device Classes	p. 532
Utility Classes	p. 533
Configuration Management	p. 533
Object Manager	p. 534
Concurrency/Communication Model	p. 537
Plotting and Control Tuning Capabilities	p. 538
Math Library	p. 540
Error Management and the Front-End GUI	p. 542
10.4 Operation of the Robotic Platform	p. 543
Scene Viewer and Control Panels	p. 543
Utility Programs for Moving the Robot	p. 544
Writing, Compiling, Linking, and Starting Control Programs	p. 545
10.5 Programming Examples	p. 548
Comparison of Simulation and Implementation	p. 548
Virtual Walls	p. 548
10.6 Summary	p. 550
References	p. 551
A Review of Robot Kinematics and Jacobians	p. 555
A.1 Basic Manipulator Geometries	p. 555
A.2 Robot Kinematics	p. 558
A.3 The Manipulator Jacobian	p. 576
References	p. 589
B Software for Controller Simulation	p. 591
References	p. 597
C Dynamics of Some Common Robot Arms	p. 599
C.1 SCARA ARM	p. 600
C.2 Stanford Manipulator	p. 601
C.3 PUMA 560 Manipulator	p. 603
References	p. 607
Index	p. 609

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Summary

Author Notes

Table of Contents