Flexible Robot Manipulators - Modelling, Simulation and Control

Contents......Page 6
Preface......Page 16
List of contributors......Page 18
List of abbreviations......Page 22
List of notations......Page 26
1.1 Introduction......Page 34
1.2 Modelling and simulation techniques......Page 35
1.3.1 Passive control......Page 37
1.3.3 Closed-loop control......Page 38
1.3.4 Artificial intelligence control......Page 42
1.4 Flexible manipulator systems......Page 44
1.4.1 Typical FMSs......Page 45
1.4.2 Flexible manipulators for industrial applications......Page 46
1.4.4 Two-link flexible manipulators......Page 47
1.4.5 Single-link flexible manipulators......Page 50
1.5 Applications......Page 52
1.6 Summary......Page 53
2.1 Introduction......Page 56
2.2.1 The flexible manipulator system......Page 58
2.2.2 Energies associated with the system......Page 59
2.2.3 The dynamic equations of motion......Page 60
2.3 Mode shapes......Page 62
2.4 State-space model......Page 63
2.5 Transfer function model......Page 65
2.6 Experimentation......Page 66
2.6.1 Natural frequencies......Page 68
2.6.2 Damping ratios......Page 72
2.6.3 Modal gain......Page 76
2.7 Model validation......Page 77
2.8 Summary......Page 78
3.1 Introduction......Page 80
3.2 Kinematics: the reference frames......Page 81
3.2.1 Deformation assumptions......Page 82
3.2.2 Kinematics of a flexible link......Page 84
3.3 The strain-displacement relations......Page 85
3.3.2 Parameterisation of the neutral axis tangent vector......Page 88
3.3.3 Displacement of the neutral axis......Page 89
3.4.1 The inertial force term......Page 90
3.4.2 The elastic force term......Page 93
3.4.4 The external force term......Page 94
3.4.5 Rayleigh-Ritz discretisation......Page 95
3.5 The dynamic model of a multi-link manipulator......Page 98
3.5.1 Joint kinematics......Page 99
3.5.2 Dynamics of a rigid body......Page 102
3.5.3 Dynamics of a rigid-flexible-rigid body......Page 103
3.5.4 Dynamics of a serial multi-RFR body system......Page 105
3.6 Summary......Page 108
4.1 Introduction......Page 110
4.2.2 RLS algorithm......Page 112
4.2.3 Genetic algorithms......Page 113
4.3 Non-parametric identification techniques......Page 114
4.3.1 Multi-layered perceptron neural networks......Page 115
4.3.2 Radial basis function neural networks......Page 116
4.4 Model validation......Page 118
4.6.1 Parametric modelling......Page 120
4.6.2 Non-parametric modelling......Page 123
4.6.2.1 Modelling with MLP NN......Page 124
4.6.2.2 Modelling with RBF NN......Page 127
4.7 Comparative assessment......Page 128
4.8 Summary......Page 129
5.1 Introduction......Page 132
5.2 The flexible manipulator system......Page 133
5.3 The FD method......Page 136
5.3.1 Development of the simulation algorithm......Page 137
5.3.3 The end-point displacement......Page 138
5.3.4 Matrix formulation......Page 139
5.3.5 State-space formulation......Page 140
5.4.1 Elemental matrices......Page 141
5.4.1.1 Scalar energy functions......Page 142
5.4.2 A single-link flexible manipulator......Page 143
5.4.3 A two-link flexible manipulator......Page 144
\"5.4.3.1 Boundary conditions, payload and damping\"......Page 145
5.5.2 Simulation and experiments......Page 146
5.6 Summary......Page 150
6.1 Introduction......Page 152
6.2 FE approach to symbolic modelling......Page 153
6.2.2 Dynamic equation of motion......Page 154
6.2.4 Analysis......Page 157
6.2.4.1 System without payload and hub inertia......Page 158
6.2.4.2 System with payload......Page 159
6.2.5 Validation and performance analysis......Page 164
6.3.1 Piezoelectric laminate electromechanical relationships......Page 167
6.3.2 Dynamic modelling......Page 169
6.3.3 Transfer functions......Page 172
6.3.4 Rational Laplace domain transfer functions......Page 174
6.3.5 Experimental system......Page 175
6.3.6 Experimental results......Page 178
6.4 Summary......Page 179
7.1 Introduction......Page 180
7.2 Symofros......Page 182
7.2.1 Overview......Page 183
7.2.2 Software architecture......Page 184
7.2.3 Flexible beam modelling: a combined FE and assumed-modes approach......Page 185
7.3.1.1 Experimental set-up......Page 191
7.3.1.2 Simulation results......Page 192
7.3.2 Flexible manipulator end-point detection and validation......Page 194
7.3.2.1 Flexible manipulator kinematics......Page 195
7.3.2.2 Statics......Page 198
7.3.2.3 End-point detection using strain gauges......Page 201
7.4.2 SPDM task verification facility concept......Page 211
7.4.3.1 The SPDM task verification facility test-bed simulator......Page 213
7.4.3.2 The SPDM task verification facility test-bed robot and robot controller......Page 214
7.4.3.3 Computer architecture......Page 216
7.4.4 Experimental contact parameter estimation using STVF......Page 217
7.4.4.1 Description of the simulation environment......Page 218
\"7.4.4.2 Experiments, simulations and results\"......Page 220
7.5 On-orbit MSS training simulator......Page 232
7.5.3 Software architecture......Page 234
7.5.4 Simulation validation......Page 235
7.5.7 Ground and on-orbit results......Page 236
7.7 Acknowledgements......Page 239
8.1 Introduction......Page 240
8.2 Identification of natural frequencies......Page 241
8.2.2 Experimental approach......Page 242
8.2.4 Neural modelling......Page 244
8.2.5 Natural frequencies from the genetic and neural modelling......Page 245
8.3 Gaussian shaped torque input......Page 247
8.4 Shaped torque input......Page 249
8.5 Filtered torque input......Page 251
8.6 Experimentation and results......Page 253
8.6.1 Unshaped bang-bang torque input......Page 254
8.6.2 Shaped torque input......Page 255
8.6.3 Gaussian shaped input......Page 257
8.6.4 Filtered input torque......Page 258
8.6.5 System with payload......Page 261
8.7 Comparative performance assessment......Page 263
8.8 Summary......Page 266
9.1 Introduction......Page 268
9.2.1 Gantry crane example......Page 271
9.2.2 Generating zero vibration commands......Page 274
9.2.3 Using ZV impulse sequences to generate ZV commands......Page 277
9.2.4 Robustness to modelling errors......Page 278
9.2.5 Multi-mode input shaping......Page 281
9.2.6 Real-time implementation......Page 282
9.2.8 Applications......Page 283
9.3.1 Feedforward control of a simple system with time delay......Page 285
9.3.2 Zero phase error tracking control......Page 288
9.4 ZPETC as command shaping......Page 289
9.5 Summary......Page 290
10.1 Introduction......Page 292
10.2.2 Discrete-time algorithm......Page 295
10.3.1 Basic notations......Page 298
10.3.2 Decoupling algorithm......Page 299
10.3.2.1 Strategy A......Page 300
10.3.2.2 Strategy B......Page 301
10.3.2.3 Strategy C......Page 303
10.4 Experimental set-up......Page 305
10.5 Simulation and experimental results......Page 307
10.6 Summary......Page 310
11.1 Introduction......Page 312
11.2 Modelling......Page 315
11.3.1 First stage......Page 319
11.3.3 Simulation......Page 321
11.4.1 Composite control strategy......Page 325
11.4.2 Force and position regulation......Page 327
11.4.3 Force regulation and position tracking......Page 329
11.4.4 Simulation......Page 330
11.5 Summary......Page 332
12.1 Introduction......Page 334
12.2 JBC control......Page 336
12.2.2 Experimental results......Page 337
12.3 Collocated and non-collocated feedback control involving PD and PID......Page 338
12.3.1 Simulation results......Page 339
12.4 Adaptive JBC control......Page 342
12.4.1 Simulation results......Page 344
12.4.2 Experimental results......Page 345
12.5 Adaptive collocated and non-collocated control......Page 346
12.5.2 Experimental results......Page 348
12.6 Collocated and non-collocated feedback control with PD and neuro-inverse model......Page 352
12.7 Summary......Page 354
13.1 Introduction......Page 358
13.2 Multivariable control basics......Page 359
13.3.1 Rigid-flexible robot case......Page 361
13.3.2 Modelling the 2D flexible robot......Page 362
13.4.1 Rigid-flexible robot case......Page 365
13.4.1.1 Column dominance for the rigidŒflexible robot......Page 367
13.4.2.1 Design of the decoupling filter for the 2D flexible robot......Page 368
13.5 Jacobian control of a 1D flexible manipulator......Page 371
13.5.1 Jacobian control......Page 372
13.5.2 Control results......Page 374
13.6 Summary......Page 375
14.1 Introduction......Page 378
14.2 Model of flexible manipulators......Page 381
14.3.1 Definition of VRM......Page 383
14.3.2 Kinematic relations of RFM and VRM......Page 384
14.4.1 PD-control for joint variables......Page 388
14.4.2 Stability of linearised system......Page 389
14.5.1 Control methods using the VRM concept......Page 390
14.5.2 Asymptotic stability of positioning control......Page 391
14.5.3 Stability of continuous path control......Page 392
14.6.1 Positioning control......Page 394
14.6.2 Path control: hardware experiment......Page 395
14.6.3 Composite control......Page 396
14.7 Summary......Page 397
14.8 Acknowledgement......Page 398
15.1 Introduction......Page 400
15.2 The flexible manipulator system......Page 402
15.3 Modular NN controller......Page 403
15.3.1.1 Genetic encoding of NNs......Page 404
15.3.1.2 Genetic learning for NNs......Page 405
15.3.2.1 End-point position tracking......Page 407
15.3.2.2 Performance of MNN controller......Page 408
15.4.1 PD-type fuzzy logic control......Page 410
15.4.2 PI-type fuzzy logic control......Page 412
15.4.2.1 Integral wind-up action......Page 414
15.4.3 PID-type fuzzy logic controller......Page 415
15.4.3.1 PD-PI-type fuzzy controller......Page 416
15.4.3.2 Experimental results......Page 417
15.4.4.1 Genetic representation for membership functions......Page 420
15.4.4.2 Experimental results......Page 423
15.5 Summary......Page 426
16.1 Introduction......Page 428
16.2 Dynamic modelling of a single-link smart material robot......Page 431
16.2.1 AMM modelling......Page 435
16.2.2.1 FE analysis......Page 437
16.2.2.2 Dynamic equations......Page 440
16.3.1 System description......Page 442
16.3.2.1 Decentralised model-free control......Page 443
16.3.2.2 Centralised model-free controller......Page 444
16.4.1 Singular perturbed smart material robots......Page 455
16.4.2 Adaptive composite controller design......Page 458
16.4.2.1 Adaptive control of the slow subsystem......Page 459
16.4.2.2 Stabilisation of fast subsystem......Page 460
16.5 Summary......Page 464
17.1 Introduction......Page 466
17.2 Dynamic modelling......Page 467
17.2.1 Discrete equations of motion......Page 470
17.3 Coupling between rigid and flexible motion......Page 472
17.4 Impact response......Page 474
17.5 Control of rigid-flexible manipulators......Page 477
17.5.1 Stability of independent joint control for a two-link rigidŒflexible manipulator......Page 479
17.5.2 Closed-loop simulations......Page 480
17.6 Summary......Page 483
18.1 Introduction......Page 486
18.2 Computer aided control engineering design paradigm......Page 488
18.3 Mechatronic Simulink library......Page 491
18.4 Design models......Page 493
18.4.1 Dynamics of actuators......Page 494
18.4.2 Modal models......Page 497
18.4.3 FE model......Page 503
18.5 Control design......Page 505
18.6 CACE environment......Page 506
18.7 Summary......Page 509
19.1 Introduction......Page 510
19.2 The flexible manipulator system......Page 511
19.3 Structure of SCEFMAS......Page 512
19.3.1 FD simulation and control......Page 514
19.3.1.2 Controller designs......Page 515
19.3.2 Intelligent modelling and model validation......Page 516
19.3.2.2 GA modelling......Page 517
19.3.3 Graphical user interfaces......Page 518
19.3.3.3 NN modelling and validation GUIs......Page 519
19.4.1 Open-loop FD simulation......Page 520
19.4.2 Adaptive inverse dynamic active control......Page 524
19.4.3 NN modelling and validation......Page 526
19.4.4 GA modelling and validation......Page 528
19.5 Summary......Page 531
References......Page 534
Index......Page 576