Robot control is the backbone of robotics, an essential discipline in the maintenance of high quality and productivity in modern industry. The most common method of control for industrial robotic manipulators relies on the measurement and amendment of joint displacement: so-called "joint-space control". Control of Robot Manipulators in Joint Space addresses robot control in depth, treating a range of model-based controllers in detail: proportional derivative; proportional integral derivative; computed torque and some adaptive variants. Using varying combinations of the text’s four parts: robot dynamics and mathematical preliminaries; set-point model-based control; tracking model-based control; and adaptive and velocity-independent control A complete course in robot control based on joint space can be constructed for senior undergraduates or masters students. Other areas of study important to robotics, such as kinematics, receive attention within the case studies which are based around a 2-degrees-of-freedom planar articulated arm termed the Pelican prototype and used throughout to test the examined controllers by experimentation. In addition to the written text, auxiliary resources are available in the form of pdf projector presentations for the instructor to use in lectures and as printed class aids for students, and a pdf solutions manual. All of this labour-saving supplementary material can be downloaded from the Springer website.
Author(s): Rafael Kelly, Victor Santibanez Davila, Julio Antonio Loria Perez
Edition: 1
Publisher: Springer
Year: 2005
Language: English
Pages: 452
Series Editors’ Foreword......Page 9
Preface......Page 11
Contents......Page 17
List of Figures......Page 23
Part I Preliminaries......Page 27
Introduction to Part I......Page 29
1 What Does “Control of Robots” Involve?......Page 33
1.1 Familiarization with the Physical System under Consideration......Page 34
1.2 Dynamic Model......Page 36
1.4 Motion Control of Robot Manipulators......Page 38
Bibliography......Page 41
2 Mathematical Preliminaries......Page 45
2.1 Linear Algebra......Page 46
2.2 Fixed Points......Page 52
2.3 Lyapunov Stability......Page 53
Bibliography......Page 79
Problems......Page 80
3 Robot Dynamics......Page 85
3.1 Lagrange’s Equations of Motion......Page 88
3.2 Dynamic Model in Compact Form......Page 97
3.3 Dynamic Model of Robots with Friction......Page 101
3.4 Dynamic Model of Elastic-joint Robots......Page 103
3.5 Dynamic Model of Robots with Actuators......Page 108
Bibliography......Page 114
Problems......Page 116
4.1 The Inertia Matrix......Page 120
4.2 The Centrifugal and Coriolis Forces Matrix......Page 123
4.3 The Gravitational Torques Vector......Page 127
4.4 The Residual Dynamics......Page 128
4.5 Conclusions......Page 134
Bibliography......Page 135
Problems......Page 136
5 Case Study: The Pelican Prototype Robot......Page 139
5.1 Direct Kinematics......Page 141
5.2 Inverse Kinematics......Page 142
5.3 Dynamic Model......Page 145
5.4 Desired Reference Trajectories......Page 154
Problems......Page 157
Part II Position Control......Page 159
Introduction to Part II......Page 161
Bibliography......Page 165
6 Proportional Control plus Velocity Feedback and PD Control......Page 167
6.1 Robots without Gravity Term......Page 169
6.2 Robots with Gravity Term......Page 172
Problems......Page 179
7 PD Control with Gravity Compensation......Page 183
7.1 Global Asymptotic Stability by La Salle’s Theorem......Page 185
7.2 Lyapunov Function for Global Asymptotic Stability......Page 189
Bibliography......Page 193
Problems......Page 194
8 PD Control with Desired Gravity Compensation......Page 197
8.1 Boundedness of Position and Velocity Errors,......Page 200
8.2 Unicity of Equilibrium......Page 206
8.3 Global Asymptotic Stability......Page 207
8.4 Lyapunov Function for Global Asymptotic Stability......Page 216
Bibliography......Page 221
Problems......Page 222
9 PID Control......Page 227
9.1 Lyapunov Function Candidate......Page 233
9.2 Time Derivative of the Lyapunov Function Candidate......Page 235
9.3 Asymptotic Stability......Page 237
9.4 Tuning Procedure......Page 239
9.5 Conclusions......Page 242
Bibliography......Page 243
Problems......Page 244
Part III Motion Control......Page 247
Introduction to Part III......Page 249
10.1 Computed-torque Control......Page 253
10.2 Computed-torque+ Control......Page 258
10.3 Conclusions......Page 263
Bibliography......Page 264
Problems......Page 265
11 PD+ Control and PD Control with Compensation......Page 269
11.1 PD Control with Compensation......Page 270
11.2 PD+ Control......Page 274
11.3 Conclusions......Page 284
Bibliography......Page 285
Problems......Page 286
12 Feedforward Control and PD Control plus Feedforward......Page 289
12.1 Feedforward Control......Page 290
12.2 PD Control plus Feedforward......Page 295
Bibliography......Page 308
Problems......Page 310
Part IV Advanced Topics......Page 313
Introduction to Part IV......Page 315
13 P“D” Control with Gravity Compensation and P“D” Control with Desired Gravity Compensation......Page 317
13.1 P“D” Control with Gravity Compensation......Page 318
13.2 P“D” Control with Desired Gravity Compensation......Page 326
13.3 Conclusions......Page 333
Bibliography......Page 334
Problems......Page 335
14 Introduction to Adaptive Robot Control......Page 339
14.1 Parameterization of the Dynamic Model......Page 340
14.2 The Adaptive Robot Control Problem......Page 351
14.3 Parameterization of the Adaptive Controller......Page 353
Bibliography......Page 357
Problems......Page 360
15 PD Control with Adaptive Desired Gravity Compensation......Page 363
15.1 The Control and Adaptive Laws......Page 364
15.2 Stability Analysis......Page 368
15.3 Examples......Page 375
15.4 Conclusions......Page 383
Bibliography......Page 384
Problems......Page 385
16.1 The Control and Adaptive Laws......Page 387
16.2 Stability Analysis......Page 391
16.3 Examples......Page 394
Bibliography......Page 403
Problems......Page 404
Appendices......Page 407
A.1 Some Lemmas on Linear Algebra......Page 409
A.2 Vector Calculus......Page 410
A.3 Functional Spaces......Page 416
Bibliography......Page 423
Problems......Page 424
B.1 Conditions for Positive De.niteness of Functions......Page 427
Proof of Property 4.1.3......Page 433
Proof of Property 4.2.6......Page 434
Proof of Property 4.3.3......Page 436
D Dynamics of Direct-current Motors......Page 437
Negligible Armature Inductance (L≈ 0)......Page 439
D.1 Motor Model with Linear Friction......Page 442
D.2 Motor Model with Nonlinear Friction......Page 443
Bibliography......Page 444
Index......Page 445
