Robot Manipulators Modeling, Performance Analysis and Control

by Dombre, Etienne; Khalil, Wisama

• ISBN13: 9781905209101
• ISBN10: 190520910X
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-01-30
• Publisher: Wiley-ISTE

Summary

This book presents the most recent research results on modeling and control of robot manipulators. Chapter 1 gives unified tools to derive direct and inverse geometric, kinematic and dynamic models of serial robots and addresses the issue of identification of the geometric and dynamic parameters of these models. Chapter 2 describes the main features of serial robots, the different architectures and the methods used to obtain direct and inverse geometric, kinematic and dynamic models, paying special attention to singularity analysis. Chapter 3 introduces global and local tools for performance analysis of serial robots. Chapter 4 presents an original optimization technique for point-to-point trajectory generation accounting for robot dynamics. Chapter 5 presents standard control techniques in the joint space and task space for free motion (PID, computed torque, adaptive dynamic control and variable structure control) and constrained motion (compliant force-position control). In Chapter 6, the concept of vision-based control is developed and Chapter 7 is devoted to specific issue of robots with flexible links. Efficient recursive Newton-Euler algorithms for both inverse and direct modeling are presented, as well as control methods ensuring position setting and vibration damping.

Author Biography

Etienne Dombre is director of research at the National Centre for Scientific Research (CNRS) in Paris and a researcher at the Laboratoire de Recherche en Informatique, Robotique et MicroTlectronique de Montpellier at the University of Montpellier. Wisama Khalil is a professor at the +cole Centrale–Nantes.

Table of Contents

Modeling and Identification of Serial Robots	p. 1
Introduction	p. 1
Geometric modeling	p. 2
Geometric description	p. 2
Direct geometric model	p. 6
Inverse geometric model	p. 7
Stating the problem	p. 8
Principle of Paul's method	p. 10
Kinematic modeling	p. 14
Direct kinematic model	p. 14
Calculation of the Jacobian matrix by derivation of the DGM	p. 15
Kinematic Jacobian matrix	p. 17
Decomposition of the kinematic Jacobian matrix into three matrices	p. 19
Dimension of the operational space of a robot	p. 20
Inverse kinematic model	p. 21
General form of the kinematic model	p. 21
Inverse kinematic model for the regular case	p. 22
Solution at the proximity of singular positions	p. 23
Inverse kinematic model of redundant robots	p. 24
Calibration of geometric parameters	p. 26
Introduction	p. 26
Geometric parameters	p. 26
Geometric parameters of the robot	p. 26
Parameters of the robot's location	p. 27
Geometric parameters of the end-effector	p. 28
Generalized differential model of a robot	p. 29
Principle of geometric calibration	p. 30
General form of the calibration model	p. 30
Identifying the geometric parameters	p. 31
Solving the identification equations	p. 34
Calibration methods of geometric parameters	p. 35
Calibration model by measuring the end-effector location	p. 35
Autonomous calibration models	p. 36
Correction of geometric parameters	p. 39
Dynamic modeling	p. 40
Lagrange formalism	p. 42
General form of dynamic equations	p. 43
Calculation of energy	p. 44
Properties of the dynamic model	p. 46
Taking into consideration the friction	p. 47
Taking into account the inertia of the actuator's rotor	p. 48
Taking into consideration the forces and moments exerted by the end-effector on its environment	p. 48
Newton-Euler formalism	p. 50
Newton-Euler equations linear in the inertial parameters	p. 50
Practical form of Newton-Euler equations	p. 52
Determining the base inertial parameters	p. 53
Identification of dynamic parameters	p. 59
Introduction	p. 59
Identification principle of dynamic parameters	p. 60
Solving method	p. 60
Identifiable parameters	p. 62
Choice of identification trajectories	p. 63
Evaluation of joint coordinates	p. 65
Evaluation of joint torques	p. 65
Identification model using the dynamic model	p. 66
Sequential formulation of the dynamic model	p. 68
Practical considerations	p. 69
Conclusion	p. 70
Bibliography	p. 71
Modeling of Parallel Robots	p. 81
Introduction	p. 81
Characteristics of classic robots	p. 81
Other types of robot structure	p. 82
General advantages and disadvantages	p. 86
Present day uses	p. 88
Simulators and space applications	p. 88
Industrial applications	p. 91
Medical applications	p. 93
Precise positioning	p. 94
Machine types	p. 95
Introduction	p. 95
Plane robots with three degrees of freedom	p. 100
Robots moving in space	p. 101
Manipulators with three degrees of freedom	p. 101
Manipulators with four or five degrees of freedom	p. 107
Manipulators with six degrees of freedom	p. 109
Inverse geometric and kinematic models	p. 113
Inverse geometric model	p. 113
Inverse kinematics	p. 115
Singular configurations	p. 117
Singularities and statics	p. 121
State of the art	p. 121
The geometric method	p. 122
Maneuverability and condition number	p. 125
Singularities in practice	p. 126
Direct geometric model	p. 126
Iterative method	p. 127
Algebraic method	p. 128
Reminder concerning algebraic geometry	p. 128
Planar robots	p. 130
Manipulators with six degrees of freedom	p. 133
Bibliography	p. 134
Performance Analysis of Robots	p. 141
Introduction	p. 141
Accessibility	p. 143
Various levels of accessibility	p. 143
Condition of accessibility	p. 144
Workspace of a robot manipulator	p. 146
General definition	p. 146
Space of accessible positions	p. 148
Primary space and secondary space	p. 149
Defined orientation workspace	p. 151
Free workspace	p. 152
Calculation of the workspace	p. 155
Concept of aspect	p. 157
Definition	p. 157
Mode of aspects calculation	p. 158
Free aspects	p. 160
Application of the aspects	p. 161
Concept of connectivity	p. 163
Introduction	p. 163
Characterization of n-connectivity	p. 165
Characterization of t-connectivity	p. 168
Local performances	p. 174
Definition of dexterity	p. 174
Manipulability	p. 174
Isotropy index	p. 180
Lowest singular value	p. 181
Approach lengths and angles	p. 181
Conclusion	p. 183
Bibliography	p. 183
Trajectory Generation	p. 189
Introduction	p. 189
Point-to-point trajectory in the joint space under kinematic constraints	p. 190
Fifth-order polynomial model	p. 191
Trapezoidal velocity model	p. 193
Smoothed trapezoidal velocity model	p. 198
Point-to-point trajectory in the task-space under kinematic constraints	p. 201
Trajectory generation under kinodynamic constraints	p. 204
Problem statement	p. 205
Constraints	p. 206
Objective function	p. 207
Description of the method	p. 208
Outline	p. 208
Construction of a random trajectory profile	p. 209
Handling kinodynamic constraints	p. 212
Summary	p. 216
Trapezoidal profiles	p. 218
Examples	p. 221
Case of a two dof robot	p. 221
Optimal free motion planning problem	p. 221
Optimal motion problem with geometric path constraint	p. 223
Case of a six dof robot	p. 224
Optimal free motion planning problem	p. 225
Optimal motion problem with geometric path constraints	p. 226
Optimal free motion planning problem with intermediate points	p. 227
Conclusion	p. 229
Bibliography	p. 230
Stochastic Optimization Techniques	p. 234
Position and Force Control of a Robot in a Free or Constrained Space	p. 241
Introduction	p. 241
Free space control	p. 242
Hypotheses applying to the whole chapter	p. 242
Complete dynamic modeling of a robot manipulator	p. 243
Ideal dynamic control in the joint space	p. 246
Ideal dynamic control in the operational working space	p. 248
Decentralized control	p. 250
Sliding mode control	p. 251
Robust control based on high order sliding mode	p. 254
Adaptive control	p. 255
Control in a constrained space	p. 257
Interaction of the manipulator with the environment	p. 257
Impedance control	p. 257
Force control of a mass attached to a spring	p. 258
Non-linear decoupling in a constrained space	p. 262
Position/force hybrid control	p. 263
Parallel structure	p. 263
External structure	p. 269
Specificity of the force/torque control	p. 271
Conclusion	p. 275
Bibliography	p. 275
Visual Servoing	p. 279
Introduction	p. 279
Modeling visual features	p. 281
The interaction matrix	p. 281
Eye-in-hand configuration	p. 282
Eye-to-hand configuration	p. 283
Interaction matrix	p. 284
Interaction matrix of a 2-D point	p. 284
Interaction matrix of a 2-D geometric primitive	p. 287
Interaction matrix for complex 2-D shapes	p. 290
Interaction matrix by learning or estimation	p. 293
Interaction matrix related to 3-D visual features	p. 294
Pose estimation	p. 294
Interaction matrix related to [Theta]u	p. 297
Interaction matrix related to a 3-D point	p. 298
Interaction matrix related to a 3-D plane	p. 300
Task function and control scheme	p. 301
Obtaining the desired value s*	p. 301
Regulating the task function	p. 302
Case where the dimension of s is 6 (k = 6)	p. 304
Case where the dimension of s is greater than 6 (k > 6)	p. 312
Hybrid tasks	p. 317
Virtual links	p. 317
Hybrid task function	p. 319
Target tracking	p. 323
Other exteroceptive sensors	p. 325
Conclusion	p. 326
Bibliography	p. 328
Modeling and Control of Flexible Robots	p. 337
Introduction	p. 337
Modeling of flexible robots	p. 337
Introduction	p. 337
Generalized Newton-Euler model for a kinematically free elastic body	p. 339
Definition: formalism of a dynamic model	p. 339
Choice of formalism	p. 340
Kinematic model of a free elastic body	p. 341
Balance principle compatible with the mixed formalism	p. 343
Virtual power of the field of acceleration quantities	p. 344
Virtual power of external forces	p. 346
Virtual power of elastic cohesion forces	p. 347
Balance of virtual powers	p. 348
Linear rigid balance in integral form	p. 349
Angular rigid balance in integral form	p. 349
Elastic balances in integral form	p. 350
Linear rigid balance in parametric form	p. 351
Intrinsic matrix form of the generalized Newton-Euler model	p. 353
Velocity model of a simple open robotic chain	p. 356
Acceleration model of a simple open robotic chain	p. 357
Generalized Newton-Euler model for a flexible manipulator	p. 358
Extrinsic Newton-Euler model for numerical calculus	p. 359
Geometric model of an open chain	p. 362
Recursive calculation of the inverse and direct dynamic models for a flexible robot	p. 363
Introduction	p. 363
Recursive algorithm of the inverse dynamic model	p. 364
Recursive algorithm of the direct dynamic model	p. 368
Iterative symbolic calculation	p. 373
Control of flexible robot manipulators	p. 373
Introduction	p. 373
Reminder of notations	p. 374
Control methods	p. 375
Regulation	p. 375
Point-to-point movement in fixed time	p. 375
Trajectory tracking in the joint space	p. 380
Trajectory tracking in the operational space	p. 383
Conclusion	p. 388
Bibliography	p. 389
List of Authors	p. 395
Index	p. 397
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