Modeling, performance analysis and control of robot manipulators

Title:

Publication Information:

Newport Beach, CA : ISTE Publishing Company, 2007

Physical Description:

vi, 398 p. : ill. ; 24 cm.

ISBN:

9781905209101

Subject Term:

Robotics

Manipulators (Mechanism)

Added Author:

Dombre, E. (Etienne)

Khalil, W. (Wisama)

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010185263	TJ211 M64 2007	Open Access Book	Book	Searching... Unknown
Searching... SPACE KL Main Library	30000003485830	TJ211 M64 2007	Open Access Book	Book	Searching... Unknown

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 Notes

Etienne Dombre is Director of Research at the National Centre for Scientific Research (CNRS) and is a researcher within the Laboratoire de Recherche en 'Informatique, Robotique et Microélectronique de Montpellier at the University of Montpellier, France.

Wisama Khalil is Professor at the Ecole Centrale de Nantes, France, and is a researcher at the Institute of Research in
Communication and Cybernetics.

Wisama Khalil and Etienne DombreJean-Pierre Merlet and Francois PierrotPhilippe WengerMoussa Haddad and Taha Chettibi and Wisama Khalil and Halim LehtihetPierre Dauchez and Philippe FraisseFrancois ChaumetteFrederic Boyer and Wisama Khalil and Mouhacine Benosman and George Le Vey

Chapter 1 Modeling and Identification of Serial Robots	p. 1
1.1 Introduction	p. 1
1.2 Geometric modeling	p. 2
1.2.1 Geometric description	p. 2
1.2.2 Direct geometric model	p. 6
1.2.3 Inverse geometric model	p. 7
1.2.3.1 Stating the problem	p. 8
1.2.3.2 Principle of Paul's method	p. 10
1.3 Kinematic modeling	p. 14
1.3.1 Direct kinematic model	p. 14
1.3.1.1 Calculation of the Jacobian matrix by derivation of the DGM	p. 15
1.3.1.2 Kinematic Jacobian matrix	p. 17
1.3.1.3 Decomposition of the kinematic Jacobian matrix into three matrices	p. 19
1.3.1.4 Dimension of the operational space of a robot	p. 20
1.3.2 Inverse kinematic model	p. 21
1.3.2.1 General form of the kinematic model	p. 21
1.3.2.2 Inverse kinematic model for the regular case	p. 22
1.3.2.3 Solution at the proximity of singular positions	p. 23
1.3.2.4 Inverse kinematic model of redundant robots	p. 24
1.4 Calibration of geometric parameters	p. 26
1.4.1 Introduction	p. 26
1.4.2 Geometric parameters	p. 26
1.4.2.1 Geometric parameters of the robot	p. 26
1.4.2.2 Parameters of the robot's location	p. 27
1.4.2.3 Geometric parameters of the end-effector	p. 28
1.4.3 Generalized differential model of a robot	p. 29
1.4.4 Principle of geometric calibration	p. 30
1.4.4.1 General form of the calibration model	p. 30
1.4.4.2 Identifying the geometric parameters	p. 31
1.4.4.3 Solving the identification equations	p. 34
1.4.5 Calibration methods of geometric parameters	p. 35
1.4.5.1 Calibration model by measuring the end-effector location	p. 35
1.4.5.2 Autonomous calibration models	p. 36
1.4.6 Correction of geometric parameters	p. 39
1.5 Dynamic modeling	p. 40
1.5.1 Lagrange formalism	p. 42
1.5.1.1 General form of dynamic equations	p. 43
1.5.1.2 Calculation of energy	p. 44
1.5.1.3 Properties of the dynamic model	p. 46
1.5.1.4 Taking into consideration the friction	p. 47
1.5.1.5 Taking into account the inertia of the actuator's rotor	p. 48
1.5.1.6 Taking into consideration the forces and moments exerted by the end-effector on its environment	p. 48
1.5.2 Newton-Euler formalism	p. 50
1.5.2.1 Newton-Euler equations linear in the inertial parameters	p. 50
1.5.2.2 Practical form of Newton-Euler equations	p. 52
1.5.3 Determining the base inertial parameters	p. 53
1.6 Identification of dynamic parameters	p. 59
1.6.1 Introduction	p. 59
1.6.2 Identification principle of dynamic parameters	p. 60
1.6.2.1 Solving method	p. 60
1.6.2.2 Identifiable parameters	p. 62
1.6.2.3 Choice of identification trajectories	p. 63
1.6.2.4 Evaluation of joint coordinates	p. 65
1.6.2.5 Evaluation of joint torques	p. 65
1.6.3 Identification model using the dynamic model	p. 66
1.6.4 Sequential formulation of the dynamic model	p. 68
1.6.5 Practical considerations	p. 69
1.7 Conclusion	p. 70
1.8 Bibliography	p. 71
Chapter 2 Modeling of Parallel Robots	p. 81
2.1 Introduction	p. 81
2.1.1 Characteristics of classic robots	p. 81
2.1.2 Other types of robot structure	p. 82
2.1.3 General advantages and disadvantages	p. 86
2.1.4 Present day uses	p. 88
2.1.4.1 Simulators and space applications	p. 88
2.1.4.2 Industrial applications	p. 91
2.1.4.3 Medical applications	p. 93
2.1.4.4 Precise positioning	p. 94
2.2 Machine types	p. 95
2.2.1 Introduction	p. 95
2.2.2 Plane robots with three degrees of freedom	p. 100
2.2.3 Robots moving in space	p. 101
2.2.3.1 Manipulators with three degrees of freedom	p. 101
2.2.3.2 Manipulators with four or five degrees of freedom	p. 107
2.2.3.3 Manipulators with six degrees of freedom	p. 109
2.3 Inverse geometric and kinematic models	p. 113
2.3.1 Inverse geometric model	p. 113
2.3.2 Inverse kinematics	p. 115
2.3.3 Singular configurations	p. 117
2.3.3.1 Singularities and statics	p. 121
2.3.3.2 State of the art	p. 121
2.3.3.3 The geometric method	p. 122
2.3.3.4 Maneuverability and condition number	p. 125
2.3.3.5 Singularities in practice	p. 126
2.4 Direct geometric model	p. 126
2.4.1 Iterative method	p. 127
2.4.2 Algebraic method	p. 128
2.4.2.1 Reminder concerning algebraic geometry	p. 128
2.4.2.2 Planar robots	p. 130
2.4.2.3 Manipulators with six degrees of freedom	p. 133
2.5 Bibliography	p. 134
Chapter 3 Performance Analysis of Robots	p. 141
3.1 Introduction	p. 141
3.2 Accessibility	p. 143
3.2.1 Various levels of accessibility	p. 143
3.2.2 Condition of accessibility	p. 144
3.3 Workspace of a robot manipulator	p. 146
3.3.1 General definition	p. 146
3.3.2 Space of accessible positions	p. 148
3.3.3 Primary space and secondary space	p. 149
3.3.4 Defined orientation workspace	p. 151
3.3.5 Free workspace	p. 152
3.3.6 Calculation of the workspace	p. 155
3.4 Concept of aspect	p. 157
3.4.1 Definition	p. 157
3.4.2 Mode of aspects calculation	p. 158
3.4.3 Free aspects	p. 160
3.4.4 Application of the aspects	p. 161
3.5 Concept of connectivity	p. 163
3.5.1 Introduction	p. 163
3.5.2 Characterization of n-connectivity	p. 165
3.5.3 Characterization of t-connectivity	p. 168
3.6 Local performances	p. 174
3.6.1 Definition of dexterity	p. 174
3.6.2 Manipulability	p. 174
3.6.3 Isotropy index	p. 180
3.6.4 Lowest singular value	p. 181
3.6.5 Approach lengths and angles	p. 181
3.7 Conclusion	p. 183
3.8 Bibliography	p. 183
Chapter 4 Trajectory Generation	p. 189
4.1 Introduction	p. 189
4.2 Point-to-point trajectory in the joint space under kinematic constraints	p. 190
4.2.1 Fifth-order polynomial model	p. 191
4.2.2 Trapezoidal velocity model	p. 193
4.2.3 Smoothed trapezoidal velocity model	p. 198
4.3 Point-to-point trajectory in the task-space under kinematic constraints	p. 201
4.4 Trajectory generation under kinodynamic constraints	p. 204
4.4.1 Problem statement	p. 205
4.4.1.1 Constraints	p. 206
4.4.1.2 Objective function	p. 207
4.4.2 Description of the method	p. 208
4.4.2.1 Outline	p. 208
4.4.2.2 Construction of a random trajectory profile	p. 209
4.4.2.3 Handling kinodynamic constraints	p. 212
4.4.2.4 Summary	p. 216
4.4.3 Trapezoidal profiles	p. 218
4.5 Examples	p. 221
4.5.1 Case of a two dof robot	p. 221
4.5.1.1 Optimal free motion planning problem	p. 221
4.5.1.2 Optimal motion problem with geometric path constraint	p. 223
4.5.2 Case of a six dof robot	p. 224
4.5.2.1 Optimal free motion planning problem	p. 225
4.5.2.2 Optimal motion problem with geometric path constraints	p. 226
4.5.2.3 Optimal free motion planning problem with intermediate points	p. 227
4.6 Conclusion	p. 229
4.7 Bibliography	p. 230
Appendix Stochastic Optimization Techniques	p. 234
Chapter 5 Position and Force Control of a Robot in a Free or Constrained Space	p. 241
5.1 Introduction	p. 241
5.2 Free space control	p. 242
5.2.1 Hypotheses applying to the whole chapter	p. 242
5.2.2 Complete dynamic modeling of a robot manipulator	p. 243
5.2.3 Ideal dynamic control in the joint space	p. 246
5.2.4 Ideal dynamic control in the operational working space	p. 248
5.2.5 Decentralized control	p. 250
5.2.6 Sliding mode control	p. 251
5.2.7 Robust control based on high order sliding mode	p. 254
5.2.8 Adaptive control	p. 255
5.3 Control in a constrained space	p. 257
5.3.1 Interaction of the manipulator with the environment	p. 257
5.3.2 Impedance control	p. 257
5.3.3 Force control of a mass attached to a spring	p. 258
5.3.4 Non-linear decoupling in a constrained space	p. 262
5.3.5 Position/force hybrid control	p. 263
5.3.5.1 Parallel structure	p. 263
5.3.5.2 External structure	p. 269
5.3.6 Specificity of the force/torque control	p. 271
5.4 Conclusion	p. 275
5.5 Bibliography	p. 275
Chapter 6 Visual Servoing	p. 279
6.1 Introduction	p. 279
6.2 Modeling visual features	p. 281
6.2.1 The interaction matrix	p. 281
6.2.2 Eye-in-hand configuration	p. 282
6.2.3 Eye-to-hand configuration	p. 283
6.2.4 Interaction matrix	p. 284
6.2.4.1 Interaction matrix of a 2-D point	p. 284
6.2.4.2 Interaction matrix of a 2-D geometric primitive	p. 287
6.2.4.3 Interaction matrix for complex 2-D shapes	p. 290
6.2.4.4 Interaction matrix by learning or estimation	p. 293
6.2.5 Interaction matrix related to 3-D visual features	p. 294
6.2.5.1 Pose estimation	p. 294
6.2.5.2 Interaction matrix related to [Theta]u	p. 297
6.2.5.3 Interaction matrix related to a 3-D point	p. 298
6.2.5.4 Interaction matrix related to a 3-D plane	p. 300
6.3 Task function and control scheme	p. 301
6.3.1 Obtaining the desired value s*	p. 301
6.3.2 Regulating the task function	p. 302
6.3.2.1 Case where the dimension of s is 6 (k = 6)	p. 304
6.3.2.2 Case where the dimension of s is greater than 6 (k > 6)	p. 312
6.3.3 Hybrid tasks	p. 317
6.3.3.1 Virtual links	p. 317
6.3.3.2 Hybrid task function	p. 319
6.3.4 Target tracking	p. 323
6.4 Other exteroceptive sensors	p. 325
6.5 Conclusion	p. 326
6.6 Bibliography	p. 328
Chapter 7 Modeling and Control of Flexible Robots	p. 337
7.1 Introduction	p. 337
7.2 Modeling of flexible robots	p. 337
7.2.1 Introduction	p. 337
7.2.2 Generalized Newton-Euler model for a kinematically free elastic body	p. 339
7.2.2.1 Definition: formalism of a dynamic model	p. 339
7.2.2.2 Choice of formalism	p. 340
7.2.2.3 Kinematic model of a free elastic body	p. 341
7.2.2.4 Balance principle compatible with the mixed formalism	p. 343
7.2.2.5 Virtual power of the field of acceleration quantities	p. 344
7.2.2.6 Virtual power of external forces	p. 346
7.2.2.7 Virtual power of elastic cohesion forces	p. 347
7.2.2.8 Balance of virtual powers	p. 348
7.2.2.9 Linear rigid balance in integral form	p. 349
7.2.2.10 Angular rigid balance in integral form	p. 349
7.2.2.11 Elastic balances in integral form	p. 350
7.2.2.12 Linear rigid balance in parametric form	p. 351
7.2.2.13 Intrinsic matrix form of the generalized Newton-Euler model	p. 353
7.2.3 Velocity model of a simple open robotic chain	p. 356
7.2.4 Acceleration model of a simple open robotic chain	p. 357
7.2.5 Generalized Newton-Euler model for a flexible manipulator	p. 358
7.2.6 Extrinsic Newton-Euler model for numerical calculus	p. 359
7.2.7 Geometric model of an open chain	p. 362
7.2.8 Recursive calculation of the inverse and direct dynamic models for a flexible robot	p. 363
7.2.8.1 Introduction	p. 363
7.2.8.2 Recursive algorithm of the inverse dynamic model	p. 364
7.2.8.3 Recursive algorithm of the direct dynamic model	p. 368
7.2.8.4 Iterative symbolic calculation	p. 373
7.3 Control of flexible robot manipulators	p. 373
7.3.1 Introduction	p. 373
7.3.2 Reminder of notations	p. 374
7.3.3 Control methods	p. 375
7.3.3.1 Regulation	p. 375
7.3.3.2 Point-to-point movement in fixed time	p. 375
7.3.3.3 Trajectory tracking in the joint space	p. 380
7.3.3.4 Trajectory tracking in the operational space	p. 383
7.4 Conclusion	p. 388
7.5 Bibliography	p. 389
List of Authors	p. 395
Index	p. 397

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