Cover image for Modeling, performance analysis and control of robot manipulators
Title:
Modeling, performance analysis and control of robot manipulators
Publication Information:
Newport Beach, CA : ISTE Publishing Company, 2007
Physical Description:
vi, 398 p. : ill. ; 24 cm.
ISBN:
9781905209101

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30000010185263 TJ211 M64 2007 Open Access Book Book
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30000003485830 TJ211 M64 2007 Open Access Book Book
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Summary

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 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.


Table of Contents

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 Robotsp. 1
1.1 Introductionp. 1
1.2 Geometric modelingp. 2
1.2.1 Geometric descriptionp. 2
1.2.2 Direct geometric modelp. 6
1.2.3 Inverse geometric modelp. 7
1.2.3.1 Stating the problemp. 8
1.2.3.2 Principle of Paul's methodp. 10
1.3 Kinematic modelingp. 14
1.3.1 Direct kinematic modelp. 14
1.3.1.1 Calculation of the Jacobian matrix by derivation of the DGMp. 15
1.3.1.2 Kinematic Jacobian matrixp. 17
1.3.1.3 Decomposition of the kinematic Jacobian matrix into three matricesp. 19
1.3.1.4 Dimension of the operational space of a robotp. 20
1.3.2 Inverse kinematic modelp. 21
1.3.2.1 General form of the kinematic modelp. 21
1.3.2.2 Inverse kinematic model for the regular casep. 22
1.3.2.3 Solution at the proximity of singular positionsp. 23
1.3.2.4 Inverse kinematic model of redundant robotsp. 24
1.4 Calibration of geometric parametersp. 26
1.4.1 Introductionp. 26
1.4.2 Geometric parametersp. 26
1.4.2.1 Geometric parameters of the robotp. 26
1.4.2.2 Parameters of the robot's locationp. 27
1.4.2.3 Geometric parameters of the end-effectorp. 28
1.4.3 Generalized differential model of a robotp. 29
1.4.4 Principle of geometric calibrationp. 30
1.4.4.1 General form of the calibration modelp. 30
1.4.4.2 Identifying the geometric parametersp. 31
1.4.4.3 Solving the identification equationsp. 34
1.4.5 Calibration methods of geometric parametersp. 35
1.4.5.1 Calibration model by measuring the end-effector locationp. 35
1.4.5.2 Autonomous calibration modelsp. 36
1.4.6 Correction of geometric parametersp. 39
1.5 Dynamic modelingp. 40
1.5.1 Lagrange formalismp. 42
1.5.1.1 General form of dynamic equationsp. 43
1.5.1.2 Calculation of energyp. 44
1.5.1.3 Properties of the dynamic modelp. 46
1.5.1.4 Taking into consideration the frictionp. 47
1.5.1.5 Taking into account the inertia of the actuator's rotorp. 48
1.5.1.6 Taking into consideration the forces and moments exerted by the end-effector on its environmentp. 48
1.5.2 Newton-Euler formalismp. 50
1.5.2.1 Newton-Euler equations linear in the inertial parametersp. 50
1.5.2.2 Practical form of Newton-Euler equationsp. 52
1.5.3 Determining the base inertial parametersp. 53
1.6 Identification of dynamic parametersp. 59
1.6.1 Introductionp. 59
1.6.2 Identification principle of dynamic parametersp. 60
1.6.2.1 Solving methodp. 60
1.6.2.2 Identifiable parametersp. 62
1.6.2.3 Choice of identification trajectoriesp. 63
1.6.2.4 Evaluation of joint coordinatesp. 65
1.6.2.5 Evaluation of joint torquesp. 65
1.6.3 Identification model using the dynamic modelp. 66
1.6.4 Sequential formulation of the dynamic modelp. 68
1.6.5 Practical considerationsp. 69
1.7 Conclusionp. 70
1.8 Bibliographyp. 71
Chapter 2 Modeling of Parallel Robotsp. 81
2.1 Introductionp. 81
2.1.1 Characteristics of classic robotsp. 81
2.1.2 Other types of robot structurep. 82
2.1.3 General advantages and disadvantagesp. 86
2.1.4 Present day usesp. 88
2.1.4.1 Simulators and space applicationsp. 88
2.1.4.2 Industrial applicationsp. 91
2.1.4.3 Medical applicationsp. 93
2.1.4.4 Precise positioningp. 94
2.2 Machine typesp. 95
2.2.1 Introductionp. 95
2.2.2 Plane robots with three degrees of freedomp. 100
2.2.3 Robots moving in spacep. 101
2.2.3.1 Manipulators with three degrees of freedomp. 101
2.2.3.2 Manipulators with four or five degrees of freedomp. 107
2.2.3.3 Manipulators with six degrees of freedomp. 109
2.3 Inverse geometric and kinematic modelsp. 113
2.3.1 Inverse geometric modelp. 113
2.3.2 Inverse kinematicsp. 115
2.3.3 Singular configurationsp. 117
2.3.3.1 Singularities and staticsp. 121
2.3.3.2 State of the artp. 121
2.3.3.3 The geometric methodp. 122
2.3.3.4 Maneuverability and condition numberp. 125
2.3.3.5 Singularities in practicep. 126
2.4 Direct geometric modelp. 126
2.4.1 Iterative methodp. 127
2.4.2 Algebraic methodp. 128
2.4.2.1 Reminder concerning algebraic geometryp. 128
2.4.2.2 Planar robotsp. 130
2.4.2.3 Manipulators with six degrees of freedomp. 133
2.5 Bibliographyp. 134
Chapter 3 Performance Analysis of Robotsp. 141
3.1 Introductionp. 141
3.2 Accessibilityp. 143
3.2.1 Various levels of accessibilityp. 143
3.2.2 Condition of accessibilityp. 144
3.3 Workspace of a robot manipulatorp. 146
3.3.1 General definitionp. 146
3.3.2 Space of accessible positionsp. 148
3.3.3 Primary space and secondary spacep. 149
3.3.4 Defined orientation workspacep. 151
3.3.5 Free workspacep. 152
3.3.6 Calculation of the workspacep. 155
3.4 Concept of aspectp. 157
3.4.1 Definitionp. 157
3.4.2 Mode of aspects calculationp. 158
3.4.3 Free aspectsp. 160
3.4.4 Application of the aspectsp. 161
3.5 Concept of connectivityp. 163
3.5.1 Introductionp. 163
3.5.2 Characterization of n-connectivityp. 165
3.5.3 Characterization of t-connectivityp. 168
3.6 Local performancesp. 174
3.6.1 Definition of dexterityp. 174
3.6.2 Manipulabilityp. 174
3.6.3 Isotropy indexp. 180
3.6.4 Lowest singular valuep. 181
3.6.5 Approach lengths and anglesp. 181
3.7 Conclusionp. 183
3.8 Bibliographyp. 183
Chapter 4 Trajectory Generationp. 189
4.1 Introductionp. 189
4.2 Point-to-point trajectory in the joint space under kinematic constraintsp. 190
4.2.1 Fifth-order polynomial modelp. 191
4.2.2 Trapezoidal velocity modelp. 193
4.2.3 Smoothed trapezoidal velocity modelp. 198
4.3 Point-to-point trajectory in the task-space under kinematic constraintsp. 201
4.4 Trajectory generation under kinodynamic constraintsp. 204
4.4.1 Problem statementp. 205
4.4.1.1 Constraintsp. 206
4.4.1.2 Objective functionp. 207
4.4.2 Description of the methodp. 208
4.4.2.1 Outlinep. 208
4.4.2.2 Construction of a random trajectory profilep. 209
4.4.2.3 Handling kinodynamic constraintsp. 212
4.4.2.4 Summaryp. 216
4.4.3 Trapezoidal profilesp. 218
4.5 Examplesp. 221
4.5.1 Case of a two dof robotp. 221
4.5.1.1 Optimal free motion planning problemp. 221
4.5.1.2 Optimal motion problem with geometric path constraintp. 223
4.5.2 Case of a six dof robotp. 224
4.5.2.1 Optimal free motion planning problemp. 225
4.5.2.2 Optimal motion problem with geometric path constraintsp. 226
4.5.2.3 Optimal free motion planning problem with intermediate pointsp. 227
4.6 Conclusionp. 229
4.7 Bibliographyp. 230
Appendix Stochastic Optimization Techniquesp. 234
Chapter 5 Position and Force Control of a Robot in a Free or Constrained Spacep. 241
5.1 Introductionp. 241
5.2 Free space controlp. 242
5.2.1 Hypotheses applying to the whole chapterp. 242
5.2.2 Complete dynamic modeling of a robot manipulatorp. 243
5.2.3 Ideal dynamic control in the joint spacep. 246
5.2.4 Ideal dynamic control in the operational working spacep. 248
5.2.5 Decentralized controlp. 250
5.2.6 Sliding mode controlp. 251
5.2.7 Robust control based on high order sliding modep. 254
5.2.8 Adaptive controlp. 255
5.3 Control in a constrained spacep. 257
5.3.1 Interaction of the manipulator with the environmentp. 257
5.3.2 Impedance controlp. 257
5.3.3 Force control of a mass attached to a springp. 258
5.3.4 Non-linear decoupling in a constrained spacep. 262
5.3.5 Position/force hybrid controlp. 263
5.3.5.1 Parallel structurep. 263
5.3.5.2 External structurep. 269
5.3.6 Specificity of the force/torque controlp. 271
5.4 Conclusionp. 275
5.5 Bibliographyp. 275
Chapter 6 Visual Servoingp. 279
6.1 Introductionp. 279
6.2 Modeling visual featuresp. 281
6.2.1 The interaction matrixp. 281
6.2.2 Eye-in-hand configurationp. 282
6.2.3 Eye-to-hand configurationp. 283
6.2.4 Interaction matrixp. 284
6.2.4.1 Interaction matrix of a 2-D pointp. 284
6.2.4.2 Interaction matrix of a 2-D geometric primitivep. 287
6.2.4.3 Interaction matrix for complex 2-D shapesp. 290
6.2.4.4 Interaction matrix by learning or estimationp. 293
6.2.5 Interaction matrix related to 3-D visual featuresp. 294
6.2.5.1 Pose estimationp. 294
6.2.5.2 Interaction matrix related to [Theta]up. 297
6.2.5.3 Interaction matrix related to a 3-D pointp. 298
6.2.5.4 Interaction matrix related to a 3-D planep. 300
6.3 Task function and control schemep. 301
6.3.1 Obtaining the desired value s*p. 301
6.3.2 Regulating the task functionp. 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 tasksp. 317
6.3.3.1 Virtual linksp. 317
6.3.3.2 Hybrid task functionp. 319
6.3.4 Target trackingp. 323
6.4 Other exteroceptive sensorsp. 325
6.5 Conclusionp. 326
6.6 Bibliographyp. 328
Chapter 7 Modeling and Control of Flexible Robotsp. 337
7.1 Introductionp. 337
7.2 Modeling of flexible robotsp. 337
7.2.1 Introductionp. 337
7.2.2 Generalized Newton-Euler model for a kinematically free elastic bodyp. 339
7.2.2.1 Definition: formalism of a dynamic modelp. 339
7.2.2.2 Choice of formalismp. 340
7.2.2.3 Kinematic model of a free elastic bodyp. 341
7.2.2.4 Balance principle compatible with the mixed formalismp. 343
7.2.2.5 Virtual power of the field of acceleration quantitiesp. 344
7.2.2.6 Virtual power of external forcesp. 346
7.2.2.7 Virtual power of elastic cohesion forcesp. 347
7.2.2.8 Balance of virtual powersp. 348
7.2.2.9 Linear rigid balance in integral formp. 349
7.2.2.10 Angular rigid balance in integral formp. 349
7.2.2.11 Elastic balances in integral formp. 350
7.2.2.12 Linear rigid balance in parametric formp. 351
7.2.2.13 Intrinsic matrix form of the generalized Newton-Euler modelp. 353
7.2.3 Velocity model of a simple open robotic chainp. 356
7.2.4 Acceleration model of a simple open robotic chainp. 357
7.2.5 Generalized Newton-Euler model for a flexible manipulatorp. 358
7.2.6 Extrinsic Newton-Euler model for numerical calculusp. 359
7.2.7 Geometric model of an open chainp. 362
7.2.8 Recursive calculation of the inverse and direct dynamic models for a flexible robotp. 363
7.2.8.1 Introductionp. 363
7.2.8.2 Recursive algorithm of the inverse dynamic modelp. 364
7.2.8.3 Recursive algorithm of the direct dynamic modelp. 368
7.2.8.4 Iterative symbolic calculationp. 373
7.3 Control of flexible robot manipulatorsp. 373
7.3.1 Introductionp. 373
7.3.2 Reminder of notationsp. 374
7.3.3 Control methodsp. 375
7.3.3.1 Regulationp. 375
7.3.3.2 Point-to-point movement in fixed timep. 375
7.3.3.3 Trajectory tracking in the joint spacep. 380
7.3.3.4 Trajectory tracking in the operational spacep. 383
7.4 Conclusionp. 388
7.5 Bibliographyp. 389
List of Authorsp. 395
Indexp. 397