Robot Manipulators : Modeling, Performance Analysis and Control

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  • Format: Hardcover
  • Copyright: 2007-01-30
  • Publisher: Iste/Hermes Science Pub

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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 Robotsp. 1
Introductionp. 1
Geometric modelingp. 2
Geometric descriptionp. 2
Direct geometric modelp. 6
Inverse geometric modelp. 7
Stating the problemp. 8
Principle of Paul's methodp. 10
Kinematic modelingp. 14
Direct kinematic modelp. 14
Calculation of the Jacobian matrix by derivation of the DGMp. 15
Kinematic Jacobian matrixp. 17
Decomposition of the kinematic Jacobian matrix into three matricesp. 19
Dimension of the operational space of a robotp. 20
Inverse kinematic modelp. 21
General form of the kinematic modelp. 21
Inverse kinematic model for the regular casep. 22
Solution at the proximity of singular positionsp. 23
Inverse kinematic model of redundant robotsp. 24
Calibration of geometric parametersp. 26
Introductionp. 26
Geometric parametersp. 26
Geometric parameters of the robotp. 26
Parameters of the robot's locationp. 27
Geometric parameters of the end-effectorp. 28
Generalized differential model of a robotp. 29
Principle of geometric calibrationp. 30
General form of the calibration modelp. 30
Identifying the geometric parametersp. 31
Solving the identification equationsp. 34
Calibration methods of geometric parametersp. 35
Calibration model by measuring the end-effector locationp. 35
Autonomous calibration modelsp. 36
Correction of geometric parametersp. 39
Dynamic modelingp. 40
Lagrange formalismp. 42
General form of dynamic equationsp. 43
Calculation of energyp. 44
Properties of the dynamic modelp. 46
Taking into consideration the frictionp. 47
Taking into account the inertia of the actuator's rotorp. 48
Taking into consideration the forces and moments exerted by the end-effector on its environmentp. 48
Newton-Euler formalismp. 50
Newton-Euler equations linear in the inertial parametersp. 50
Practical form of Newton-Euler equationsp. 52
Determining the base inertial parametersp. 53
Identification of dynamic parametersp. 59
Introductionp. 59
Identification principle of dynamic parametersp. 60
Solving methodp. 60
Identifiable parametersp. 62
Choice of identification trajectoriesp. 63
Evaluation of joint coordinatesp. 65
Evaluation of joint torquesp. 65
Identification model using the dynamic modelp. 66
Sequential formulation of the dynamic modelp. 68
Practical considerationsp. 69
Conclusionp. 70
Bibliographyp. 71
Modeling of Parallel Robotsp. 81
Introductionp. 81
Characteristics of classic robotsp. 81
Other types of robot structurep. 82
General advantages and disadvantagesp. 86
Present day usesp. 88
Simulators and space applicationsp. 88
Industrial applicationsp. 91
Medical applicationsp. 93
Precise positioningp. 94
Machine typesp. 95
Introductionp. 95
Plane robots with three degrees of freedomp. 100
Robots moving in spacep. 101
Manipulators with three degrees of freedomp. 101
Manipulators with four or five degrees of freedomp. 107
Manipulators with six degrees of freedomp. 109
Inverse geometric and kinematic modelsp. 113
Inverse geometric modelp. 113
Inverse kinematicsp. 115
Singular configurationsp. 117
Singularities and staticsp. 121
State of the artp. 121
The geometric methodp. 122
Maneuverability and condition numberp. 125
Singularities in practicep. 126
Direct geometric modelp. 126
Iterative methodp. 127
Algebraic methodp. 128
Reminder concerning algebraic geometryp. 128
Planar robotsp. 130
Manipulators with six degrees of freedomp. 133
Bibliographyp. 134
Performance Analysis of Robotsp. 141
Introductionp. 141
Accessibilityp. 143
Various levels of accessibilityp. 143
Condition of accessibilityp. 144
Workspace of a robot manipulatorp. 146
General definitionp. 146
Space of accessible positionsp. 148
Primary space and secondary spacep. 149
Defined orientation workspacep. 151
Free workspacep. 152
Calculation of the workspacep. 155
Concept of aspectp. 157
Definitionp. 157
Mode of aspects calculationp. 158
Free aspectsp. 160
Application of the aspectsp. 161
Concept of connectivityp. 163
Introductionp. 163
Characterization of n-connectivityp. 165
Characterization of t-connectivityp. 168
Local performancesp. 174
Definition of dexterityp. 174
Manipulabilityp. 174
Isotropy indexp. 180
Lowest singular valuep. 181
Approach lengths and anglesp. 181
Conclusionp. 183
Bibliographyp. 183
Trajectory Generationp. 189
Introductionp. 189
Point-to-point trajectory in the joint space under kinematic constraintsp. 190
Fifth-order polynomial modelp. 191
Trapezoidal velocity modelp. 193
Smoothed trapezoidal velocity modelp. 198
Point-to-point trajectory in the task-space under kinematic constraintsp. 201
Trajectory generation under kinodynamic constraintsp. 204
Problem statementp. 205
Constraintsp. 206
Objective functionp. 207
Description of the methodp. 208
Outlinep. 208
Construction of a random trajectory profilep. 209
Handling kinodynamic constraintsp. 212
Summaryp. 216
Trapezoidal profilesp. 218
Examplesp. 221
Case of a two dof robotp. 221
Optimal free motion planning problemp. 221
Optimal motion problem with geometric path constraintp. 223
Case of a six dof robotp. 224
Optimal free motion planning problemp. 225
Optimal motion problem with geometric path constraintsp. 226
Optimal free motion planning problem with intermediate pointsp. 227
Conclusionp. 229
Bibliographyp. 230
Stochastic Optimization Techniquesp. 234
Position and Force Control of a Robot in a Free or Constrained Spacep. 241
Introductionp. 241
Free space controlp. 242
Hypotheses applying to the whole chapterp. 242
Complete dynamic modeling of a robot manipulatorp. 243
Ideal dynamic control in the joint spacep. 246
Ideal dynamic control in the operational working spacep. 248
Decentralized controlp. 250
Sliding mode controlp. 251
Robust control based on high order sliding modep. 254
Adaptive controlp. 255
Control in a constrained spacep. 257
Interaction of the manipulator with the environmentp. 257
Impedance controlp. 257
Force control of a mass attached to a springp. 258
Non-linear decoupling in a constrained spacep. 262
Position/force hybrid controlp. 263
Parallel structurep. 263
External structurep. 269
Specificity of the force/torque controlp. 271
Conclusionp. 275
Bibliographyp. 275
Visual Servoingp. 279
Introductionp. 279
Modeling visual featuresp. 281
The interaction matrixp. 281
Eye-in-hand configurationp. 282
Eye-to-hand configurationp. 283
Interaction matrixp. 284
Interaction matrix of a 2-D pointp. 284
Interaction matrix of a 2-D geometric primitivep. 287
Interaction matrix for complex 2-D shapesp. 290
Interaction matrix by learning or estimationp. 293
Interaction matrix related to 3-D visual featuresp. 294
Pose estimationp. 294
Interaction matrix related to [Theta]up. 297
Interaction matrix related to a 3-D pointp. 298
Interaction matrix related to a 3-D planep. 300
Task function and control schemep. 301
Obtaining the desired value s*p. 301
Regulating the task functionp. 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 tasksp. 317
Virtual linksp. 317
Hybrid task functionp. 319
Target trackingp. 323
Other exteroceptive sensorsp. 325
Conclusionp. 326
Bibliographyp. 328
Modeling and Control of Flexible Robotsp. 337
Introductionp. 337
Modeling of flexible robotsp. 337
Introductionp. 337
Generalized Newton-Euler model for a kinematically free elastic bodyp. 339
Definition: formalism of a dynamic modelp. 339
Choice of formalismp. 340
Kinematic model of a free elastic bodyp. 341
Balance principle compatible with the mixed formalismp. 343
Virtual power of the field of acceleration quantitiesp. 344
Virtual power of external forcesp. 346
Virtual power of elastic cohesion forcesp. 347
Balance of virtual powersp. 348
Linear rigid balance in integral formp. 349
Angular rigid balance in integral formp. 349
Elastic balances in integral formp. 350
Linear rigid balance in parametric formp. 351
Intrinsic matrix form of the generalized Newton-Euler modelp. 353
Velocity model of a simple open robotic chainp. 356
Acceleration model of a simple open robotic chainp. 357
Generalized Newton-Euler model for a flexible manipulatorp. 358
Extrinsic Newton-Euler model for numerical calculusp. 359
Geometric model of an open chainp. 362
Recursive calculation of the inverse and direct dynamic models for a flexible robotp. 363
Introductionp. 363
Recursive algorithm of the inverse dynamic modelp. 364
Recursive algorithm of the direct dynamic modelp. 368
Iterative symbolic calculationp. 373
Control of flexible robot manipulatorsp. 373
Introductionp. 373
Reminder of notationsp. 374
Control methodsp. 375
Regulationp. 375
Point-to-point movement in fixed timep. 375
Trajectory tracking in the joint spacep. 380
Trajectory tracking in the operational spacep. 383
Conclusionp. 388
Bibliographyp. 389
List of Authorsp. 395
Indexp. 397
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