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Modeling, Identification and Control of Robots, First Edition : Kogan Page Science Paper Edition - W Khalil

Modeling, Identification and Control of Robots, First Edition

Kogan Page Science Paper Edition

Paperback Published: 20th July 2004
ISBN: 9781903996669
Number Of Pages: 480

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Written by two of Europe's leading robotics experts, this book provides the tools for a unified approach to the modelling of robotic manipulators, whatever their mechanical structure.
No other publication covers the three fundamental issues of robotics: modelling, identification and control. It covers the development of various mathematical models required for the control and simulation of robots.

· World class authority
· Unique range of coverage not available in any other book
· Provides a complete course on robotic control at an undergraduate and graduate level

'....provides necessary tools to deal with various problems that can be encountered in the design, control synthesis and exploitation of robotic manipulators. It can also be recommended to students as a texbook.'
--European Mathematical Society

Introductionp. xvii
Terminology and general definitionsp. 1
Introductionp. 1
Mechanical components of a robotp. 2
Definitionsp. 4
Jointsp. 4
Joint spacep. 5
Task spacep. 5
Redundancyp. 6
Singular configurationsp. 6
Choosing the number of degrees of freedom of a robotp. 7
Architectures of robot manipulatorsp. 7
Characteristics of a robotp. 11
Conclusionp. 12
Transformation matrix between vectors, frames and screwsp. 13
Introductionp. 13
Homogeneous coordinatesp. 14
Representation of a pointp. 14
Representation of a directionp. 14
Representation of a planep. 15
Homogeneous transformationsp. 15
Transformation of framesp. 15
Transformation of vectorsp. 16
Transformation of planesp. 17
Transformation matrix of a pure translationp. 17
Transformation matrices of a rotation about the principle axesp. 18
Properties of homogeneous transformation matricesp. 20
Transformation matrix of a rotation about a general vector located at the originp. 23
Equivalent angle and axis of a general rotationp. 25
Kinematic screwp. 27
Definition of a screwp. 27
Representation of velocity (kinematic screw)p. 28
Transformation of screwsp. 28
Differential translation and rotation of framesp. 29
Representation of forces (wrench)p. 32
Conclusionp. 33
Direct geometric model of serial robotsp. 35
Introductionp. 35
Description of the geometry of serial robotsp. 36
Direct geometric modelp. 42
Optimization of the computation of the direct geometric modelp. 45
Transformation matrix of the end-effector in the world framep. 47
Specification of the orientationp. 48
Euler anglesp. 49
Roll-Pitch-Yaw anglesp. 51
Quaternionsp. 53
Conclusionp. 55
Inverse geometric model of serial robotsp. 57
Introductionp. 57
Mathematical statement of the problemp. 58
Inverse geometric model of robots with simple geometryp. 59
Principlep. 59
Special case: robots with a spherical wristp. 61
Inverse geometric model of robots with more than six degrees of freedomp. 67
Inverse geometric model of robots with less than six degrees of freedomp. 68
Inverse geometric model of decoupled six degree-of-freedom robotsp. 71
Introductionp. 71
Inverse geometric model of six degree-of-freedom robots having a spherical jointp. 72
Inverse geometric model of robots with three prismatic jointsp. 79
Inverse geometric model of general robotsp. 80
Conclusionp. 83
Direct kinematic model of serial robotsp. 85
Introductionp. 85
Computation of the Jacobian matrix from the direct geometric modelp. 86
Basic Jacobian matrixp. 87
Computation of the basic Jacobian matrixp. 88
Computation of the matrix [superscript i]J[subscript n]p. 90
Decomposition of the Jacobian matrix into three matricesp. 92
Efficient computation of the end-effector velocityp. 94
Dimension of the task space of a robotp. 95
Analysis of the robot workspacep. 96
Workspacep. 96
Singularity branchesp. 97
Jacobian surfacesp. 98
Concept of aspectp. 99
t-connected subspacesp. 101
Velocity transmission between joint space and task spacep. 103
Singular value decompositionp. 103
Velocity ellipsoid: velocity transmission performancep. 105
Static modelp. 107
Representation of a wrenchp. 107
Mapping of an external wrench into joint torquesp. 107
Velocity-force dualityp. 108
Second order kinematic modelp. 110
Kinematic model associated with the task coordinate representationp. 111
Direction cosinesp. 112
Euler anglesp. 113
Roll-Pitch-Yaw anglesp. 114
Quaternionsp. 114
Conclusionp. 115
Inverse kinematic model of serial robotsp. 117
Introductionp. 117
General form of the kinematic modelp. 117
Inverse kinematic model for a regular casep. 118
First methodp. 119
Second methodp. 119
Solution in the neighborhood of singularitiesp. 121
Use of the pseudoinversep. 122
Use of the damped pseudoinversep. 123
Other approaches for controlling motion near singularitiesp. 125
Inverse kinematic model of redundant robotsp. 126
Extended Jacobianp. 126
Jacobian pseudoinversep. 128
Weighted pseudoinversep. 128
Jacobian pseudoinverse with an optimization termp. 129
Task-priority conceptp. 131
Numerical calculation of the inverse geometric problemp. 133
Minimum description of tasksp. 134
Principle of the descriptionp. 135
Differential models associated with the minimum description of tasksp. 137
Conclusionp. 144
Geometric and kinematic models of complex chain robotsp. 145
Introductionp. 145
Description of tree structured robotsp. 145
Description of robots with closed chainsp. 148
Direct geometric model of tree structured robotsp. 153
Direct geometric model of robots with closed chainsp. 154
Inverse geometric model of closed chain robotsp. 155
Resolution of the geometric constraint equations of a simple loopp. 155
Introductionp. 155
General principlep. 156
Particular case of a parallelogram loopp. 160
Kinematic model of complex chain robotsp. 162
Numerical calculation of q[subscript p] and q[subscript c] in terms of q[subscript a]p. 167
Number of degrees of freedom of robots with closed chainsp. 168
Classification of singular positionsp. 169
Conclusionp. 169
Introduction to geometric and kinematic modeling of parallel robotsp. 171
Introductionp. 171
Parallel robot definitionp. 171
Comparing performance of serial and parallel robotsp. 172
Number of degrees of freedomp. 174
Parallel robot architecturesp. 175
Planar parallel robotsp. 175
Spatial parallel robotsp. 176
The Delta robot and its familyp. 179
Modeling the six degree-of-freedom parallel robotsp. 181
Geometric descriptionp. 181
Inverse geometric modelp. 183
Inverse kinematic modelp. 184
Direct geometric modelp. 185
Singular configurationsp. 189
Conclusionp. 190
Dynamic modeling of serial robotsp. 191
Introductionp. 191
Notationsp. 192
Lagrange formulationp. 193
Introductionp. 193
General form of the dynamic equationsp. 194
Computation of the elements of A, C and Qp. 195
Considering frictionp. 199
Considering the rotor inertia of actuatorsp. 201
Considering the forces and moments exerted by the end-effector on the environmentp. 201
Relation between joint torques and actuator torquesp. 201
Modeling of robots with elastic jointsp. 202
Determination of the base inertial parametersp. 205
Computation of the base parameters using the dynamic modelp. 205
Determination of the base parameters using the energy modelp. 207
Newton-Euler formulationp. 219
Introductionp. 219
Newton-Euler inverse dynamics linear in the inertial parametersp. 219
Practical form of the Newton-Euler algorithmp. 221
Real time computation of the inverse dynamic modelp. 222
Introductionp. 222
Customization of the Newton-Euler formulationp. 225
Utilization of the base inertial parametersp. 227
Direct dynamic modelp. 228
Using the inverse dynamic model to solve the direct dynamic problemp. 228
Recursive computation of the direct dynamic modelp. 230
Conclusionp. 233
Dynamics of robots with complex structurep. 235
Introductionp. 235
Dynamic modeling of tree structured robotsp. 235
Lagrange equationsp. 235
Newton-Euler formulationp. 236
Direct dynamic model of tree structured robotsp. 236
Determination of the base inertial parametersp. 237
Dynamic model of robots with closed kinematic chainsp. 242
Description of the systemp. 242
Computation of the inverse dynamic modelp. 243
Computation of the direct dynamic modelp. 245
Base inertial parameters of closed chain robotsp. 248
Base inertial parameters of parallelogram loopsp. 249
Practical computation of the base inertial parametersp. 250
Conclusionp. 256
Geometric calibration of robotsp. 257
Introductionp. 257
Geometric parametersp. 258
Robot parametersp. 258
Parameters of the base framep. 259
End-effector parametersp. 260
Generalized differential model of a robotp. 261
Principle of geometric calibrationp. 263
General calibration modelp. 263
Identifiability of the geometric parametersp. 265
Solution of the identification equationp. 268
Calibration methodsp. 270
Calibration using the end-effector coordinatesp. 270
Calibration using distance measurementp. 272
Calibration using location constraint and position constraintp. 273
Calibration methods using plane constraintp. 274
Correction and compensation of errorsp. 279
Calibration of parallel robotsp. 282
IGM calibration modelp. 283
DGM calibration modelp. 285
Measurement techniques for robot calibrationp. 285
Three-cable systemp. 286
Theodolitesp. 286
Laser tracking systemp. 287
Camera-type devicesp. 287
Conclusionp. 288
Identification of the dynamic parametersp. 291
Introductionp. 291
Estimation of inertial parametersp. 292
Principle of the identification procedurep. 292
Resolution of the identification equationsp. 293
Identifiability of the dynamic parametersp. 295
Estimation of the friction parametersp. 295
Trajectory selectionp. 296
Calculation of the joint velocities and accelerationsp. 298
Calculation of joint torquesp. 299
Dynamic identification modelp. 300
Other approaches to the dynamic identification modelp. 301
Sequential formulation of the dynamic modelp. 301
Filtered dynamic model (reduced order dynamic model)p. 302
Energy (or integral) identification modelp. 306
Principle of the energy modelp. 306
Power modelp. 308
Recommendations for experimental applicationp. 309
Conclusionp. 310
Trajectory generationp. 313
Introductionp. 313
Trajectory generation and control loopsp. 314
Point-to-point trajectory in the joint spacep. 315
Polynomial interpolationp. 316
Bang-bang acceleration profilep. 320
Trapeze velocity profilep. 321
Continuous acceleration profile with constant velocity phasep. 326
Point-to-point trajectory in the task spacep. 329
Trajectory generation with via pointsp. 331
Linear interpolations with continuous acceleration blendsp. 331
Trajectory generation with cubic spline functionsp. 337
Trajectory generation on a continuous path in the task spacep. 342
Conclusionp. 344
Motion controlp. 347
Introductionp. 347
Equations of motionp. 347
PID controlp. 348
PID control in the joint spacep. 348
Stability analysisp. 350
PID control in the task spacep. 352
Linearizing and decoupling controlp. 353
Introductionp. 353
Computed torque control in the joint spacep. 354
Computed torque control in the task spacep. 358
Passivity-based controlp. 360
Introductionp. 360
Hamiltonian formulation of the robot dynamicsp. 360
Passivity-based position controlp. 362
Passivity-based tracking controlp. 363
Lyapunov-based methodp. 368
Adaptive controlp. 368
Introductionp. 368
Adaptive feedback linearizing controlp. 369
Adaptive passivity-based controlp. 371
Conclusionp. 376
Compliant motion controlp. 377
Introductionp. 377
Description of a compliant motionp. 378
Passive stiffness controlp. 378
Active stiffness controlp. 379
Impedance controlp. 381
Hybrid position/force controlp. 385
Parallel hybrid position/force controlp. 386
External hybrid control schemep. 391
Conclusionp. 393
Appendices
Solution of the inverse geometric model equations (Table 4.1)p. 395
Type 2p. 395
Type 3p. 396
Type 4p. 397
Type 5p. 397
Type 6p. 398
Type 7p. 398
Type 8p. 399
The inverse robotp. 401
Dyalitic eliminationp. 403
Solution of systems of linear equationsp. 405
Problem statementp. 405
Resolution based on the generalized inversep. 406
Resolution based on the pseudoinversep. 407
Resolution based on the QR decompositionp. 413
Numerical computation of the base parametersp. 417
Introductionp. 417
Base inertial parameters of serial and tree structured robotsp. 418
Base inertial parameters of closed loop robotsp. 420
Generality of the numerical methodp. 420
Recursive equations between the energy functionsp. 421
Recursive equation between the kinetic energy functions of serial robotsp. 421
Recursive equation between the potential energy functions of serial robotsp. 423
Recursive equation between the total energy functions of serial robotsp. 424
Expression of [superscript a(j) lambda subscript j] in the case of the tree structured robotp. 424
Dynamic model of the Staubli RX-90 robotp. 427
Computation of the inertia matrix of tree structured robotsp. 431
Inertial parameters of a composite linkp. 431
Computation of the inertia matrixp. 433
Stability analysis using Lyapunov theoryp. 435
Autonomous systemsp. 435
Non-autonomous systemsp. 437
Computation of the dynamic control law in the task spacep. 439
Calculation of the location error e[subscript x]p. 439
Calculation of the velocity of the terminal link Xp. 440
Calculation of J qp. 441
Calculation of J(q)[superscript -1] yp. 442
Modified dynamic modelp. 442
Stability of passive systemsp. 443
Definitionsp. 443
Stability analysis of closed-loop positive feedbackp. 444
Stability properties of passive systemsp. 445
Referencesp. 447
Indexp. 475
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781903996669
ISBN-10: 190399666X
Series: Kogan Page Science Paper Edition
Audience: General
Format: Paperback
Language: English
Number Of Pages: 480
Published: 20th July 2004
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 23.32 x 15.85  x 3.81
Weight (kg): 0.78
Edition Type: New edition