Klienditugi: 7440010 (E-R 10-18)

Modeling, Identification and Control of Robots [Pehme köide]

W. Khalil (Professor at the Ecole Centrale, Nantes, France), E. Dombre (Head of the Robotics department at University of Montpelier, France)

Formaat: Paperback / softback, 500 pages, kõrgus x laius: 234x156 mm, kaal: 780 g
Ilmumisaeg: 01-Jul-2004
Kirjastus: Hermes Penton
ISBN-10: 190399666X
ISBN-13: 9781903996669

Teised raamatud teemal:

Robotics

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Formaat: Paperback / softback, 500 pages, kõrgus x laius: 234x156 mm, kaal: 780 g
Ilmumisaeg: 01-Jul-2004
Kirjastus: Hermes Penton
ISBN-10: 190399666X
ISBN-13: 9781903996669

Teised raamatud teemal:

Robotics

Püsilink: https://www.kriso.ee/db/9781903996669.html

Märksõnad:

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

Introduction

xvii

Terminology and general definitions

(12)

Introduction

(1)

Mechanical components of a robot

(2)

Definitions

(3)

Joints

(1)

Revolute joint

(1)

Prismatic joint

(1)

Joint space

(1)

Task space

(1)

Redundancy

(1)

Singular configurations

(1)

Choosing the number of degrees of freedom of a robot

(1)

Architectures of robot manipulators

(4)

Characteristics of a robot

(1)

Conclusion

(1)

Transformation matrix between vectors, frames and screws

(22)

Introduction

(1)

Homogeneous coordinates

(1)

Representation of a point

(1)

Representation of a direction

(1)

Representation of a plane

(1)

Homogeneous transformations

(12)

Transformation of frames

(1)

Transformation of vectors

(1)

Transformation of planes

(1)

Transformation matrix of a pure translation

(1)

Transformation matrices of a rotation about the principle axes

(1)

Transformation matrix of a rotation about the x axis by an angle θ

(1)

Transformation matrix of a rotation about the y axis by an angle θ

(1)

Transformation matrix of a rotation θ about the z axis by an angle θ

(1)

Properties of homogeneous transformation matrices

(3)

Transformation matrix of a rotation about a general vector located at the origin

(2)

Equivalent angle and axis of a general rotation

(2)

Kinematic screw

(2)

Definition of a screw

(1)

Representation of velocity (kinematic screw)

(1)

Transformation of screws

(1)

Differential translation and rotation of frames

(3)

Representation of forces (wrench)

(1)

Conclusion

(2)

Direct geometric model of serial robots

(22)

Introduction

(1)

Description of the geometry of serial robots

(6)

Direct geometric model

(3)

Optimization of the computation of the direct geometric model

(2)

Transformation matrix of the end-effector in the world frame

(1)

Specification of the orientation

(7)

Euler angles

(2)

Roll-Pitch-Yaw angles

(2)

Quaternions

(2)

Conclusion

(2)

Inverse geometric model of serial robots

(28)

Introduction

(1)

Mathematical statement of the problem

(1)

Inverse geometric model of robots with simple geometry

(12)

Principle

(2)

Special case: robots with a spherical wrist

(1)

Position equation

(1)

Orientation equation

(5)

Inverse geometric model of robots with more than six degrees of freedom

(1)

Inverse geometric model of robots with less than six degrees of freedom

(3)

Inverse geometric model of decoupled six degree-of-freedom robots

(9)

Introduction

(1)

Inverse geometric model of six degree-of-freedom robots having a spherical joint

(1)

General solution of the position equation

(6)

General solution of the orientation equation

(1)

Inverse geometric model of robots with three prismatic joints

(1)

Solution of the orientation equation

(1)

Solution of the position equation

(1)

Inverse geometric model of general robots

(3)

Conclusion

(2)

Direct kinematic model of serial robots

(32)

Introduction

(1)

Computation of the Jacobian matrix from the direct geometric model

(1)

Basic Jacobian matrix

(5)

Computation of the basic Jacobian matrix

(2)

Computation of the matrix iJn

(2)

Decomposition of the Jacobian matrix into three matrices

(2)

Efficient computation of the end-effector velocity

(1)

Dimension of the task space of a robot

(1)

Analysis of the robot workspace

(7)

Workspace

(1)

Singularity branches

(1)

Jacobian surfaces

(1)

Concept of aspect

(2)

t-connected subspaces

101

(2)

Velocity transmission between joint space and task space

103

(4)

Singular value decomposition

103

(2)

Velocity ellipsoid: velocity transmission performance

105

(2)

Static model

107

(3)

Representation of a wrench

107

(1)

Mapping of an external wrench into joint torques

107

(1)

Velocity-force duality

108

(2)

Second order kinematic model

110

(1)

Kinematic model associated with the task coordinate representation

111

(4)

Direction cosines

112

(1)

Euler angles

113

(1)

Roll-Pitch-Yaw angles

114

(1)

Quaternions

114

(1)

Conclusion

115

(2)

Inverse kinematic model of serial robots

117

(28)

Introduction

117

(1)

General form of the kinematic model

117

(1)

Inverse kinematic model for a regular case

118

(3)

First method

119

(1)

Second method

119

(2)

Solution in the neighborhood of singularities

121

(5)

Use of the pseudoinverse

122

(1)

Use of the damped pseudoinverse

123

(2)

Other approaches for controlling motion near singularities

125

(1)

Inverse kinematic model of redundant robots

126

(7)

Extended Jacobian

126

(2)

Jacobian pseudoinverse

128

(1)

Weighted pseudoinverse

128

(1)

Jacobian pseudoinverse with an optimization term

129

(1)

Avoiding joint limits

129

(1)

Increasing the manipulability

130

(1)

Task-priority concept

131

(2)

Numerical calculation of the inverse geometric problem

133

(1)

Minimum description of tasks

134

(10)

Principle of the description

135

(2)

Differential models associated with the minimum description of tasks

137

(1)

Point contact (point on plane)

138

(1)

Line contact (line on plane)

139

(1)

Planar contact (plane on plane)

140

(1)

Cylindrical groove joint (point on line)

140

(1)

Cylindrical joint (line on line)

141

(1)

Spherical joint (point on point)

142

(1)

Revolute joint (line-point on line-point)

142

(1)

Prismatic joint (plane-plane on plane-plane)

142

(2)

Conclusion

144

(1)

Geometric and kinematic models of complex chain robots

145

(26)

Introduction

145

(1)

Description of tree structured robots

145

(3)

Description of robots with closed chains

148

(5)

Direct geometric model of tree structured robots

153

(1)

Direct geometric model of robots with closed chains

154

(1)

Inverse geometric model of closed chain robots

155

(1)

Resolution of the geometric constraint equations of a simple loop

155

(7)

Introduction

155

(1)

General principle

156

(4)

Particular case of a parallelogram loop

160

(2)

Kinematic model of complex chain robots

162

(5)

Numerical calculation of qp and qc in terms of qa

167

(1)

Number of degrees of freedom of robots with closed chains

168

(1)

Classification of singular positions

169

(1)

Conclusion

169

(2)

Introduction to geometric and kinematic modeling of parallel robots

171

(20)

Introduction

171

(1)

Parallel robot definition

171

(1)

Comparing performance of serial and parallel robots

172

(2)

Number of degrees of freedom

174

(1)

Parallel robot architectures

175

(6)

Planar parallel robots

175

(1)

Spatial parallel robots

176

(1)

Three degree-of-freedom spatial robots

177

(1)

Six degree-of-freedom spatial robots

177

(2)

The Delta robot and its family

179

(2)

Modeling the six degree-of-freedom parallel robots

181

(8)

Geometric description

181

(2)

Inverse geometric model

183

(1)

Inverse kinematic model

184

(1)

Direct geometric model

185

(1)

Closed-form solution

185

(3)

Numerical solution

188

(1)

Singular configurations

189

(1)

Conclusion

190

(1)

Dynamic modeling of serial robots

191

(44)

Introduction

191

(1)

Notations

192

(1)

Lagrange formulation

193

(12)

Introduction

193

(1)

General form of the dynamic equations

194

(1)

Computation of the elements of A, C and Q

195

(1)

Computation of the kinetic energy

195

(3)

Computation of the potential energy

198

(1)

Dynamic model properties

198

(1)

Considering friction

199

(2)

Considering the rotor inertia of actuators

201

(1)

Considering the forces and moments exerted by the end-effector on the environment

201

(1)

Relation between joint torques and actuator torques

201

(1)

Modeling of robots with elastic joints

202

(3)

Determination of the base inertial parameters

205

(14)

Computation of the base parameters using the dynamic model

205

(2)

Determination of the base parameters using the energy model

207

(1)

Determination of the parameters having no effect on the dynamic model

208

(2)

General grouping relations

210

(2)

Particular grouped parameters

212

(1)

Practical determination of the base parameters

213

(1)

Considering the inertia of rotors

214

(5)

Newton-Euler formulation

219

(3)

Introduction

219

(1)

Newton-Euler inverse dynamics linear in the inertial parameters

219

(2)

Practical form of the Newton-Euler algorithm

221

(1)

Real time computation of the inverse dynamic model

222

(6)

Introduction

222

(3)

Customization of the Newton-Euler formulation

225

(2)

Utilization of the base inertial parameters

227

(1)

Direct dynamic model

228

(5)

Using the inverse dynamic model to solve the direct dynamic problem

228

(2)

Recursive computation of the direct dynamic model

230

(3)

Conclusion

233

(2)

Dynamics of robots with complex structure

235

(22)

Introduction

235

(1)

Dynamic modeling of tree structured robots

235

(7)

Lagrange equations

235

(1)

Newton-Euler formulation

236

(1)

Direct dynamic model of tree structured robots

236

(1)

Determination of the base inertial parameters

237

(1)

General grouping equations

238

(2)

Particular grouped parameters

240

(2)

Dynamic model of robots with closed kinematic chains

242

(14)

Description of the system

242

(1)

Computation of the inverse dynamic model

243

(2)

Computation of the direct dynamic model

245

(3)

Base inertial parameters of closed chain robots

248

(1)

Base inertial parameters of parallelogram loops

249

(1)

Practical computation of the base inertial parameters

250

(6)

Conclusion

256

(1)

Geometric calibration of robots

257

(34)

Introduction

257

(1)

Geometric parameters

258

(3)

Robot parameters

258

(1)

Parameters of the base frame

259

(1)

End-effector parameters

260

(1)

Generalized differential model of a robot

261

(2)

Principle of geometric calibration

263

(7)

General calibration model

263

(2)

Identifiability of the geometric parameters

265

(1)

Determination of the identifiable parameters

266

(1)

Optimum calibration configurations

267

(1)

Solution of the identification equation

268

(2)

Calibration methods

270

(9)

Calibration using the end-effector coordinates

270

(2)

Calibration using distance measurement

272

(1)

Calibration using location constraint and position constraint

273

(1)

Calibration methods using plane constraint

274

(1)

Calibration using plane equation

274

(2)

Calibration using normal coordinates to the plane

276

(3)

Correction and compensation of errors

279

(3)

Calibration of parallel robots

282

(3)

IGM calibration model

283

(2)

DGM calibration model

285

(1)

Measurement techniques for robot calibration

285

(3)

Three-cable system

286

(1)

Theodolites

286

(1)

Laser tracking system

287

(1)

Camera-type devices

287

(1)

Conclusion

288

(3)

Identification of the dynamic parameters

291

(22)

Introduction

291

(1)

Estimation of inertial parameters

292

(1)

Principle of the identification procedure

292

(8)

Resolution of the identification equations

293

(2)

Identifiability of the dynamic parameters

295

(1)

Estimation of the friction parameters

295

(1)

Trajectory selection

296

(1)

Trajectory optimization

296

(2)

Sequential identification

298

(1)

Calculation of the joint velocities and accelerations

298

(1)

Calculation of joint torques

299

(1)

Dynamic identification model

300

(1)

Other approaches to the dynamic identification model

301

(5)

Sequential formulation of the dynamic model

301

(1)

Filtered dynamic model (reduced order dynamic model)

302

(4)

Energy (or integral) identification model

306

(3)

Principle of the energy model

306

(2)

Power model

308

(1)

Recommendations for experimental application

309

(1)

Conclusion

310

(3)

Trajectory generation

313

(34)

Introduction

313

(1)

Trajectory generation and control loops

314

(1)

Point-to-point trajectory in the joint space

315

(14)

Polynomial interpolation

316

(1)

Linear interpolation

316

(1)

Cubic polynomial

316

(1)

Quintic polynomial

317

(2)

Computation of the minimum traveling time

319

(1)

Bang-bang acceleration profile

320

(1)

Trapeze velocity profile

321

(5)

Continuous acceleration profile with constant velocity phase

326

(3)

Point-to-point trajectory in the task space

329

(2)

Trajectory generation with via points

331

(13)

Linear interpolations with continuous acceleration blends

331

(1)

Joint space scheme

331

(4)

Task space scheme

335

(2)

Trajectory generation with cubic spline functions

337

(1)

Principle of the method

337

(3)

Calculation of the minimum traveling time on each segment

340

(2)

Trajectory generation on a continuous path in the task space

342

(2)

Conclusion

344

(3)

Motion control

347

(30)

Introduction

347

(1)

Equations of motion

347

(1)

PID control

348

(5)

PID control in the joint space

348

(2)

Stability analysis

350

(2)

PID control in the task space

352

(1)

Linearizing and decoupling control

353

(7)

Introduction

353

(1)

Computed torque control in the joint space

354

(1)

Principle of the control

354

(1)

Tracking control scheme

355

(1)

Position control scheme

356

(1)

Predictive dynamic control

357

(1)

Practical computation of the computed torque control laws

357

(1)

Computed torque control in the task space

358

(2)

Passivity-based control

360

(8)

Introduction

360

(1)

Hamiltonian formulation of the robot dynamics

360

(2)

Passivity-based position control

362

(1)

Passivity-based tracking control

363

(5)

Lyapunov-based method

368

(1)

Adaptive control

368

(8)

Introduction

368

(1)

Adaptive feedback linearizing control

369

(2)

Adaptive passivity-based control

371

(5)

Conclusion

376

(1)

Compliant motion control

377

(70)

Introduction

377

(1)

Description of a compliant motion

378

(1)

Passive stiffness control

378

(1)

Active stiffness control

379

(2)

Impedance control

381

(4)

Hybrid position/force control

385

(8)

Parallel hybrid position/force control

386

(5)

External hybrid control scheme

391

(2)

Conclusion

393

(2)

Appendices

Solution of the inverse geometric model equations (Table 4.1)

395

(6)

Type 2

395

(1)

Type 3

396

(1)

Type 4

397

(1)

Type 5

397

(1)

Type 6

398

(1)

Type 7

398

(1)

Type 8

399

(2)

The inverse robot

401

(2)

Dyalitic elimination

403

(2)

Solution of systems of linear equations

405

(12)

Problem statement

405

(1)

Resolution based on the generalized inverse

406

(1)

Definitions

406

(1)

Computation of a generalized inverse

406

(1)

Resolution based on the pseudoinverse

407

(1)

Definition

407

(1)

Pseudoinverse computation methods

408

(1)

Method requiring explicit computation of the rank

408

(1)

Greville method

408

(2)

Method based on the singular value decomposition of W

410

(3)

Resolution based on the QR decomposition

413

(1)

Full rank system

413

(1)

Rank deficient system

414

(3)

Numerical computation of the base parameters

417

(4)

Introduction

417

(1)

Base inertial parameters of serial and tree structured robots

418

(2)

Base inertial parameters of closed loop robots

420

(1)

Generality of the numerical method

420

(1)

Recursive equations between the energy functions

421

(6)

Recursive equation between the kinetic energy functions of serial robots

421

(2)

Recursive equation between the potential energy functions of serial robots

423

(1)

Recursive equation between the total energy functions of serial robots

424

(1)

Expression of a(j)λj in the case of the tree structured robot

424

(3)

Dynamic model of the Staubli RX-90 robot

427

(4)

Computation of the inertia matrix of tree structured robots

431

(4)

Inertial parameters of a composite link

431

(2)

Computation of the inertia matrix

433

(2)

Stability analysis using Lyapunov theory

435

(4)

Autonomous systems

435

(1)

Definition of stability

435

(1)

Positive definite and positive semi-definite functions

436

(1)

Lyapunov direct theorem (sufficient conditions)

436

(1)

La Salle theorem and invariant set principle

437

(1)

Non-autonomous systems

437

(1)

Definition of stability

437

(1)

Lyapunov direct method

437

(2)

Computation of the dynamic control law in the task space

439

(4)

Calculation of the location error ex

439

(1)

Calculation of the velocity of the terminal link X

440

(1)

Calculation of J q

441

(1)

Calculation of J(q)-1 y

442

(1)

Modified dynamic model

442

(1)

Stability of passive systems

443

(4)

Definitions

443

(1)

Stability analysis of closed-loop positive feedback

444

(1)

Stability properties of passive systems

445

(2)

References

447

(28)

Index

475

Modeling, Identification and Control of Robots [Pehme köide]

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