Paperback
Published: 20th July 2004
ISBN: 9781903996669
Number Of Pages: 480
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.
Â· World class authority
Â· Unique range of coverage not available in any other book
Â· 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
Introduction | p. xvii |
Terminology and general definitions | p. 1 |
Introduction | p. 1 |
Mechanical components of a robot | p. 2 |
Definitions | p. 4 |
Joints | p. 4 |
Joint space | p. 5 |
Task space | p. 5 |
Redundancy | p. 6 |
Singular configurations | p. 6 |
Choosing the number of degrees of freedom of a robot | p. 7 |
Architectures of robot manipulators | p. 7 |
Characteristics of a robot | p. 11 |
Conclusion | p. 12 |
Transformation matrix between vectors, frames and screws | p. 13 |
Introduction | p. 13 |
Homogeneous coordinates | p. 14 |
Representation of a point | p. 14 |
Representation of a direction | p. 14 |
Representation of a plane | p. 15 |
Homogeneous transformations | p. 15 |
Transformation of frames | p. 15 |
Transformation of vectors | p. 16 |
Transformation of planes | p. 17 |
Transformation matrix of a pure translation | p. 17 |
Transformation matrices of a rotation about the principle axes | p. 18 |
Properties of homogeneous transformation matrices | p. 20 |
Transformation matrix of a rotation about a general vector located at the origin | p. 23 |
Equivalent angle and axis of a general rotation | p. 25 |
Kinematic screw | p. 27 |
Definition of a screw | p. 27 |
Representation of velocity (kinematic screw) | p. 28 |
Transformation of screws | p. 28 |
Differential translation and rotation of frames | p. 29 |
Representation of forces (wrench) | p. 32 |
Conclusion | p. 33 |
Direct geometric model of serial robots | p. 35 |
Introduction | p. 35 |
Description of the geometry of serial robots | p. 36 |
Direct geometric model | p. 42 |
Optimization of the computation of the direct geometric model | p. 45 |
Transformation matrix of the end-effector in the world frame | p. 47 |
Specification of the orientation | p. 48 |
Euler angles | p. 49 |
Roll-Pitch-Yaw angles | p. 51 |
Quaternions | p. 53 |
Conclusion | p. 55 |
Inverse geometric model of serial robots | p. 57 |
Introduction | p. 57 |
Mathematical statement of the problem | p. 58 |
Inverse geometric model of robots with simple geometry | p. 59 |
Principle | p. 59 |
Special case: robots with a spherical wrist | p. 61 |
Inverse geometric model of robots with more than six degrees of freedom | p. 67 |
Inverse geometric model of robots with less than six degrees of freedom | p. 68 |
Inverse geometric model of decoupled six degree-of-freedom robots | p. 71 |
Introduction | p. 71 |
Inverse geometric model of six degree-of-freedom robots having a spherical joint | p. 72 |
Inverse geometric model of robots with three prismatic joints | p. 79 |
Inverse geometric model of general robots | p. 80 |
Conclusion | p. 83 |
Direct kinematic model of serial robots | p. 85 |
Introduction | p. 85 |
Computation of the Jacobian matrix from the direct geometric model | p. 86 |
Basic Jacobian matrix | p. 87 |
Computation of the basic Jacobian matrix | p. 88 |
Computation of the matrix [superscript i]J[subscript n] | p. 90 |
Decomposition of the Jacobian matrix into three matrices | p. 92 |
Efficient computation of the end-effector velocity | p. 94 |
Dimension of the task space of a robot | p. 95 |
Analysis of the robot workspace | p. 96 |
Workspace | p. 96 |
Singularity branches | p. 97 |
Jacobian surfaces | p. 98 |
Concept of aspect | p. 99 |
t-connected subspaces | p. 101 |
Velocity transmission between joint space and task space | p. 103 |
Singular value decomposition | p. 103 |
Velocity ellipsoid: velocity transmission performance | p. 105 |
Static model | p. 107 |
Representation of a wrench | p. 107 |
Mapping of an external wrench into joint torques | p. 107 |
Velocity-force duality | p. 108 |
Second order kinematic model | p. 110 |
Kinematic model associated with the task coordinate representation | p. 111 |
Direction cosines | p. 112 |
Euler angles | p. 113 |
Roll-Pitch-Yaw angles | p. 114 |
Quaternions | p. 114 |
Conclusion | p. 115 |
Inverse kinematic model of serial robots | p. 117 |
Introduction | p. 117 |
General form of the kinematic model | p. 117 |
Inverse kinematic model for a regular case | p. 118 |
First method | p. 119 |
Second method | p. 119 |
Solution in the neighborhood of singularities | p. 121 |
Use of the pseudoinverse | p. 122 |
Use of the damped pseudoinverse | p. 123 |
Other approaches for controlling motion near singularities | p. 125 |
Inverse kinematic model of redundant robots | p. 126 |
Extended Jacobian | p. 126 |
Jacobian pseudoinverse | p. 128 |
Weighted pseudoinverse | p. 128 |
Jacobian pseudoinverse with an optimization term | p. 129 |
Task-priority concept | p. 131 |
Numerical calculation of the inverse geometric problem | p. 133 |
Minimum description of tasks | p. 134 |
Principle of the description | p. 135 |
Differential models associated with the minimum description of tasks | p. 137 |
Conclusion | p. 144 |
Geometric and kinematic models of complex chain robots | p. 145 |
Introduction | p. 145 |
Description of tree structured robots | p. 145 |
Description of robots with closed chains | p. 148 |
Direct geometric model of tree structured robots | p. 153 |
Direct geometric model of robots with closed chains | p. 154 |
Inverse geometric model of closed chain robots | p. 155 |
Resolution of the geometric constraint equations of a simple loop | p. 155 |
Introduction | p. 155 |
General principle | p. 156 |
Particular case of a parallelogram loop | p. 160 |
Kinematic model of complex chain robots | p. 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 chains | p. 168 |
Classification of singular positions | p. 169 |
Conclusion | p. 169 |
Introduction to geometric and kinematic modeling of parallel robots | p. 171 |
Introduction | p. 171 |
Parallel robot definition | p. 171 |
Comparing performance of serial and parallel robots | p. 172 |
Number of degrees of freedom | p. 174 |
Parallel robot architectures | p. 175 |
Planar parallel robots | p. 175 |
Spatial parallel robots | p. 176 |
The Delta robot and its family | p. 179 |
Modeling the six degree-of-freedom parallel robots | p. 181 |
Geometric description | p. 181 |
Inverse geometric model | p. 183 |
Inverse kinematic model | p. 184 |
Direct geometric model | p. 185 |
Singular configurations | p. 189 |
Conclusion | p. 190 |
Dynamic modeling of serial robots | p. 191 |
Introduction | p. 191 |
Notations | p. 192 |
Lagrange formulation | p. 193 |
Introduction | p. 193 |
General form of the dynamic equations | p. 194 |
Computation of the elements of A, C and Q | p. 195 |
Considering friction | p. 199 |
Considering the rotor inertia of actuators | p. 201 |
Considering the forces and moments exerted by the end-effector on the environment | p. 201 |
Relation between joint torques and actuator torques | p. 201 |
Modeling of robots with elastic joints | p. 202 |
Determination of the base inertial parameters | p. 205 |
Computation of the base parameters using the dynamic model | p. 205 |
Determination of the base parameters using the energy model | p. 207 |
Newton-Euler formulation | p. 219 |
Introduction | p. 219 |
Newton-Euler inverse dynamics linear in the inertial parameters | p. 219 |
Practical form of the Newton-Euler algorithm | p. 221 |
Real time computation of the inverse dynamic model | p. 222 |
Introduction | p. 222 |
Customization of the Newton-Euler formulation | p. 225 |
Utilization of the base inertial parameters | p. 227 |
Direct dynamic model | p. 228 |
Using the inverse dynamic model to solve the direct dynamic problem | p. 228 |
Recursive computation of the direct dynamic model | p. 230 |
Conclusion | p. 233 |
Dynamics of robots with complex structure | p. 235 |
Introduction | p. 235 |
Dynamic modeling of tree structured robots | p. 235 |
Lagrange equations | p. 235 |
Newton-Euler formulation | p. 236 |
Direct dynamic model of tree structured robots | p. 236 |
Determination of the base inertial parameters | p. 237 |
Dynamic model of robots with closed kinematic chains | p. 242 |
Description of the system | p. 242 |
Computation of the inverse dynamic model | p. 243 |
Computation of the direct dynamic model | p. 245 |
Base inertial parameters of closed chain robots | p. 248 |
Base inertial parameters of parallelogram loops | p. 249 |
Practical computation of the base inertial parameters | p. 250 |
Conclusion | p. 256 |
Geometric calibration of robots | p. 257 |
Introduction | p. 257 |
Geometric parameters | p. 258 |
Robot parameters | p. 258 |
Parameters of the base frame | p. 259 |
End-effector parameters | p. 260 |
Generalized differential model of a robot | p. 261 |
Principle of geometric calibration | p. 263 |
General calibration model | p. 263 |
Identifiability of the geometric parameters | p. 265 |
Solution of the identification equation | p. 268 |
Calibration methods | p. 270 |
Calibration using the end-effector coordinates | p. 270 |
Calibration using distance measurement | p. 272 |
Calibration using location constraint and position constraint | p. 273 |
Calibration methods using plane constraint | p. 274 |
Correction and compensation of errors | p. 279 |
Calibration of parallel robots | p. 282 |
IGM calibration model | p. 283 |
DGM calibration model | p. 285 |
Measurement techniques for robot calibration | p. 285 |
Three-cable system | p. 286 |
Theodolites | p. 286 |
Laser tracking system | p. 287 |
Camera-type devices | p. 287 |
Conclusion | p. 288 |
Identification of the dynamic parameters | p. 291 |
Introduction | p. 291 |
Estimation of inertial parameters | p. 292 |
Principle of the identification procedure | p. 292 |
Resolution of the identification equations | p. 293 |
Identifiability of the dynamic parameters | p. 295 |
Estimation of the friction parameters | p. 295 |
Trajectory selection | p. 296 |
Calculation of the joint velocities and accelerations | p. 298 |
Calculation of joint torques | p. 299 |
Dynamic identification model | p. 300 |
Other approaches to the dynamic identification model | p. 301 |
Sequential formulation of the dynamic model | p. 301 |
Filtered dynamic model (reduced order dynamic model) | p. 302 |
Energy (or integral) identification model | p. 306 |
Principle of the energy model | p. 306 |
Power model | p. 308 |
Recommendations for experimental application | p. 309 |
Conclusion | p. 310 |
Trajectory generation | p. 313 |
Introduction | p. 313 |
Trajectory generation and control loops | p. 314 |
Point-to-point trajectory in the joint space | p. 315 |
Polynomial interpolation | p. 316 |
Bang-bang acceleration profile | p. 320 |
Trapeze velocity profile | p. 321 |
Continuous acceleration profile with constant velocity phase | p. 326 |
Point-to-point trajectory in the task space | p. 329 |
Trajectory generation with via points | p. 331 |
Linear interpolations with continuous acceleration blends | p. 331 |
Trajectory generation with cubic spline functions | p. 337 |
Trajectory generation on a continuous path in the task space | p. 342 |
Conclusion | p. 344 |
Motion control | p. 347 |
Introduction | p. 347 |
Equations of motion | p. 347 |
PID control | p. 348 |
PID control in the joint space | p. 348 |
Stability analysis | p. 350 |
PID control in the task space | p. 352 |
Linearizing and decoupling control | p. 353 |
Introduction | p. 353 |
Computed torque control in the joint space | p. 354 |
Computed torque control in the task space | p. 358 |
Passivity-based control | p. 360 |
Introduction | p. 360 |
Hamiltonian formulation of the robot dynamics | p. 360 |
Passivity-based position control | p. 362 |
Passivity-based tracking control | p. 363 |
Lyapunov-based method | p. 368 |
Adaptive control | p. 368 |
Introduction | p. 368 |
Adaptive feedback linearizing control | p. 369 |
Adaptive passivity-based control | p. 371 |
Conclusion | p. 376 |
Compliant motion control | p. 377 |
Introduction | p. 377 |
Description of a compliant motion | p. 378 |
Passive stiffness control | p. 378 |
Active stiffness control | p. 379 |
Impedance control | p. 381 |
Hybrid position/force control | p. 385 |
Parallel hybrid position/force control | p. 386 |
External hybrid control scheme | p. 391 |
Conclusion | p. 393 |
Appendices | |
Solution of the inverse geometric model equations (Table 4.1) | p. 395 |
Type 2 | p. 395 |
Type 3 | p. 396 |
Type 4 | p. 397 |
Type 5 | p. 397 |
Type 6 | p. 398 |
Type 7 | p. 398 |
Type 8 | p. 399 |
The inverse robot | p. 401 |
Dyalitic elimination | p. 403 |
Solution of systems of linear equations | p. 405 |
Problem statement | p. 405 |
Resolution based on the generalized inverse | p. 406 |
Resolution based on the pseudoinverse | p. 407 |
Resolution based on the QR decomposition | p. 413 |
Numerical computation of the base parameters | p. 417 |
Introduction | p. 417 |
Base inertial parameters of serial and tree structured robots | p. 418 |
Base inertial parameters of closed loop robots | p. 420 |
Generality of the numerical method | p. 420 |
Recursive equations between the energy functions | p. 421 |
Recursive equation between the kinetic energy functions of serial robots | p. 421 |
Recursive equation between the potential energy functions of serial robots | p. 423 |
Recursive equation between the total energy functions of serial robots | p. 424 |
Expression of [superscript a(j) lambda subscript j] in the case of the tree structured robot | p. 424 |
Dynamic model of the Staubli RX-90 robot | p. 427 |
Computation of the inertia matrix of tree structured robots | p. 431 |
Inertial parameters of a composite link | p. 431 |
Computation of the inertia matrix | p. 433 |
Stability analysis using Lyapunov theory | p. 435 |
Autonomous systems | p. 435 |
Non-autonomous systems | p. 437 |
Computation of the dynamic control law in the task space | p. 439 |
Calculation of the location error e[subscript x] | p. 439 |
Calculation of the velocity of the terminal link X | p. 440 |
Calculation of J q | p. 441 |
Calculation of J(q)[superscript -1] y | p. 442 |
Modified dynamic model | p. 442 |
Stability of passive systems | p. 443 |
Definitions | p. 443 |
Stability analysis of closed-loop positive feedback | p. 444 |
Stability properties of passive systems | p. 445 |
References | p. 447 |
Index | p. 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