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Modeling and Identification of Serial Robots | p. 1 |
Introduction | p. 1 |
Geometric modeling | p. 2 |
Geometric description | p. 2 |
Direct geometric model | p. 6 |
Inverse geometric model | p. 7 |
Stating the problem | p. 8 |
Principle of Paul's method | p. 10 |
Kinematic modeling | p. 14 |
Direct kinematic model | p. 14 |
Calculation of the Jacobian matrix by derivation of the DGM | p. 15 |
Kinematic Jacobian matrix | p. 17 |
Decomposition of the kinematic Jacobian matrix into three matrices | p. 19 |
Dimension of the operational space of a robot | p. 20 |
Inverse kinematic model | p. 21 |
General form of the kinematic model | p. 21 |
Inverse kinematic model for the regular case | p. 22 |
Solution at the proximity of singular positions | p. 23 |
Inverse kinematic model of redundant robots | p. 24 |
Calibration of geometric parameters | p. 26 |
Introduction | p. 26 |
Geometric parameters | p. 26 |
Geometric parameters of the robot | p. 26 |
Parameters of the robot's location | p. 27 |
Geometric parameters of the end-effector | p. 28 |
Generalized differential model of a robot | p. 29 |
Principle of geometric calibration | p. 30 |
General form of the calibration model | p. 30 |
Identifying the geometric parameters | p. 31 |
Solving the identification equations | p. 34 |
Calibration methods of geometric parameters | p. 35 |
Calibration model by measuring the end-effector location | p. 35 |
Autonomous calibration models | p. 36 |
Correction of geometric parameters | p. 39 |
Dynamic modeling | p. 40 |
Lagrange formalism | p. 42 |
General form of dynamic equations | p. 43 |
Calculation of energy | p. 44 |
Properties of the dynamic model | p. 46 |
Taking into consideration the friction | p. 47 |
Taking into account the inertia of the actuator's rotor | p. 48 |
Taking into consideration the forces and moments exerted by the end-effector on its environment | p. 48 |
Newton-Euler formalism | p. 50 |
Newton-Euler equations linear in the inertial parameters | p. 50 |
Practical form of Newton-Euler equations | p. 52 |
Determining the base inertial parameters | p. 53 |
Identification of dynamic parameters | p. 59 |
Introduction | p. 59 |
Identification principle of dynamic parameters | p. 60 |
Solving method | p. 60 |
Identifiable parameters | p. 62 |
Choice of identification trajectories | p. 63 |
Evaluation of joint coordinates | p. 65 |
Evaluation of joint torques | p. 65 |
Identification model using the dynamic model | p. 66 |
Sequential formulation of the dynamic model | p. 68 |
Practical considerations | p. 69 |
Conclusion | p. 70 |
Bibliography | p. 71 |
Modeling of Parallel Robots | p. 81 |
Introduction | p. 81 |
Characteristics of classic robots | p. 81 |
Other types of robot structure | p. 82 |
General advantages and disadvantages | p. 86 |
Present day uses | p. 88 |
Simulators and space applications | p. 88 |
Industrial applications | p. 91 |
Medical applications | p. 93 |
Precise positioning | p. 94 |
Machine types | p. 95 |
Introduction | p. 95 |
Plane robots with three degrees of freedom | p. 100 |
Robots moving in space | p. 101 |
Manipulators with three degrees of freedom | p. 101 |
Manipulators with four or five degrees of freedom | p. 107 |
Manipulators with six degrees of freedom | p. 109 |
Inverse geometric and kinematic models | p. 113 |
Inverse geometric model | p. 113 |
Inverse kinematics | p. 115 |
Singular configurations | p. 117 |
Singularities and statics | p. 121 |
State of the art | p. 121 |
The geometric method | p. 122 |
Maneuverability and condition number | p. 125 |
Singularities in practice | p. 126 |
Direct geometric model | p. 126 |
Iterative method | p. 127 |
Algebraic method | p. 128 |
Reminder concerning algebraic geometry | p. 128 |
Planar robots | p. 130 |
Manipulators with six degrees of freedom | p. 133 |
Bibliography | p. 134 |
Performance Analysis of Robots | p. 141 |
Introduction | p. 141 |
Accessibility | p. 143 |
Various levels of accessibility | p. 143 |
Condition of accessibility | p. 144 |
Workspace of a robot manipulator | p. 146 |
General definition | p. 146 |
Space of accessible positions | p. 148 |
Primary space and secondary space | p. 149 |
Defined orientation workspace | p. 151 |
Free workspace | p. 152 |
Calculation of the workspace | p. 155 |
Concept of aspect | p. 157 |
Definition | p. 157 |
Mode of aspects calculation | p. 158 |
Free aspects | p. 160 |
Application of the aspects | p. 161 |
Concept of connectivity | p. 163 |
Introduction | p. 163 |
Characterization of n-connectivity | p. 165 |
Characterization of t-connectivity | p. 168 |
Local performances | p. 174 |
Definition of dexterity | p. 174 |
Manipulability | p. 174 |
Isotropy index | p. 180 |
Lowest singular value | p. 181 |
Approach lengths and angles | p. 181 |
Conclusion | p. 183 |
Bibliography | p. 183 |
Trajectory Generation | p. 189 |
Introduction | p. 189 |
Point-to-point trajectory in the joint space under kinematic constraints | p. 190 |
Fifth-order polynomial model | p. 191 |
Trapezoidal velocity model | p. 193 |
Smoothed trapezoidal velocity model | p. 198 |
Point-to-point trajectory in the task-space under kinematic constraints | p. 201 |
Trajectory generation under kinodynamic constraints | p. 204 |
Problem statement | p. 205 |
Constraints | p. 206 |
Objective function | p. 207 |
Description of the method | p. 208 |
Outline | p. 208 |
Construction of a random trajectory profile | p. 209 |
Handling kinodynamic constraints | p. 212 |
Summary | p. 216 |
Trapezoidal profiles | p. 218 |
Examples | p. 221 |
Case of a two dof robot | p. 221 |
Optimal free motion planning problem | p. 221 |
Optimal motion problem with geometric path constraint | p. 223 |
Case of a six dof robot | p. 224 |
Optimal free motion planning problem | p. 225 |
Optimal motion problem with geometric path constraints | p. 226 |
Optimal free motion planning problem with intermediate points | p. 227 |
Conclusion | p. 229 |
Bibliography | p. 230 |
Stochastic Optimization Techniques | p. 234 |
Position and Force Control of a Robot in a Free or Constrained Space | p. 241 |
Introduction | p. 241 |
Free space control | p. 242 |
Hypotheses applying to the whole chapter | p. 242 |
Complete dynamic modeling of a robot manipulator | p. 243 |
Ideal dynamic control in the joint space | p. 246 |
Ideal dynamic control in the operational working space | p. 248 |
Decentralized control | p. 250 |
Sliding mode control | p. 251 |
Robust control based on high order sliding mode | p. 254 |
Adaptive control | p. 255 |
Control in a constrained space | p. 257 |
Interaction of the manipulator with the environment | p. 257 |
Impedance control | p. 257 |
Force control of a mass attached to a spring | p. 258 |
Non-linear decoupling in a constrained space | p. 262 |
Position/force hybrid control | p. 263 |
Parallel structure | p. 263 |
External structure | p. 269 |
Specificity of the force/torque control | p. 271 |
Conclusion | p. 275 |
Bibliography | p. 275 |
Visual Servoing | p. 279 |
Introduction | p. 279 |
Modeling visual features | p. 281 |
The interaction matrix | p. 281 |
Eye-in-hand configuration | p. 282 |
Eye-to-hand configuration | p. 283 |
Interaction matrix | p. 284 |
Interaction matrix of a 2-D point | p. 284 |
Interaction matrix of a 2-D geometric primitive | p. 287 |
Interaction matrix for complex 2-D shapes | p. 290 |
Interaction matrix by learning or estimation | p. 293 |
Interaction matrix related to 3-D visual features | p. 294 |
Pose estimation | p. 294 |
Interaction matrix related to [Theta]u | p. 297 |
Interaction matrix related to a 3-D point | p. 298 |
Interaction matrix related to a 3-D plane | p. 300 |
Task function and control scheme | p. 301 |
Obtaining the desired value s* | p. 301 |
Regulating the task function | p. 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 tasks | p. 317 |
Virtual links | p. 317 |
Hybrid task function | p. 319 |
Target tracking | p. 323 |
Other exteroceptive sensors | p. 325 |
Conclusion | p. 326 |
Bibliography | p. 328 |
Modeling and Control of Flexible Robots | p. 337 |
Introduction | p. 337 |
Modeling of flexible robots | p. 337 |
Introduction | p. 337 |
Generalized Newton-Euler model for a kinematically free elastic body | p. 339 |
Definition: formalism of a dynamic model | p. 339 |
Choice of formalism | p. 340 |
Kinematic model of a free elastic body | p. 341 |
Balance principle compatible with the mixed formalism | p. 343 |
Virtual power of the field of acceleration quantities | p. 344 |
Virtual power of external forces | p. 346 |
Virtual power of elastic cohesion forces | p. 347 |
Balance of virtual powers | p. 348 |
Linear rigid balance in integral form | p. 349 |
Angular rigid balance in integral form | p. 349 |
Elastic balances in integral form | p. 350 |
Linear rigid balance in parametric form | p. 351 |
Intrinsic matrix form of the generalized Newton-Euler model | p. 353 |
Velocity model of a simple open robotic chain | p. 356 |
Acceleration model of a simple open robotic chain | p. 357 |
Generalized Newton-Euler model for a flexible manipulator | p. 358 |
Extrinsic Newton-Euler model for numerical calculus | p. 359 |
Geometric model of an open chain | p. 362 |
Recursive calculation of the inverse and direct dynamic models for a flexible robot | p. 363 |
Introduction | p. 363 |
Recursive algorithm of the inverse dynamic model | p. 364 |
Recursive algorithm of the direct dynamic model | p. 368 |
Iterative symbolic calculation | p. 373 |
Control of flexible robot manipulators | p. 373 |
Introduction | p. 373 |
Reminder of notations | p. 374 |
Control methods | p. 375 |
Regulation | p. 375 |
Point-to-point movement in fixed time | p. 375 |
Trajectory tracking in the joint space | p. 380 |
Trajectory tracking in the operational space | p. 383 |
Conclusion | p. 388 |
Bibliography | p. 389 |
List of Authors | p. 395 |
Index | p. 397 |
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