Advances in Robot Control (eBook)

Preface 7
Curriculum Vitae: Suguru Arimoto 11
Professional Activities 11
Awards and Honors 12
List of Ph.D. Students 13
Main Scientific Contributions 17
1 Information Theory 17
2 Signal Processing 18
3 General Control Theory 18
4 Theory of Robot Control 19
List of Contributors 27
Contents 31
Human Robotics: A Vision and A Dream 33
References 37
Part I From Everyday Physics to Robot Control 39
Natural Motion and Singularity-Consistent Inversion of Robot Manipulators 41
1 Introduction 41
2 Singularity-Consistent Formulation of Inverse Kinematics 42
3 Natural Motion of a Manipulator 45
4 Vector-Parameterization of Configuration Space 46
5 Second-Order Singularity-Consistent Inverse Kinematics 47
6 Dynamic Analysis 48
7 An Example 51
8 Singularity-Consistent Controllers 55
9 Conclusions 61
References 63
Approximate Jacobian Control for Robot Manipulators 67
1 Introduction 67
2 Robot Kinematics and Dynamics 68
3 Approximate Jacobian Setpoint Control of Robots 70
4 Adaptive Jacobian Tracking Control of Robots 76
5 Conclusion 83
References 83
Adaptive Visual Servoing of Robot Manipulators 87
1 Introduction 87
2 Kinematics and Dynamics 90
3 Adaptive Dynamic Visual Servoing 96
4 Uncalibrated Visual Servoing for Multiple Feature Points 103
5 Experiments 105
6 Conclusions 111
References 111
Orthogonalization Principle for Dynamic Visual Servoing of Constrained Robot Manipulators 115
1 Introduction 115
2 The Orthogonalization Principle: Robot Force Control 116
3 The Visual Force Control Problem 118
4 Dynamics of the Visually Driven Constrained Robot 121
5 Control Design 125
6 Discussions 126
7 Experimental System 127
8 Conclusions 131
Appendix: Proof of Theorem 1 131
References 136
Passivity-Based Control of Multi-Agent Systems 139
1 Introduction and Motivation 139
2 Output Synchronization 142
3 Nonlinear Coupling with Time-Delay 151
4 Examples 155
Navigation Functions for Dynamical, Nonholonomically Constrained Mechanical Systems 167
1 Introduction 167
2 Hybrid Controller for Nonholonomic Kinematic Systems 169
3 Hybrid Controller for Nonholonomic Dynamic Systems 176
4 Simulations 180
5 Conclusions 184
6 Acknowledgments 186
References 186
Planning and Control of Robot Motion Based on Time- Scale Transformation 189
1 Introduction 189
2 Characterization of Robot and Environment Dynamics 192
3 Planning and Control of Robot Motion under an Endpoint Constraint 194
4 Planning and Control of the Underwater Robot’s Motion 201
5 Experiments 206
6 Conclusion 208
7 Acknowledgments 209
References 210
Part II From Robot Control to Human-Like Movements 212
Modularity, Synchronization, and What Robotics May Yet Learn from the Brain 213
1 Introduction 213
2 Modularity, Stability, and Evolution 214
3 Synchronization 217
4 Polyrhythms 220
References 228
Force Control with A Muscle-Activated Endoskeleton 233
1 Introduction 233
2 Workless Forces 235
3 Coordinating Muscle Forces 238
4 Kinematic Instability 241
5 Concluding Remarks 246
Acknowledgements 247
References 247
On Dynamic Control Mechanisms of Redundant Human Musculo- Skeletal System 249
1 Introduction 249
2 Human-Like Reaching Movements 252
3 Human-Like Pinching Movements 264
4 Summary 274
References 278
Principle of Superposition in Human Prehension 281
1 History of the Principle of Superposition 281
2 Arimoto’s Principle of Superposition 282
3 Major Issues in the Control of Redundant Biological Systems 283
4 Prehension Synergies: The Hierarchical Control 284
5 Prehension Synergies: The Principle of Superposition in Static Tasks 286
6 Prehension Synergies: The Principle of Superposition in Reactions to Perturbations 288
7 Concluding Comments 290
References 291
Motion Planning of Human-Like Movements in the Manipulation of Flexible Objects 295
1 Introduction 295
2 Beta Function as a Model of Reaching Movements 297
3 Reaching Movements in Dynamic Environments 303
4 Experimental Results 313
5 Conclusions 321
References 321
Haptic Feedback Enhancement Through Adaptive Force Scaling: Theory and Experiment 325
1 Introduction 326
2 Position Based 3-D Force Scaling during Human- Robot Co- Manipulation: Problem Statement 328
3 Three Force Control Algorithms: A Review 330
4 Theory of Pushing and Poking 331
5 Three Force Scaling Algorithms 333
6 Experimental Results 335
7 Conclusions 345
Acknowledgments 346
References 347
Learning to Dynamically Manipulate: A Table Tennis Robot Controls a Ball and Rallies with a Human Being 349
1 Introduction 349
2 Robot Table Tennis 351
3 Ball Events in One Stroke 353
4 Paddle Motion Decision 355
5 Generation of Paddle Movement 359
6 Experimental Results 362
7 Conclusion 369
Appendix: Locally Weighted Regression(LWR)[8] 371
References 372

Approximate Jacobian Control for Robot Manipulators (P. 35)

Chien Chern Cheah
School of Electrical and Electronic Engineering
Nanyang Technological University
Block S1, Nanyang Avenue, S(639798)
Republic of Singapore

Summary.

Most research so far in robot control has assumed either kinematics or Jacobian matrix of the robots from joint space to task space is known exactly. Unfortunately, no physical parameters can be derived exactly. In addition, when the robot picks up objects of uncertain lengths, orientations or gripping points, the kinematics and dynamics become uncertain and change according to different tasks.

This paper presents several approximate Jacobian control laws for robots with uncertainties in kinematics and dynamics. Lyapunov functions are presented for stability analysis of feedback control problems with uncertain kinematics. We shall show that the end-effector’s position converges to a desired position even when the kinematics and Jacobian matrix are uncertain.

1 Introduction

It is interesting to observe from human reaching movements that we do not need an accurate knowledge of kinematics and dynamics of our arms. We are also able to pick up a new tool or object and manipulate it skillfully to accomplish a task, using only the approximate knowledge of the length, mass, orientation and gripping point of the tool. Such basic ability of sensing and responding to changes without an accurate knowledge of sensory-to-motor transformation gives us a high degree of flexibility in dealing with unforseen changes in the real world.

The kinematics and dynamics of robot manipulators are highly nonlinear. By exploring physical properties of the robot system and using Lyapunov method, Takegaki and Arimoto [1], Arimoto and Miyazaki [2] showed that simple controllers such as the PD and PID feedback are effective for setpoint control despite the nonlinearity and uncertainty of the robot dynamics.

To deal with trajectory-tracking control, Slotine and Li [3, 4] proposed an adaptive control law for robotic manipulator using Lyapunov method. After more than two decades of research, much progress has been made in control of robots with dynamic uncertainty [1]-[19].

However, most research on robot control has assumed that the exact kinematics and Jacobian matrix of the manipulator from joint space to Cartesian space are known. In the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end effector path by solving the inverse kinematics problem.

In addition, the Jacobian matrix of the mapping from joint space to task space could not be exactly derived. This assumption leads us to several problems in the development of robot control laws today. In free motion [20], this implies that the exact lengths of the links, joint o.sets and the object which the robot is holding, must be known. Unfortunately, no physical parameters could be derived exactly.

In addition, when the robot picks up objects or tools of di.erent lengths, unknown orientations and gripping points, the overall kinematics are changing and therefore difficult to derive exactly.