Time-Optimal Trajectory Planning for Redundant Robots (eBook)

Alexander Reiter is a Senior Scientist at the Institute of Robotics of the Johannes Kepler University Linz in Austria. His major fields of research are kinematics, dynamics, and trajectory planning for kinematically redundant serial robots.

Foreword 6
Abstract 8
Kurzfassung 9
Contents 10
List of Figures 12
List of Tables 14
1 Introduction 15
2 NURBS Curves 18
2.1 Basics 18
2.1.1 Properties of NURBS curves 20
2.1.2 Recursion formula 22
2.1.3 Curve approximation 26
2.2 Application in optimization 27
3 Modeling: Kinematics and Dynamics of Redundant Robots 28
3.1 Projection Equation 28
3.2 Modeling example: subsystem motor, gear, arm 31
4 Approaches to Minimum-Time Trajectory Planning 36
4.1 Minimum-time optimization problem 36
4.2 Optimization basics 38
4.3 Algorithms for redundant manipulators 39
4.3.1 First-order inverse kinematics algorithms 39
4.3.2 Second-order inverse kinematics algorithm 44
4.3.3 Null space projection 45
4.3.4 Kinematic manipulability 46
4.3.5 Dynamic manipulability 48
4.3.6 Manipulability along known paths 51
4.3.7 B-spline-based minimum-time trajectories 54
5 Joint Space Decomposition Approach 57
5.1 Method 58
5.1.1 Use of B-spline curves 60
5.2 Optimization problem 60
5.3 Initial trajectories 62
5.4 Remaining challenges 62
6 Examples 64
6.1 Planar robot 64
6.1.1 Forward kinematics 65
6.1.2 Inverse kinematics qr = q1 67
6.1.3 Inverse kinematics qr = q2 68
6.1.4 Inverse kinematics qr = q3 70
6.1.5 Avoidance of singularities due to choice of inverse kinematics approach 72
6.1.6 Kinematic chain 74
6.1.7 Dynamic model 77
6.1.8 Optimization Results 79
6.2 Spatial robot 85
6.2.1 Forward kinematics 85
6.2.2 Inverse kinematics qr = q1 88
6.2.3 Optimization results 91
7 Conclusion 97
Bibliography 99