Reiter Time-Optimal Trajectory Planning for Redundant Robots

Joint Space Decomposition for Redundancy Resolution in Non-Linear Optimization
1. Auflage 2016
ISBN: 978-3-658-12701-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 100 Seiten

Reihe: BestMasters

This master's thesis presents a novel approach to finding trajectories with minimal end time for kinematically redundant manipulators. Emphasis is given to a general applicability of the developed method to industrial tasks such as gluing or welding. Minimum-time trajectories may yield economic advantages as a shorter trajectory duration results in a lower task cycle time. Whereas kinematically redundant manipulators possess increased dexterity, compared to conventional non-redundant manipulators, their inverse kinematics is not unique and requires further treatment. In this work a joint space decomposition approach is introduced that takes advantage of the closed form inverse kinematics solution of non-redundant robots. Kinematic redundancy can be fully exploited to achieve minimum-time trajectories for prescribed end-effector paths.

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.

Autoren/Hrsg.

Reiter, Alexander

Inhaltsverzeichnis

1;Foreword;6
2;Abstract;8
3;Kurzfassung;9
4;Contents;10
5;List of Figures;12
6;List of Tables;14
7;1 Introduction;15
8;2 NURBS Curves;18
8.1;2.1 Basics;18
8.1.1;2.1.1 Properties of NURBS curves;20
8.1.2;2.1.2 Recursion formula;22
8.1.3;2.1.3 Curve approximation;26
8.2;2.2 Application in optimization;27
9;3 Modeling: Kinematics and Dynamics of Redundant Robots;28
9.1;3.1 Projection Equation;28
9.2;3.2 Modeling example: subsystem motor, gear, arm;31
10;4 Approaches to Minimum-Time Trajectory Planning;36
10.1;4.1 Minimum-time optimization problem;36
10.2;4.2 Optimization basics;38
10.3;4.3 Algorithms for redundant manipulators;39
10.3.1;4.3.1 First-order inverse kinematics algorithms;39
10.3.2;4.3.2 Second-order inverse kinematics algorithm;44
10.3.3;4.3.3 Null space projection;45
10.3.4;4.3.4 Kinematic manipulability;46
10.3.5;4.3.5 Dynamic manipulability;48
10.3.6;4.3.6 Manipulability along known paths;51
10.3.7;4.3.7 B-spline-based minimum-time trajectories;54
11;5 Joint Space Decomposition Approach;57
11.1;5.1 Method;58
11.1.1;5.1.1 Use of B-spline curves;60
11.2;5.2 Optimization problem;60
11.3;5.3 Initial trajectories;62
11.4;5.4 Remaining challenges;62
12;6 Examples;64
12.1;6.1 Planar robot;64
12.1.1;6.1.1 Forward kinematics;65
12.1.2;6.1.2 Inverse kinematics qr = q1;67
12.1.3;6.1.3 Inverse kinematics qr = q2;68
12.1.4;6.1.4 Inverse kinematics qr = q3;70
12.1.5;6.1.5 Avoidance of singularities due to choice of inverse kinematics approach;72
12.1.6;6.1.6 Kinematic chain;74
12.1.7;6.1.7 Dynamic model;77
12.1.8;6.1.8 Optimization Results;79
12.2;6.2 Spatial robot;85
12.2.1;6.2.1 Forward kinematics;85
12.2.2;6.2.2 Inverse kinematics qr = q1;88
12.2.3;6.2.3 Optimization results;91
13;7 Conclusion;97
14;Bibliography;99