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Time-optimal motions of robotic manipulators

Published online by Cambridge University Press:  23 April 2001

Miroslaw Galicki
Affiliation:
Institute of Organization and Management, Technical University of Zielona Góra, ul. Podgórna 50, 65–246 Zielona Góra (Poland) Institute of Medical Statistics, Computer Science and Documentation, Friedrich-Schiller-University, Jahnstr. 3, D-07740 Jena (Germany)galicki@imsid.uni-jena.de
Dariusz Uciński
Affiliation:
Institute of Medical Statistics, Computer Science and Documentation, Friedrich-Schiller-University, Jahnstr. 3, D-07740 Jena (Germany)galicki@imsid.uni-jena.de

Abstract

An approach to planning time-optimal collision-free motions of robotic manipulators is presented. It is based on using a negative formulation of the Pontryagin Maximum Principle which handles efficiently various control and/or state constraints imposed on the manipulator motions, which arise naturally out of manipulator joint limits and obstacle avoidance. This approach becomes similar to that described by Weinreb and Bryson, as well as by Bryson and Ho if no state inequality constraints are imposed. In contrast to the penalty function method, the proposed algorithm does not require an initial admissible solution (i.e. an initial admissible trajectory) and finds manipulator trajectories with a smaller cost value than the penalty function approach. A computer example involving a planar redundant manipulator of three revolute kinematic pairs is included. The numerical results are compared with those obtained using an exterior penalty function method.

Type
Research Article
Copyright
© 2000 Cambridge University Press

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