Hostname: page-component-cb9f654ff-d5ftd Total loading time: 0 Render date: 2025-08-20T11:22:04.586Z Has data issue: false hasContentIssue false
  • English
  • Français

On optimal control of multi-link vertical planar robot arms systems moving under the effect of gravity

Published online by Cambridge University Press:  17 February 2009

H. W. J. Lee ,
K. L. Teo  and
L. S. Jennings
L. S. Jennings
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, WA 6907, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

How to obtain a workable initial guess to start an optimal control (control parametrization) algorithm is an important question. In particular, for a system of multi-link vertical planar robot arms moving under the effect of gravity and applied torques (which can exhibit chaotic behaviour), a non-workable initial guess of torques may cause integration failure regardless of what numerical packages are used. In this paper, we address this problem by introducing a simple and intuitive “Blind Man” algorithm. Theoretical justification as well as a numerical example is provided.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 2 , October 1997 , pp. 195 - 213
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Ahmed, N. U., “Elements of finite-dimensional systems and control theory”, Pitman Monographs and Surveys in Pure and Applied Mathematics 37 (Longman Sciences and Technical, 1988).Google Scholar
[2]Craven, B. D., Control and optimization (Chapman and Hall, 1995).CrossRefGoogle Scholar
[3]Jennings, L. S., Fisher, M. E., Teo, K. L. and Goh, C. J., “MISER3 Optimal Control Software”: Theory and User Manual (EMCOSS Pty Ltd, 1990).Google Scholar
[4]Kubota, Koichi and Iri, Masao, PADRE2, version 1 — User's Manual Research Memorandum (RMI 90–01, 1990).Google Scholar
[5]Lee, H. W. J., Teo, K. L. and Rehbock, V., “Sub-optimal local feedback control for a class of nonlinear control problems”, Dynamics of Continuous, Discrete and Impulsive systems 1 (1995).Google Scholar
[6]Lee, H. W. J., Teo, K. L. and Rehbock, V., “Sub-optimal local feedback control for a class of constrained discrete time nonlinear control problems”, Computers and Mathematics and Applications, to appear.Google Scholar
[7]Murray, John J., Computational robot dynamics, Ph. D. Thesis, Carnegie Mellon University, 1986.Google Scholar
[8]Miele, A., “Gradient Algorithms for the Optimization of Dynamic Systems”, in: Control and Dynamic Systems Advances in Theory and Applications 16 (ed. leondes, C. T.) (Academic Press, New York, 1980) 1–52.CrossRefGoogle Scholar
[9]Polak, E. and Mayne, D. Q., “A feasible directions algorithm for optimal control problems with control and terminal inequality constraints”, IEEE Trans. Aut. Control AC-22 (1977) 741–751.CrossRefGoogle Scholar
[10]Sakawa, Y., “On local convergence of an algorithm for optimal control”, Numerical Funct. Anal. Opt. 3 (1981) 301–319.CrossRefGoogle Scholar
[11]Sirisena, H. R. and Chou, F. S., “Convergence of the control parametrization ritz method for nonlinear optimal control problems”, J. Optimaization Theory and Applications (11 1979).CrossRefGoogle Scholar
[12]Skowronski, Jan M., Control Theory of Robotic Systems (World Scientific, 1989).CrossRefGoogle Scholar
[13]Teo, K. L., Goh, C. J. and Wong, K. H., A Unified Computational Approach to Optimal Control Problems (Longman Sciences and Technical, 1991).Google Scholar