Abstract
This paper is concerned with the problem of the existence and structure of time-optimal control for models derived from Lagrange equations of motion of mechanical systems involving links. The condition which ensures the existence of time-optimal control is demonstrated. The study conducted in this paper involves a highly nonlinear mathematical model of a two-degree-of-freedom mechanical system. However, the procedure and the results presented in this paper can be extended to mechanical systems with any finite number of degrees of freedom.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kahn, M. E., andRoth, B.,The Near Minimum-Time Control of Open-Loop Articulated Kinematic Chains, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 93, pp. 164–172, 1971.
Karihaloo, B. L., andParbery, R. D.,Optimal Control of a Dynamical System Representing a Gantry Crane, Journal of Optimization Theory and Applications, Vol. 36, pp. 409–417, 1982.
Sakawa, Y., Shindo, Y., andHashimoto, Y.,Optimal Control of a Rotary Crane, Journal of Optimization Theory and Applications, Vol. 35, pp. 535–557, 1981.
Luh, J. Y. S., andLin, C. S.,Optimum Path Planning for Mechanical Manipulators, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 102, pp. 142–151, 1981.
Gamkrelidze, R. V.,The Theory of Time-Optimal Processes in Linear Systems, Izvestiya Akademii Nauk SSSR, Vol. 22, pp. 449–474, 1958.
Lee, E. B., andMarkus, L.,Optimal Control for Nonlinear Processes, Archive for Rational Mechanics and Analysis, Vol. 8, pp. 36–58, 1961.
Cesari, L.,An Existence Theorem in Problems of Optimal Control, SIAM Journal on Control, Series A, Vol. 3, pp. 7–22, 1965.
Roxin, E.,The Existence of Optimal Controls, Michigan Mathematical Journal, Vol. 9, pp. 109–119, 1962.
Meirovitch, L.,Methods of Analytical Dynamics, McGraw-Hill, New York, New York, 1970.
Cronin, J.,Differential Equations: Introduction and Qualitative Theory, Marcel Dekker, New York, New York, 1980.
Kirk, D. E.,Optimal Control Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1970.
Author information
Authors and Affiliations
Additional information
Communicated by D. G. Hull
The authors wish to thank Professor D. G. Hull and the reviewers for their most valuable comments and suggestions.
Rights and permissions
About this article
Cite this article
Ailon, A., Langholz, G. On the existence of time-optimal control of mechanical manipulators. J Optim Theory Appl 46, 1–21 (1985). https://doi.org/10.1007/BF00938755
Issue Date:
DOI: https://doi.org/10.1007/BF00938755