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RESEARCH PAPERS

The Near-Minimum-Time Control Of Open-Loop Articulated Kinematic Chains

[+] Author and Article Information
M. E. Kahn

Memorex Corporation, Santa Clara, Calif.

B. Roth

Stanford University, Stanford, Calif.

J. Dyn. Sys., Meas., Control 93(3), 164-172 (Sep 01, 1971) (9 pages) doi:10.1115/1.3426492 History: Received September 04, 1970; Online July 13, 2010

Abstract

The time-optimal control of a system of rigid bodies connected in series by single-degree-of-freedom joints is studied. The dynamical equations of the system are highly nonlinear, and a closed-form representation of the minimum-time feedback control is not possible. However, a suboptimal feedback control, which provides a close approximation to the optimal control, is developed. The suboptimal control is expressed in terms of switching curves for each of the system controls. These curves are obtained from the linearized equations of motion for the system. Approximations are made for the effects of gravity loads and angular velocity terms in the nonlinear equations of motion. Digital simulation is used to obtain a comparison of response times of the optimal and suboptimal controls. The speed of response of the suboptimal control is found to compare quite favorably with the response speed of the optimal control.

Copyright © 1971 by ASME
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