Global stability for distributed systems with changing contact states

Abstract

Analyzes the global stability of distributed manipulation control schemes. The "programmable vector field" approach, which assumes that the system's control actions can be approximated by a continuous vector force field, is a commonly proposed scheme for distributed manipulation control. In practical implementations, the continuous control force field idealization must then be adapted to the specifics of the discrete physical actuator array. However, in Murphey and Burdick (2001) it was shown that when one takes into account the discreteness of actuator arrays and realistic models of the actuator/object contact mechanics, the controls designed by the continuous approximation approach can be unstable at the desired equilibrium configuration. We introduced a discontinuous feedback law that locally stabilizes the manipulated object at the equilibrium. However, the stability of this feedback law only holds in a neighborhood of the equilibrium. In this paper we show how to combine the programmable vector field approach and our local feedback stabilization law to achieve a globally stable distributed manipulation control system. Simulations illustrate the method.

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