On the stability and design of distributed manipulation control systems

This paper analyzes the stability of distributed manipulation control schemes. A commonly proposed method for designing a distributed actuator array control scheme assumes that the system's control action can be approximated by a continuous vector force field. The continuous control vector field idealization must then be adapted to the physical actuator array. However, we show in this paper 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. For this analysis we introduce and use a "power dissipation" method that captures the contact mechanics in a general but tractable way. We show that the quasi-static contact equations have the form of a switched hybrid system. We introduce a discontinuous feedback law can produce stability which is robust with respect to variations in contact state.