Feedback Control Methods for Distributed Manipulation Systems that Involve Mechanical Contacts

This paper introduces feedback control methods for distributed manipulation systems that move objects via rolling and slipping point contacts. Due to the intermittent nature of these mechanical contacts, the governing mechanics of these systems are inherently nonsmooth. We first present a methodology to model these nonsmooth mechanical effects in a manner that is tractable for nonsmooth control analysis. Using these models, we show that when considerations of these nonsmooth effects are taken into account, a class of traditional open loop distributed manipulation control methods cannot stabilize objects near an equilibrium. However, stability can be achieved through the use of feedback, and we present nonsmooth feedback laws with guaranteed stability properties. We then describe an experimental modular distributed manipulation test-bed upon which one can implement a variety of control schemes. Experiments with this test-bed confirm the validity of our control algorithms. Multimedia extensions include videos of these experiments.