Global exponential stabilizability for distributed manipulation systems

Considers the global exponential stability of planar distributed manipulation control schemes. The programmable vector field approach is a commonly proposed method for distributed manipulation control. The authors (2001) showed that when one takes into account the discreteness of actuator arrays and the mechanics of actuator/object contact, the controls designed by the programmable vector field approach can be unstable at the desired equilibrium configuration. We show here how a discontinuous feedback law that locally stabilizes the manipulated object at the equilibrium can be combined with the programmable vector field approach to control the object´s motions. We prove that the combined system is globally exponentially stabilizable even in the presence of changes in contact state. Simulations illustrate the results