Global exponential stabilizability for distributed manipulation systems

This paper 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. In [13] it was shown 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 stabilizers 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.