Control of under-actuated mechanical systems subject to smooth impacts

The paper deals with a mechanical system, subject to smooth impacts with external objects, actuated only along the contact coordinates involved in the impacts. The considered control problem is the development of a control law, to be used both in free motion and during contact, that asymptotically leads the system in a contact condition with the external objects, corresponding to zero exchanged contact forces. Two control solutions are proposed, by using only the contact coordinates and their time derivatives as outputs of the system: a pure static output feedback algorithm, and a dynamic controllers family. The stability properties of the closed-loop systems thus obtained are analytically proven, and confirmed by simulation results.