Control of contact problem in constrained Euler-Lagrange systems

In this paper, we investigate the contact problem for constrained Euler-Lagrange systems. We model the constrained equations as a set of nonsmooth differential equations depending on whether the system lies on the constraint surface (active phase) or the system repeatedly makes and loses contact with the constraint surface (transition phase). We concentrate on the initial condition problem for the transition phase, i.e., the system hits the constraint with a nonzero normal-velocity. We state a generic impact model to describe the impact behavior. The control laws are designed such that during the contact/noncontact phase of the system there is a potential force field that will always direct the system towards the constraint