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 non-smooth 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 non-zero normal velocity. We state a generic impact model to describe the impact behavior. The control laws are designed such that during the contact/non-contact phase of the system there is a potential force field that will always direct the system towards the constraint.