Control of mechanical systems subject to unilateral constraints

In this work we consider the problem of control of mechanical systems subject to unilateral constraints. Impulsive forces arise whenever the constraints become active and these forces give rise to nonsmooth dynamics. The dynamics of the system is defined by a set of differential equations with discontinuous righthand side using Hamilton´s equations of motion. A nonlinear transformation is applied and the dynamics of the system is written in two sets of differential equations in the transformed coordinates. Three different phases (inactive, transition and active) for the system are formulated depending on the activation/deactivation of the constraints. A discontinuous controller is designed for the three phases for tracking the desired trajectories of the system. Stability analysis is conducted for all the phases using tools like Filippov´s differential inclusions, nonsmooth Lyapunov analysis and generalized gradients. We give an illustrative example for the theory developed