Contact Transition Control of Nonlinear Mechanical Systems Subject to a Unilateral Constraint

In this paper, contact transition control of mechanical systems subject to a unilateral constraint is presented. A systematic way is proposed for designing control laws for unilaterally constrained mechanical systems. Three phases of motion (inactive, transition, active) are formulated depending on the activation/deactivation of the constraint. Our framework describes the complete behaviour of the mechanical system under the action of a unilateral constraint. We propose stable control laws for all the phases of the system. Exponential stability in each phase is shown. Of special interest is the contact transition problem. During this phase the dynamics is discontinuous. Nonsmooth Lyapunov techniques are used to show exponential stability in the transition phase. Composite Lyapunov functions are constructed for each phase and these are used to show asymptotic stability of the overall system taking into consideration switching from one phase to another. The proposed method is successfully implemented on robots interacting with an environment, and we present results of those experiments. Experimental results confirm the theoretically predicted behavior.