Feedback stabilization and force control using sliding modes in a mechanical system subject to unilateral constraints

Force feedback sometimes produces an undesirable chattering behavior, where the mechanical system repeatedly makes and breaks contact with the constraint surface this have been shown in experiments on single degree of freedom (1-DOF). This behavior is an example of a limit cycle, and is likely caused by the nonlinearity in the system dynamics introduced by the unilateral (i.e. one-sided) constraint. Yet most published stability analyses of force-controlled robots assume that the constraint is bilateral, meaning the mechanical system never loses contact with the constraint. In this note, we analyze the stability of a 1-DOF force-controlled mechanical system in contact with a rigid unilateral constraint applying a sliding mode control algorithm, with the force sensor modeled as a stiff spring. It is proved that the nonlinear system is globally asymptotically stable and achieves zero steady-state force error.