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Stability of robot force control applied to unilateral constraints

Experiments on single degree of freedom (1-DOF) robots have shown that force feedback sometimes produces an undesirable chattering behaviour, where the robot repeatedly makes and breaks contact with the constraint surface. This behaviour 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 robot never loses contact with the constraint. In this paper, we analyse the stability of a 1-DOF force-controlled robot in contact with a rigid unilateral constraint, with the force sensor modelled as a stiff spring. It is proved that the nonlinear system is globally, asymptotically stable and achieves zero steady-state force error.