Guaranteeing stable tracking of hybrid position–force trajectories for a robot manipulator interacting with a stiff environment

Abstract

This work considers the control of a manipulator with the aim of executing desired time-varying motion–force trajectories in the presence of a stiff environment. In several situations, the interaction with the environment constrains just one degree of freedom of the manipulator end-effector. Focusing on this contact degree of freedom, a switching position–force controller is considered to perform the hybrid motion–force tracking task. To guarantee input-to-state stability of the switching closed-loop system, a novel stability result and sufficient conditions are presented. The switching occurs when the manipulator makes or breaks contact with the environment. The analysis shows that to guarantee closed-loop stability while tracking arbitrary time-varying motion–force profiles with a rigid manipulator, the controller should implement a considerable (and often unrealistic) amount of damping, resulting in inferior tracking performance. Therefore, we use the stability analysis technique developed in this paper to analyze a manipulator equipped with a compliant wrist. Guidelines are provided for the design of the wrist compliancy while employing the switching control strategy, such that stable tracking of a motion–force reference trajectory can be achieved and bouncing of the manipulator against the stiff environment can be avoided. Numerical simulations are presented to illustrate the effectiveness of the approach.