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.
Bibliographical noteThe material in this paper was partially presented at the 2015 American Control
Conference, July 1–3, 2015, Chicago, IL, USA.