  This work proposes a control law for a manipulator with the aim of realizing
desired time-varying motion-force profiles in the presence of a stiff
environment. In many cases, the interaction with the environment affects only
one degree of freedom of the end-effector of the manipulator. Therefore, the
focus is on this contact degree of freedom, and a switching position-force
controller is proposed to perform the hybrid position-force tracking task.
Sufficient conditions are presented to guarantee input-to-state stability of
the switching closed-loop system with respect to perturbations related to the
time-varying desired motion-force profile. 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, the controller should implement a considerable (and
often unrealistic) amount of damping, resulting in inferior tracking
performance. Therefore, we propose to redesign the manipulator with a compliant
wrist. Guidelines are provided for the design of the compliant wrist while
employing the designed switching control strategy, such that stable tracking of
a motion-force reference trajectory can be achieved and bouncing of the
manipulator while making contact with the stiff environment can be avoided.
Finally, numerical simulations are presented to illustrate the effectiveness of
the approach.
