Steering a class of redundant mechanisms through end-effector generalized forces

A particular class of underactuated systems is obtained by considering kinematically redundant manipulators for which all joints are passive and the only available inputs are forces/torques acting on the end-effector. Under the assumption that the degree of redundancy is provided by prismatic joints located at the base, we address the problem of steering the robot between two arbitrary equilibrium configurations. By performing a preliminary partial feedback linearization, the dynamic equations take a convenient triangular form, which is further simplified under additional hypotheses. We give sufficient conditions for controllability of this kind of mechanisms. With a PPR robot as a case study, an algorithm is proposed for computing end-effector commands that produce the desired reconfiguration in finite time. Simulation results and a discussion on possible generalizations are given.