Kinetic-Potential Energy Shaping for Mechanical Systems With Applications to Tracking

Abstract

In this letter, we propose a new closed-loop structure for mechanical systems with dissipation, controlled via energy shaping. The structure generalizes the well-established potential energy shaping technique by introducing a kinetic-potential function which has both configuration and momentum states as arguments. As a consequence of this generalization, dissipation terms are able to be added to the configuration coordinates of the system, resulting in both exponential stability and input-to-state stability (ISS) properties of the closed-loop. The developments are applied to the tracking problem where it is shown that the scheme is ISS with respect to friction modelling error.