Stabilization of Equilibrium for Underactuated Mechanical Systems Without Potential Energy

This paper investigates the equilibrium stabilization problem for a class of underactuated mechanical systems which do not possess potential energy. The dynamics of the system is established under the framework of Rimannian geometry, and differential geometric methods are employed in the design of stabilization controller. The main novelty of this paper is that we stabilize the equilibrium by constructing an artificial potential for the closed-loop system, which is related to the designed configuration feedback. Once the artificial potential satisfy certain requirements with respect to the equilibrium, the stability of the system can be guaranteed. Furthermore, by incorporating dissipative feedback into the control strategy, we successfully obtain the exponential stability of the equilibrium. Copyright (C) 2020 The Authors.