Strict Lyapunov functions for control of robot manipulators (Q1361329)

This paper presents a methodology for deriving strict Lyapunov functions for a class of global regulators of robotic manipulators. The authors' approach is based on the energy shaping techniques of Takegaki and Arimoto. The regulators are described by control laws composed of the gradient of an artificial potential energy plus a linear velocity feedback. The authors provide an explicit set of sufficient conditions on the artificial potential energy. These conditions provide a direct means of obtaining strict Lyapunov functions that insure global asymptotic stability of the closed-loop system. The authors also establish a framework for designing adaptive versions for this class of regulators. They propose an explicit update law that guarantees closed-loop stability and global positioning. In addition, they characterize the class of tracking controllers for which global uniform asymptotic stability is insured by strict Lyapunov functions.