Finite-Time Regulation of Robots: a Strict Lyapunov Function Approach

Abstract

Motivated by the energy shaping framework and the properties of homogeneous systems, we introduce a methodology to derive strict Lyapunov functions (SLFs) for a class of global finite-time (FT) controllers for robot manipulators. These controllers are described by the gradient of the controller potential energy plus the gradient of (nonlinear) energy dissipation-like functions. Sufficient conditions on the controller potential energy and energy dissipation-like functions are provided in order to obtain, in a straightforward manner, a SLF that ensures global asymptotic stability at the desired equilibrium. Finite-time stability is concluded by constructing a local SLF. As an important practical outcome, we illustrate the proposed methodology by constructing SLFs for some particular FT controllers.