Strict Lyapunov functions for finite-time control of robot manipulators

Abstract

Motivated by the energy shaping framework and the properties of homogeneous systems, we introduce a methodology to derive strict Lyapunov Functions (LFs) for a class of global finite-time (FT) controllers for robot manipulators. As usual in the energy shaping methodology, 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, strict LFs ensuring global FT stability at the desired equilibrium. As an important practical outcome, we illustrate the proposed methodology by constructing strict LFs for some particular FT controllers. The construction of such strict LFs allows us to solve the open problem of FT trajectory tracking of robot manipulators with continuous control laws to track any bounded trajectory.