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

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. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.