A unified perspective on robot control: The energy lyapunov function approach

Abstract

Abstract A unified framework for the stability analysis of robot tracking control is presented. By using an energy‐motivated Lyapunov function candidate, the closed‐loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model‐based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete non‐linear dynamics, or linearized or non‐linear dynamics with parameter adaptation. As a result, the dichotomous approaches to the robot control problem based on the open‐loop linearization and non‐linear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade‐offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a priori model information are derived.