A Unified Perspective on Robot Control: The Energy Lyapunov Function Approach

A unified framework for stability analysis for robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As a result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear 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, real-time computation load, and required a priori model information are derived.