Robust trajectory‐tracking in finite‐time for robot manipulators using nonlinear proportional‐derivative control plus feed‐forward compensation

Abstract

Abstract In this article, we propose a novel nonlinear control scheme for the trajectory tracking in finite‐time of robot manipulators. Our control proposal is composed of two parts: a proportional‐derivative (PD) nonlinear feedback and a feed‐forward compensation term. The (discontinuous) nonlinear PD term is designed like a twisting sliding mode controller that ensures robust global uniform finite‐time stabilization of the tracking error, in spite of model uncertainties and nonvanishing perturbations. Moreover, in order to decrease the (possible) chattering phenomena, we also propose two alternatives: a variable‐gain version and a continuous version of the PD term. The feed‐forward term allows us to deal intelligently with Coriolis and gravity effects because the compensation for these terms is generated off‐line. In the continuous case, practical stability is guaranteed in the presence of model uncertainties and nonvanishing perturbations. The stability conclusions are established, in both cases, designing novel strict Lyapunov functions.