Nonsingular predefined-time sliding mode trajectory tracking control for uncertain manipulator with predefined-time extended state observer.

Abstract

In this study, a global predefined-time-embedded two-layer sliding mode control strategy is established for the manipulator under the model uncertainties, exterior disturbances, unknown velocity measurements, and actuator saturation, enabling global trajectory tracking within the predefined time. Initially, a predefined-time extended state observer (PTESO) is devised in view of the first layer sliding mode manifold to observe the unknown velocity information and composite disturbance resulting from model uncertainty and exterior interference. Through the first layer sliding mode manifold, the auxiliary control policy is put forward to address the bounded total perturbations and guarantee the stability of the PTESO. Subsequently, a nonlinear predefined-time sliding mode control (PTSMC) methodology is presented, introducing the second layer sliding mode surface that integrates a piecewise nonlinear function concerning the joint position tracking error, thereby alleviating the singularity issue associated with PTSMC. Furthermore, a predefined-time anti-saturation compensator (PTASC) is implemented to address actuator saturation issue. By dynamically adjusting the output of the controller, the PTASC effectively mitigates the adverse effects of actuator saturation, thereby preserving robust tracking performance and stability. Consequently, employing predefined-time stability theory in combination with the Lyapunov method, the comprehensive stability verification and predefined-time convergence of the closed-loop system are undertaken. Simulation outcomes substantiate that the devised control scheme attains remarkable effectiveness and practicality.