Prescribed-time Control for Perturbed Euler-Lagrange Systems with Obstacle Avoidance

TL;DR

This paper develops a novel prescribed-time control method for Euler-Lagrange systems that guarantees finite-time convergence and obstacle avoidance, even under disturbances, without chattering or disturbance observation.

Contribution

It introduces a two-step control design using a mapping technique for prescribed-time stability and disturbance rejection in Euler-Lagrange systems.

Findings

Achieves finite-time convergence independent of initial conditions.

Ensures obstacle avoidance with disturbance rejection.

Validated through numerical simulations on a two-link robot manipulator.

Abstract

This paper introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects matched disturbances with unknown upper bounds without disturbance observation. As an example, a two-link robot manipulator is considered for numerical simulations.