Adaptive control for robot manipulator with guaranteed transient performance

Abstract

A novel method to improve the transient performance of the adaptive tracking control system for robot manipulators is proposed. In short, an exponential convergence to a predetermined residual set of tracking error in the closed-loop system can be guaranteed for the robot manipulator system. In addition, the tracking error converges to zero asymptotically thereafter. The proposed controller utilize the attracting immersed manifold in the system state space, which is introduced in the non-certainty equivalent (NCE) adaptive control framework. In order to guarantee the exponential convergence of the closed-loop tracking error to the predetermined residual set, the additional stabilizing signal is designed to boost the convergence rate on top of the NCE adaptive controller. As a result, the transient response of the adaptive tracking control system is maintained to decay exponentially to the residual set whose size can be regulated. A rigorous proof for the exponential convergence of the closed-loop adaptive control system is presented in contrast to the asymptotic convergence of the conventional model reference adaptive control (MRAC) framework. Numerical simulations are performed for the demonstration of the proposed control method.