Variable structure robot control undergoing chattering attenuation: adaptive and nonadaptive cases

This paper has a twofold objective: 1) to show that, when an adaptive law designed with a Lyapunov function and dependant also of the parametric error is introduced into a variable structure controller the existence of a sliding mode is no longer guaranteed for all t; and 2) a time varying boundary layer modulated by the tracking errors to propose a variable structure robot control with asymptotic stability. It is shown that the high activity on the actuators, typical of variable structure controllers, can be arbitrarily reduced in both adaptive and nonadaptive cases. These controllers give rise to the asymptotic stability and at the same time the sliding mode is guaranteed with very small chattering. A trade off arises in terms of chattering and robustness but the convergence of tracking errors is always assured. Computer simulations show the performance of the proposed controllers with comparison of two other algorithms