Globally asymptotic adaptive controller/observer for tracking in robots without velocity measurement

Abstract

In this work, we present an adaptive observer/controller for a multiple degree of freedom robotic plant without velocity measurement and without knowledge of plant parameter values. For this considered plant, we propose and present an adaptive observer/controller that estimates or observes the velocity and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero globally asymptotically and that all closed-loop signals remain bounded. A contribution of the present paper, as compared with previous work for this same plant, can be deemed to be the fact that, to the best of our knowledge, the present paper is the first proven globally asymptotic result for this plant for which the size of the control torque does not increase exponentially with respect to the size of the tracking error. The control torque is discontinuous, however, only at isolated time instants. No sliding modes are used.