Globally exponential controller/observer for tracking in robots without velocity measurement

Abstract

In this work, we present an observer and continuous controller for a multiple degree of freedom robotic plant without velocity measurement. For this considered plant, we propose and present an 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 exponentially and that all closed loop signals remain bounded. A contribution of the present paper, as compared to previous work for this same plant, can be deemed to be the globally-exponential convergence of the present paper versus the semi-globally exponential and globally asymptotic results of previous papers. To the best of our knowledge, the present paper is the first proven globally-exponential result for this plant and also the first global result 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 continuous; however, the time derivative of the velocity estimate is discontinuous but only at isolated time instants. No sliding modes are used.