Cartesian sliding PID control schemes for tracking robots with uncertain Jacobian

Abstract

Owing to the fact that desired tasks are usually defined in operational coordinates, inverse and direct kinematics must be computed to obtain joint coordinates and Cartesian coordinates, respectively. However, in order to avoid the ill-posed nature of the inverse kinematics, Cartesian controllers have been proposed. Considering that Cartesian controllers are based on the assumption that the Jacobian is well known, an uncertain Jacobian will produce a non-exact localization of the end-effector. In this paper, we present an alternative approach to solve the problem of Cartesian tracking for free and constrained motion subject to Jacobian uncertainty. These Cartesian schemes are based on sliding PID controllers where the Cartesian errors are mapped into joint errors without any knowledge of robot dynamics. Sufficient conditions for feedback gains and stability properties of the estimate inverse Jacobian are presented to guarantee stability. Experimental results are provided to visualize the real-time stability properties of the Cartesian proposed schemes.