Robust control for robots using auxiliary polynomials: Theory and experiments

Abstract

An approach to robust control designs for trajectory tracking of robotic manipulators is presented. Two families of controllers are developed, one being continuous and the other being of switching type. The main feature of the control designs is the use of auxiliary polynomials in position and velocity tracking errors. The designs are simple in feedback gain selections and robust against non-zero initial tracking errors, disturbances and parameter uncertainties. The proposed controller structure consists of a PD feedback term and a nonlinear function in terms of the auxiliary polynomial in a simple form. The control parameters for the PD control and the nonlinear auxiliary polynomials are selected with minimum mutual dependence and based on only limited knowledge on bounds of robot dynamics. The bounds on the position and velocity tracking errors are explicitly specified by controller parameters. With very minimum knowledge of dynamic parameters, these controllers can still ensure that the closed-loop system will not become unstable and the tracking errors are bounded. The controllers are also simple to implement. Experiments are carried out using an industrial robot and results are presented.