Linear robust control of mechanical manipulators

Abstract

A linear feedback control scheme for trajectory tracking is presented. It is shown to be robust against model uncertainties. The scheme is based on an eigen-analysis of the inertia matrix of the mechanical manipulator considered and a least-squares-type approximation of the Coriolis, centrifugal, and gravity terms in the manipulator's dynamics. The eigen-analysis and least-squares approximation lead to a simple yet reasonable model which in turn defines a structure of the constant feedback control. To determine the parameters of this controller, an analysis of the tracking-error dynamics is carried out using a Lyapunov approach. It turns out that, by properly choosing a set of feedback gains, the tracking error can be kept to a prescribed range during the task in the presence of the gravity effect and model uncertainties.<>