Robust tracking in nonlinear systems and its applications to robotics

Abstract

A nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system. The tracking error is measured by a general function of system state and the input command. The controller is robust in the sense that the tracking error is ultimately bounded in the presence of modelling errors. Free parameters, which affect the form of the controller, allow flexibility in determining such factors as: the size of the ultimate bound, the rate of error delay, excursion of the control, conditions on the class of modelling errors, the level of system gain. Restrictive assumptions on the structure of the model and the modelling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature. These assumptions hold for robotic manipulators. This application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature.