Adaptive λ-Tracking for Rigid Manipulators

Abstract

This paper deals with a modification of a simple trajectory tracking algorithm for rigid manipulators, namely a modification of the classical PD controller with static gain, which does not employ any specific knowledge of the robot dynamics. In (Qu and Dorsey, 1991) it has been shown that the classical PD controller is able to keep position errors within certain bounds. It is, however, impossible to give a simple evaluation for those bounds. Here we introduce a dynamical PD controller, which allows to predefine some error bounds even in the absence of the knowledge of the robot dynamics. The region which the tracking error is converging to, depends only on the design parameters of the PD controller. The algorithm is in fact a universal adaptive control system with a dead zone of width λ > 0. This application is in the spirit of λ-tracking introduced by (Mazur, 1996, Mazur and Hossa, 1997). An interesting part of the paper is the practical evaluation of the proposed control algorithm using the rigid manipulator EDDA (Experimental Direct Drive Arm) at the Institute for Robotics and Process Control in Braunschweig, see Figure 1. The experiments will demonstrate the successful application of the algorithm in practice. They will further serve to present some relationship between the choice of control parameters and the behaviour of the position tracking error.

The authors are grateful to Dr. Achim Ilchmann, Department of Mathematics & Centre for Systems and Control Engineering, University of Exeter, for his help with completing the proof and for the revision of the mathematical parts of the paper.