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RESEARCH PAPERS

A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators

[+] Author and Article Information
Nader Sadegh

The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Roberto Horowitz, Wei-Wen Kao, Masayoshi Tomizuka

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 112(4), 618-629 (Dec 01, 1990) (12 pages) doi:10.1115/1.2896187 History: Received May 23, 1988; Revised November 01, 1989; Online March 17, 2008

Abstract

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

Copyright © 1990 by The American Society of Mechanical Engineers
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