Advertisement

Romansy 13 pp 103-112 | Cite as

Adaptive λ-Tracking for Rigid Manipulators

  • Alicja Mazur
  • Carsten Schmid
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 422)

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.

Keywords

Tracking Error Dead Zone Adaptive Controller Controller Gain Robot Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berghuis, H. (1993). Model-Based Robot Control: from Theory to Practice. Ph.D. Dissertation, Twente University, Enschede.Google Scholar
  2. Craig, J. (1988). Adaptive Control of Mechanical Manipulators. New York: Addison-Wesley.Google Scholar
  3. Rebmann, A., and Ryan, E. (1994). Universal A-tracking for nonlinearly-perturbed systems in the presence of noise. Automatica 30 (2): 337–346.CrossRefMathSciNetGoogle Scholar
  4. Lchmann, A. (1993). Non-Identifier-Based High-Gain Adaptive Control. London: Springer.Google Scholar
  5. Mazur, A., and Hossa, R. (1997). Universal adaptive A.-tracking controller for wheeled mobile robots. In Proceedings of the Fifth IFAC Symposium on Robot Control SYROCO’97, 33–38.Google Scholar
  6. Mazur, A. (1996). Robot Control Algorithms Based on the Principle of Universal Adaptive Control. PhD dissertation, (in polish), Wroclaw University of Technology, Wroclaw.Google Scholar
  7. Qu, Z., and Dorsey, J. (1991). Robust tracking control of robots by linear feedback law. IEEE Transactions on Automatic Control 36 (9): 1081–1084.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Alicja Mazur
    • 1
  • Carsten Schmid
    • 2
  1. 1.Institute of Engineering CyberneticsWroclaw University of TechnologyPoland
  2. 2.Institute for Robotics and Process ControlTechnical University of BraunschweigGermany

Personalised recommendations