Skip to main content
Log in

Tip Tracking Control of a Single-Link Flexible Robot: A Backstepping Approach

  • Published:
Dynamics and Control

Abstract

In this paper, tip tracking control is investigated for a single-link flexible robot. The flexible beam is first lumped to a spring-mass system, to which the so called backstepping approach is applicable, then two robust controllers and an adaptive controller are developed in the presence of system disturbances/uncertainties. The controllers are rigorously proven to be able to achieve stable tip position and velocity tracking control in the sense of Global Uniform Ultimate Boundedness (GUUB). Numerical simulation results are provided which show that the proposed controllers are effective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Siciliano, B. and Book, W. J., “A singular perturbation approach to control of lightweight flexible manipulators,” Int. J. Robotics Research, vol. 7, no. 4, pp. 79–90, 1988.

    Google Scholar 

  2. Aoustin, Y. and Chevallereau, C., “The singular perturbation control of a two-flexible-link robot,” Proc. IEEE conf. Rob. Auto., Atlanta, GA, pp. 737–742, 1993.

  3. Vandegrift, M. W., Lewis, F. L. and Zhu, S. Q., “Flexible-link robot arm control by a feedback linearization/ singular perturbation approach,” J. Robotic Systems, vol. 11, no. 7, pp. 591–603, 1994.

    Google Scholar 

  4. Yuan, Bau-San, Book, Wayne J. and Siciliano, Bruno, “Direct adaptive control of a one-link flexible arm with tracking,” J. Robotic Systems, vol. 6, no. 6, pp. 663–680, 1989.

    Google Scholar 

  5. Kwon, D. and Book, W. J., “A time-domain inverse dynamic tracking control of a single-link flexible manipulator,” J. Dyna. Syst, Meas, & Contr., vol. 116, pp. 193–200, 1994.

    Google Scholar 

  6. Bayo, E., “A finite-element approach to control the end-point motion of a single-link flexible robot,” J. Robotic Systems, vol. 4, no. 1, pp. 63–75, 1987.

    Google Scholar 

  7. Ge, S. S., Lee, T. H. and Zhu, G., “A new lumping method of a flexible manipulator,” Proc. American Control Conference, vol. 3, pp. 1412–1416, Albuquerque, NM, 1997.

    Google Scholar 

  8. Kokotovic, Petar V., “The joy of feedback: Nonlinear and adaptive,” IEEE Control Syst. Mag., vol. 12, pp. 7–13, Nov. 3, 1992.

    Google Scholar 

  9. Sakawa, Y., Matsuno, F. and Fukushima, S., “Modeling and feedback control of a flexible arm,” J. of Robotic Systems, vol. 2, no. 4, pp. 453–472, 1985.

    Google Scholar 

  10. Dawson, D. M., Qu, Z., Bridges, M. and Carroll, J., “Robust tracking of rigid-link flexible-joint electrically-driven robots,” Proc. 30th Conf. Deci. and Contr., Brighton, England, pp. 1409–1412, Dec. 1991.

  11. Bridges, M. M., Dawson, D. M. and Abdallah, C. T., “Control of rigid-link flexible-joint robots: A survey of backstepping approaches,” J. Robotic Systems, vol. 12, no. 3, pp. 199–216, 1995.

    Google Scholar 

  12. Khalil, Hassan K., Nonlinear Systems, Chapter 4, Macmillan Publishing Company, 1992.

  13. Bodur, M. and Sezer, M. E., “Adaptive control of flexible multilink manipulators,” Int. J. Control, vol. 58, no. 3, pp. 519–536, 1993.

    Google Scholar 

  14. Narendra, K. S., Stable Adaptive Systems, Chapter 8, Englewood Cliffs: Prentice-Hall Inc., 1989.

    Google Scholar 

  15. Kanoh, H., Tzafestas, S., Lee, H. G. and Kalat, J., “Modelling and control of flexible robot arms,” Proc. 25th Conf. Decision & Control, Athens, Greece, pp. 1866–1870, Dec. 1986.

  16. Cannon, R. H., Jr. and Schmitz, E., “Initial experiments on the end-point control of a flexible one-link robot,” Int. J. Robotics Research, vol. 3, no. 3, pp. 62–75, 1984.

    Google Scholar 

  17. Shigley, J. E., Simulation of Mechanical Systems: An Introduction, Chapter 6, McGraw-Hill Book Company, 1967.

  18. Fraser, A. R. and Daniel, R. W., Perturbation techniques for flexible manipulators, Chapter 3, pp. 63–67, Kluwer Academic Publishers, 1991.

  19. Hastings, G. G. and Book, W. J. “A linear dynamic model for flexible robotic manipulators,” IEEE Control System Magazine, vol. 7, pp. 61–64, 1987.

    Google Scholar 

  20. Marino, R. and Tomei, P., “Dynamic output-feedback linearization and global stabilization,” Systems and Control Letters, vol. 17, pp. 115–121, 1991.

    Google Scholar 

  21. Marino, R. and Tomei, P., “Global adaptive output-feedback control of nonlinear systems, part I: Linear parametrization & Part II: Nonlinear parametrization,” IEEE Trans. on Automatic Control, vol. 38, pp. 17–49, 1993.

    Google Scholar 

  22. Praly, L. and Jiang, Z. P., “Stabilization by output-feedback for systems with ISS inverse dynamics,” Systems and Control Letters, vol. 21, pp. 19–33, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhu, G., Lee, T.H. & Ge, S.S. Tip Tracking Control of a Single-Link Flexible Robot: A Backstepping Approach. Dynamics and Control 7, 341–360 (1997). https://doi.org/10.1023/A:1008220427072

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008220427072

Navigation