Skip to main content

A lagrangian formulation of nonholonomic path following

  • Conference paper
  • First Online:
The confluence of vision and control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 237))

Abstract

We address the problem of following an unknown planar contour with a nonholonomic vehicle based on visual feedback. The control task is to keep a point of the vehicle as close as possible to the contour for a choice of norm. A camera mounted on-board the vehicle provides measurements of the contour. We formulate the problem and compute the control law in a moving reference frame modeling the evolution of the contour as seen by an observer sitting on the vehicle. The result is an on-line path planning strategy and a predictive control law which leads the vehicle to land softly on the unknown curve. Depending on the choice of the tracking criterion, the controller can exhibit non-trivial behaviors including automatic maneuvering.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. De Boor, “A Practical Guide to Splines”, Springer-Verlag, 1978.

    Google Scholar 

  2. E. D. Dickmanns and V. Graefe, “Dynamic monocular machine vision”, Machine Vision and Application, vol. 1, pp. 223–240, 1988.

    Article  Google Scholar 

  3. E. D. Dickmanns and V. Graefe, “Applications of dynamic monocular machine vision”, Machine Vision and Application, vol. 1, pp. 241–261, 1988.

    Article  Google Scholar 

  4. E. D. Dickmanns and B. D. Mysliwetz, “Recursive 3-d road and relative egostate estimation”. IEEE Transactions on PAMI, 14(2): pp. 199–213, Feb. 1992.

    Google Scholar 

  5. O. Faugeras, “Three-dimensional vision: a geometric viewpoint”. MIT Press, 1993.

    Google Scholar 

  6. M. Fliess, J. Lèvine, P. Martin and P. Rouchon, “Design of trajectory stabilizing feedback for driftless flat systems”, In Proceedings Int. Conf. ECC'95, pp. 1882–1887, Rome, Italy, Sep. 1995.

    Google Scholar 

  7. R. Frezza and G. Picci, “On line path following by recursive spline updating”, In Proceedings of the 34th IEEE Conference on Decision and Control, vol. 4, pp. 4047–4052, 1995.

    Google Scholar 

  8. R. Frezza and S. Soatto, “Autonomous navigation by controlling shape”, Communication presented at MTNS'96, St. Louis, June 1996.

    Google Scholar 

  9. R. Frezza, S. Soatto and G. Picci, “Visual path following by recursive spline updating”. In Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, Dec. 1997.

    Google Scholar 

  10. Yi Ma, J. Kosecka and S. Sastry, “Vision guided navigation for nonholonomic mobile robot”. To appear in Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, Dec. 1997.

    Google Scholar 

  11. R. Murray and S. Sastry, “Nonholonomic motion planning: steering using sinusoids”, IEEE Transactions on Automatic Control, 38 (5), pp. 700–716, May, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Murray, Z. Li and S. Sastry, A Mathematical Introduction to Robotic Manipulation. CRC Press Inc., 1994.

    Google Scholar 

  13. C. Samson, M. Le Borgne and B. Espiau, Robot Control The Task Function Approach. Oxford Engineering Science Series. Clarendon Press, 1991.

    Google Scholar 

  14. G. Walsh, D. Tilbury, S. Sastry and J. P. Laumond, “Stabilization of trajectories for systems with nonholonomic constraints”. IEEE Transactions on Automatic Control, 39(1): pp. 216–222, Jan. 1994.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

David J. Kriegman PhD Gregory D. Hager PhD A. Stephen Morse PhD

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag

About this paper

Cite this paper

Frezza, R., Picci, G., Soatto, S. (1998). A lagrangian formulation of nonholonomic path following. In: Kriegman, D.J., Hager, G.D., Morse, A.S. (eds) The confluence of vision and control. Lecture Notes in Control and Information Sciences, vol 237. Springer, London. https://doi.org/10.1007/BFb0109667

Download citation

  • DOI: https://doi.org/10.1007/BFb0109667

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-025-5

  • Online ISBN: 978-1-84628-528-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics