Skip to main content
SpringerLink
Log in

Motion Planning for Drift-Free Nonholonomic Systems under a Discrete Levels Control Constraint

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

We solve the Motion Planning Problem for nonholonomic systems without drift when their inputs are restricted to take values in a prescribed discrete levels set of finite cardinality. In particular, we propose algorithms that produce the proper sequence of input levels as well as the corresponding switching times providing exact steering when the system is nilpotent or feedback nilpotentizable. For a general drift-free system, i.e. for a drift-free system that is neither nilpotent nor feedback nilpotentizable another algorithm provides approximate steering within a permissible error. Finally, we apply the proposed algorithms in motion planning for a car-like mobile robot.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Kolmanovsky, I. and McClamroch, N. H.: 1995, Developments in nonholonomic control problems, IEEE Control Systems Magazine 15, 20-36.

    Google Scholar 

  • Lafferriere, G.: 1991, A general strategy for computing steering controls of systems without drift, in: Proc. of the 30th Conf. on Decision and Control, Brighton, England, December 1991.

  • Lafferriere, G. and Sussmann, H. J.: 1993, A differential geometric approach to motion planning, in: Z. Li and J. F. Canny (eds), Nonholonomic Motion Planning, Kluwer, Dordrecht, pp. 235-270.

    Google Scholar 

  • Lafferriere, G. and Sussmann, H. J.: 1991, Motion planning of controllable systems without drift, in: Proc. of IEEE Internat. Conf. on Robotics and Automation, Sacramento, CA, April 1991, pp. 1148-1153.

  • Latombe, J. C.: 1991, Robot Motion Planning, Kluwer, Boston.

    Google Scholar 

  • Li, Z. and Canny, J. F. (eds): 1993, Nonholonomic Motion Planning, Kluwer, Dordrecht.

    Google Scholar 

  • Murray, R. M., Li, Z., and Sastry, S. S.: 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.

    Google Scholar 

  • Skiadas, Ph. and Koussoulas, N. T.: 1997, Discrete Levels Control of Nonlinear Systems, in: Proc. of the 5th IEEE Mediterranean Conf. on Control and Systems, Paphos, Cyprus, July 1997.

Download references

Author information

Authors and Affiliations

  1. Laboratory for Automation and Robotics, Electrical and Computer Engineering Department, University of Patras, Rio Patras, 265 00, Greece

    Photis G. Skiadas & Nick T. Koussoulas

Authors
  1. Photis G. Skiadas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nick T. Koussoulas
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skiadas, P.G., Koussoulas, N.T. Motion Planning for Drift-Free Nonholonomic Systems under a Discrete Levels Control Constraint. Journal of Intelligent and Robotic Systems 32, 55–74 (2001). https://doi.org/10.1023/A:1012060516299

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012060516299

Search

Navigation