Skip to main content

On Kinematic Singularities of Nonholonomic Robotic Systems

  • Conference paper

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 422))

Abstract

Using a control system representation of kinematics we define and investigate posture and configuration singularities of nonholonomic robotic systems. A significance of these singularities and their interdependence are illustrated with an example of a car pulling two trailers.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tchou, K., Mazur, A., Dulgba, I., Hossa, R., Muszynski, R.: Manipulators and Mobile Robots: Modelling, Motion Planning, and Control. Academic Publishing House, Warsaw (2000) (in Polish)

    Google Scholar 

  2. Laumond, J.-P.: Singularities and topological aspects in nonholonomic motion planning. In: Nonholonomic Motion Planning, ed. by Z. Li and J. F. Canny, Kluwer Academic Publ., Boston (1992) 755–763

    Google Scholar 

  3. Murray, R. M., Li, Z., Sastry, S. S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    Google Scholar 

  4. Laumond, J.-P., Sekhvat, S., Lamiraux, F.: Guidelines in nonholonomic motion planning for mobile robots. In: Robot Motion Planning and Control, ed. by J.-P. Laumond, Springer-Verlag, London (1998) 1–54

    Chapter  Google Scholar 

  5. Dulgba, I.: Algorithms of Motion Planning for Nonholonomic Robots. Wroclaw University of Technology Publishers, Wroclaw (1998)

    Google Scholar 

  6. Bellaiche, A., Jean, F., Risler, J.-J.: Geometry of nonholonomic systems In: Robot Motion Planning and Control, ed. by J.-P. Laumond, Springer-Verlag, London (1998) 55–91

    Chapter  Google Scholar 

  7. Vershik, A. M., Gershkovich, V. Ya.: Nonholonomic dynamical systems, geometry of distributions and variational problems. In: Dynamical Systems VII, ed by V. I. Arnold and S. P. Novikov, Springer-Verlag, Berlin (1994) 1–81

    Google Scholar 

  8. Montgomery, R.: A survey of singular curves in sub-Riemannian geometry. J. Dyn. Contr. Syst. 1 (1995) 49–90

    Article  MATH  Google Scholar 

  9. Jakubczyk, B.: Characteristic varieties of distributions and abnormal curves. Math. Inst. Polish Academy of Sci. (1999) (preprint)

    Google Scholar 

  10. Pasillas-Lépine, W., Respondek, W.: On the geometry of Goursat structures. Inst. Nat. Sci. Appl. de Rouen (1999) (preprint)

    Google Scholar 

  11. Sontag, E. D.: A general approach to path planning for systems without drift. In: Essays on Mathematical Robotics, ed. by J. Baillieul. S. S. Sastry and H. J. Sussmann, Springer-Verlag, New York (1998)

    Google Scholar 

  12. Tchou, K., Muszynski, R.: Singular inverse kinematic problem for robotic manipulators: A normal form approach. IEEE Trans. Robotics Automat. 14 (1998) 93–104

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Wien

About this paper

Cite this paper

Tchoń, K. (2000). On Kinematic Singularities of Nonholonomic Robotic Systems. In: Morecki, A., Bianchi, G., Rzymkowski, C. (eds) Romansy 13. International Centre for Mechanical Sciences, vol 422. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2498-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2498-7_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-2500-7

  • Online ISBN: 978-3-7091-2498-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics