Romansy 13 pp 75-84 | Cite as

On Kinematic Singularities of Nonholonomic Robotic Systems

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


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.


Mobile Robot Nonholonomic System Robotic Manipulator Phase Constraint Inverse Kinematic Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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. 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) 755–763Google Scholar
  3. 3.
    Murray, R. M., Li, Z., Sastry, S. S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)Google Scholar
  4. 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) 1–54CrossRefGoogle Scholar
  5. 5.
    Dulgba, I.: Algorithms of Motion Planning for Nonholonomic Robots. Wroclaw University of Technology Publishers, Wroclaw (1998)Google Scholar
  6. 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) 55–91CrossRefGoogle Scholar
  7. 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) 1–81Google Scholar
  8. 8.
    Montgomery, R.: A survey of singular curves in sub-Riemannian geometry. J. Dyn. Contr. Syst. 1 (1995) 49–90CrossRefzbMATHGoogle Scholar
  9. 9.
    Jakubczyk, B.: Characteristic varieties of distributions and abnormal curves. Math. Inst. Polish Academy of Sci. (1999) (preprint)Google Scholar
  10. 10.
    Pasillas-Lépine, W., Respondek, W.: On the geometry of Goursat structures. Inst. Nat. Sci. Appl. de Rouen (1999) (preprint)Google Scholar
  11. 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. 12.
    Tchou, K., Muszynski, R.: Singular inverse kinematic problem for robotic manipulators: A normal form approach. IEEE Trans. Robotics Automat. 14 (1998) 93–104CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • Krzysztof Tchoń
    • 1
  1. 1.Institute of Engineering CyberneticsWroclaw University of TechnologyWroclawPoland

Personalised recommendations