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Controllability and state feedback stabilizability of non holonomic mechanical systems

  • Control Of Robotic Systems With Nonholonomic Constraints
  • Conference paper
  • First Online:
Advanced Robot Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 162))

Abstract

The dynamics of non holonomic mechanical system are described by the classical Euler-Lagrange equations subjected to a set of non-integrable constraints. Non holonomic systems are strongly accessible whatever the structure of the constraints. They cannot be asymptotically stabilized by a smooth pure state feedback. However smooth state feedback control laws can be designed which guarantee the global marginal stability of non holonomic systems.

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References

  1. P. Appell, "Traité de mécanique rationnelle", Gauthier-Villars, Paris, 1903.

    Google Scholar 

  2. G. Hamel, "Die Lagrange-Euler'schen Gleichungen der Mechanik", Teubner, Leipzig, 1903.

    Google Scholar 

  3. J.P. Laumond, "Feasible trajectories for mobile robots with kinematic and environment constraints", Int. Conf. on Intelligent Autonomous Systems, Amsterdam, 1986, pp. 346,354.

    Google Scholar 

  4. J. Barraquand, J.C. Latombe, "On non holonomic mobile robots and optimal manoeuvring", Revue d'intelligence Artificielle, Vol 3–2, 1989, Ed. Hermes, pp. 77,103.

    Google Scholar 

  5. C. Samson, K. Ait-Abderrahim, "Mobile robot control. Part 1: Feedback control of non holonomic wheeled cart in Cartesian space", INRIA Report, No1288, 1990

    Google Scholar 

  6. A. Isidori, "Nonlinear control systems", Springer Verlag, 1989.

    Google Scholar 

  7. H. Nijmeijer and A.J. van der Schaft, "Nonlinear Dynamical Control Systems", Springer Verlag, 1990.

    Google Scholar 

  8. R.W. Brockett, “Asymptotic stability and feedback stabilization”, in Differential Geometric Control Theory (eds. Brockett, Millmann, Sussmann), Birkhauser, Boston, pp.181–191, 1983.

    Google Scholar 

  9. Bloch and Mc Clamroch, "Control of mechanical systems with classical non holonomic constraints", Proc. 28th IEEE Conf.on Decision and Control, Tampa, 1989, pp.201–205.

    Google Scholar 

  10. H.J. Sussmann and V. Jurdjevic, “Controllability of nonlinear systems”, J. Diff. Eqns., 12, pp.95–116, 1972.

    Google Scholar 

  11. B. d'Andrea, G.Bastin and G.Campion, “Modelling and Feedback Control of Nonholonomic Systems: The case of mobile robots”, to be presented at the IEEE Conf. on Robotics and Automation, Sacramento, 1991.

    Google Scholar 

  12. A. M. Bloch and N. H. McClamroch, "Controllability and stabilizability properties of a nonholonomic control system", Proc. 29th Conference on Decision and Control, Hawaii, pp. 1312–1314, 1990.

    Google Scholar 

  13. C. Samson, "Velocity and torque feedback control of a nonholonomic cart" Int. Workshop in Adaptive and Nonlinear Control: Issues in Robotics, Grenoble, 1990.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d'Automatique, Dynamique et Analyse des Systèmes, Université Catholique de Louvain, Place du Levant, 3-B1348, Louvain-La-Neuve, Belgium

    G. Campion & G. Bastin

  2. Centre d'Automatique, Ecole Nationale Supérieure des Mines de Paris, Rue Saint Honoré, 35-F77305, Fontainebleau, France

    B. d'Andrea-Novel

Authors
  1. G. Campion
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  2. B. d'Andrea-Novel
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  3. G. Bastin
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Editor information

Carlos Canudas de Wit

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© 1991 Springer-Verlag

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Campion, G., d'Andrea-Novel, B., Bastin, G. (1991). Controllability and state feedback stabilizability of non holonomic mechanical systems. In: Canudas de Wit, C. (eds) Advanced Robot Control. Lecture Notes in Control and Information Sciences, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039268

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  • DOI: https://doi.org/10.1007/BFb0039268

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54169-1

  • Online ISBN: 978-3-540-47479-1

  • eBook Packages: Springer Book Archive

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