Regular and Chaotic Dynamics

, Volume 17, Issue 3–4, pp 258–272 | Cite as

How to control Chaplygin’s sphere using rotors

  • Alexey V. Borisov
  • Alexander A. Kilin
  • Ivan S. Mamaev
Article

Abstract

In the paper we study the control of a balanced dynamically non-symmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic controllability is shown and the control inputs that steer the ball along a given trajectory on the plane are found. For some simple trajectories explicit tracking algorithms are proposed.

Keywords

non-holonomic constraint non-holonomic distribution control Chow-Rashevsky theorem drift 

MSC2010 numbers

37J60 37J35 70E18 70F25 70H45 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • Alexey V. Borisov
    • 1
  • Alexander A. Kilin
    • 1
  • Ivan S. Mamaev
    • 1
  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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