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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 3-4, Pages 258–272
DOI: https://doi.org/10.1134/S1560354712030045 (Mi rcd337) 		 
This article is cited in 93 scientific papers (total in 93 papers)

How to Control Chaplygin’s Sphere Using Rotors

Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (93)
DOI: https://doi.org/10.1134/S1560354712030045
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
1.1248.2011
02.740.11.0195
MK-8428.2010.1
This research was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists at Russian institutions of higher professional education (Contract No11.G34.31.0039), by the Federal Target Program “Development of Scientific Potential of Higher Schools” (2012–2014, 1.1248.2011 “Nonholonomic Dynamical Systems and Control Problems”) and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (2009—2013, “Scientific-Educational Center “Regular and Chaotic Dynamics” State Contract No 02.740.11.0195). The work of A. A.Kilin was subsidized by the Presidential Grant of the Russian Federation for Support of young Candidates of Science MK-8428.2010.1.
Received: 10.03.2012
Accepted: 02.06.2012
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Language: English
Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control Chaplygin’s Sphere Using Rotors”, Regul. Chaotic Dyn., 17:3-4 (2012), 258–272
Citation in format AMSBIB
\Bibitem{BorKilMam12}
\by Alexey V.~Borisov, Alexander A.~Kilin, Ivan S.~Mamaev
\paper How to Control Chaplygin’s Sphere Using Rotors
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 3-4
\pages 258--272
\mathnet{http://mi.mathnet.ru/rcd337}
\crossref{https://doi.org/10.1134/S1560354712030045}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2956222}
\zmath{https://zbmath.org/?q=an:1264.37016}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..258B}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865571827}
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  • https://www.mathnet.ru/eng/rcd/v17/i3/p258
    • This publication is cited in the following 93 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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