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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2012, Volume 8, Number 2, Pages 289–307 (Mi nd322)  

This article is cited in 23 scientific papers (total in 23 papers)

How to control the Chaplygin sphere using rotors

A. V. Borisov, A. A. Kilin, I. S. Mamaev

Institute of Computer Science, Udmurt State University Universitetskaya 1, Izhevsk, 426034 Russia
References:
Abstract: In the paper we study control of a balanced dynamically nonsymmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic contrability is shown and the control inputs providing motion of 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.
Received: 10.03.2012
Accepted: 02.06.2012
Document Type: Article
UDC: 532.5
Language: Russian
Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “How to control the Chaplygin sphere using rotors”, Nelin. Dinam., 8:2 (2012), 289–307
Citation in format AMSBIB
\Bibitem{BorKilMam12}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper How to control the Chaplygin sphere using rotors
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 2
\pages 289--307
\mathnet{http://mi.mathnet.ru/nd322}
Linking options:
  • https://www.mathnet.ru/eng/nd322
  • https://www.mathnet.ru/eng/nd/v8/i2/p289
    Cycle of papers
    This publication is cited in the following 23 articles:
    1. E. A. Mikishanina, “Upravlenie kacheniem dinamicheski simmetrichnogo shara po naklonnoi vraschayuscheisya ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:3 (2024), 402–414  mathnet  crossref  mathscinet
    2. E. A. Mikishanina, “Rolling motion dynamics of a spherical robot with a pendulum actuator controlled by the Bilimovich servo-constraint”, Theoret. and Math. Phys., 211:2 (2022), 679–691  mathnet  crossref  crossref  mathscinet  adsnasa
    3. E. A. Mityushov, N. E. Misyura, S. A. Berestova, “Kvaternionnaya model programmnogo upravleniya dvizheniem shara Chaplygina”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 408–421  mathnet  crossref
    4. G. P. Terekhov, V. E. Pavlovskii, “Upravlenie robotom-sharom s pomoschyu makhovikov”, Preprinty IPM im. M. V. Keldysha, 2017, 016, 31 pp.  mathnet  crossref
    5. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. P. Ivanov, “Ob upravlenii robotom-sharom pri pomoschi dvukh omnikoles”, Nelineinaya dinam., 11:2 (2015), 319–327  mathnet
    7. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, V. V. Tarasov, “Eksperimentalnoe issledovanie dvizheniya tela s osesimmetrichnym osnovaniem, skolzyaschego po sherokhovatoi ploskosti”, Nelineinaya dinam., 11:3 (2015), 547–577  mathnet
    8. V. V. Kozlov, “Dinamika sistem s servosvyazyami. II”, Nelineinaya dinam., 11:3 (2015), 579–611  mathnet
    9. A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645  mathnet
    10. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    11. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    12. A. A. Kilin, Yu. L. Karavaev, A. V. Klekovkin, “Kinematicheskaya model upravleniya vysokomanevrennym mobilnym sferorobotom s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 10:1 (2014), 113–126  mathnet
    13. T. B. Ivanova, E. N. Pivovarova, “Kommentarii k state A. V. Borisova, A. A. Kilina, I. S. Mamaeva «Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II»”, Nelineinaya dinam., 10:1 (2014), 127–132  mathnet
    14. A. A. Kilin, A. D. Bobykin, “Upravlenie telezhkoi s omnikolesami na ploskosti”, Nelineinaya dinam., 10:4 (2014), 473–481  mathnet
    15. A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511  mathnet
    16. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Kak upravlyat sharom Chaplygina pri pomoschi rotorov. II”, Nelineinaya dinam., 9:1 (2013), 59–76  mathnet
    17. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Ierarkhiya dinamiki pri kachenii tverdogo tela bez proskalzyvaniya i vercheniya po ploskosti i sfere”, Nelineinaya dinam., 9:2 (2013), 141–202  mathnet
    18. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet  crossref
    19. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    20. A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Нелинейная динамика
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