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Nelin. Dinam., 2012, Volume 8, Number 2, Pages 289–307 (Mi nd322)  

This article is cited in 20 scientific papers (total in 20 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

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

Full text: PDF file (379 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 532.5
MSC: 37J60 37J35 70E18 70F25 70H45
Received: 10.03.2012

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}


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    This publication is cited in the following articles:
    1. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Kachenie bez vercheniya shara po ploskosti: otsutstvie invariantnoi mery v sisteme s polnym naborom integralov”, Nelineinaya dinam., 8:3 (2012), 605–616  mathnet
    2. Alexey V. Borisov, Ivan S. Mamaev, Dmitrii V. Treschev, “Rolling of a rigid body without slipping and spinning: kinematics and dynamics”, 2, no. 2, 2013, 161–173  mathnet  crossref
    3. S. V. Bolotin, “Zadacha optimalnogo upravleniya kacheniem shara s rotorami”, Nelineinaya dinam., 8:4 (2012), 837–852  mathnet
    4. 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
    5. 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
    6. T. B. Ivanova, E. N. Pivovarova, “Dinamika i upravlenie sfericheskim robotom s osesimmetrichnym mayatnikovym privodom”, Nelineinaya dinam., 9:3 (2013), 507–520  mathnet
    7. 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
    8. 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
    9. 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
    10. 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
    11. A. A. Kilin, A. D. Bobykin, “Upravlenie telezhkoi s omnikolesami na ploskosti”, Nelineinaya dinam., 10:4 (2014), 473–481  mathnet
    12. A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511  mathnet
    13. A. P. Ivanov, “Ob upravlenii robotom-sharom pri pomoschi dvukh omnikoles”, Nelineinaya dinam., 11:2 (2015), 319–327  mathnet
    14. A. V. Borisov, Yu. L. Karavaev, I. S. Mamaev, N. N. Erdakova, T. B. Ivanova, V. V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, 20, no. 5, 2015, 518–541  mathnet  crossref  isi
    15. V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, 20, no. 4, 2015, 401–427  mathnet  crossref  isi
    16. 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
    17. A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734  mathnet
    18. 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
    19. 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
    20. G. P. Terekhov, V. E. Pavlovskii, “Upravlenie robotom-sharom s pomoschyu makhovikov”, Preprinty IPM im. M. V. Keldysha, 2017, 016, 31 pp.  mathnet  crossref
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