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Regul. Chaotic Dyn., 2013, Volume 18, Issue 1-2, Pages 144–158 (Mi rcd101)  

This article is cited in 47 scientific papers (total in 47 papers)

How to Control the Chaplygin Ball Using Rotors. II

Alexey V. Borisovabc, Alexander A. Kilinbac, Ivan S. Mamaevcba

a Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles, Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia
b Institute of Mathematics and Mechanics of the Ural Branch of RAS, S. Kovalevskaja str. 16, Ekaterinburg, 620990, Russia
c A.A. Blagonravov Mechanical Engineering Research Institute of RAS, Bardina str. 4, Moscow, 117334, Russia

Abstract: In our earlier paper [3] we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.

Keywords: non-holonomic constraint, control, dry friction, viscous friction, stability, periodic solutions

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation NSh-2519.2012.1
1.1248.2011
1.7734.2013
1.7734.2013
This research was supported by the Presidential grant of leading scientific schools NSh-2519.2012.1. and Target Programmes for 2012Ц2014 (State contract 1.1248.2011, 1.7734.2013, 1.7734.2013).


DOI: https://doi.org/10.1134/S1560354713010103

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Received: 12.12.2012
Language: English

Citation: Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control the Chaplygin Ball Using Rotors. II”, Regul. Chaotic Dyn., 18:1-2 (2013), 144–158

Citation in format AMSBIB
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\by Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
\paper How to Control the Chaplygin Ball Using Rotors. II
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 1-2
\pages 144--158
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\crossref{https://doi.org/10.1134/S1560354713010103}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3040988}
\zmath{https://zbmath.org/?q=an:1303.37021}
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “The problem of drift and recurrence for the rolling chaplygin ball”, Regul. Chaotic Dyn., 18:6 (2013), 832–859  mathnet  crossref  mathscinet  zmath  scopus
    5. Mikhail Svinin, Akihiro Morinaga, Motoji Yamamoto, “On the dynamic model and motion planning for a spherical rolling robot actuated by orthogonal internal rotors”, Regul. Chaotic Dyn., 18:1-2 (2013), 126–143  mathnet  crossref  mathscinet  zmath  scopus
    6. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328  mathnet  crossref  mathscinet  zmath  scopus
    7. M. Svinin, A. Morinaga, M. Yamamoto, “On the geometric phase approach to motion planning for a spherical rolling robot in dynamic formulation”, 2013 IEEE/Rsj International Conference on Intelligent Robots and Systems (Iros), IEEE International Conference on Intelligent Robots and Systems, ed. N. Amato, IEEE, 2013, 2413–2418  isi
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    11. Tatiana B. Ivanova, Elena N. Pivovarova, “Comments on the paper by a.v. borisov, a.a. kilin, i.s. mamaev “how to control the chaplygin ball using rotors. ii””, Regul. Chaotic Dyn., 19:1 (2014), 140–143  mathnet  crossref  mathscinet  zmath  scopus
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    22. 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”, Regul. Chaotic Dyn., 20:5 (2015), 518–541  mathnet  crossref  mathscinet  zmath  isi  scopus
    23. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    24. S. Ferraro, F. Jimenez, D. Martin de Diego, “New developments on the geometric nonholonomic integrator”, Nonlinearity, 28:4 (2015), 871–900  crossref  mathscinet  zmath  isi  scopus
    25. M. Svinin, Ya. Bai, M. Yamamoto, “Dynamic model and motion planning for a pendulum-actuated spherical rolling robot”, 2015 IEEE International Conference on Robotics and Automation (Icra), IEEE International Conference on Robotics and Automation Icra, IEEE Computer Soc, 2015, 656–661  isi
    26. Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic invariants, diffusion and acceleration in rigid body dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248  mathnet  crossref  mathscinet  zmath  elib  scopus
    27. Yu. L. Karavaev, A. A. Kilin, “Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: theory and experiments”, Proc. Steklov Inst. Math., 295 (2016), 158–167  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    28. P. Alexander , Ivanov, “On final motions of a chaplygin ball on a rough plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810  mathnet  crossref  mathscinet  zmath  scopus
    29. Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev, “Control of the motion of a helical body in a fluid using rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884  mathnet  crossref  mathscinet  zmath  scopus
    30. Alexey V. Borisov, Alexey O. Kazakov, Elena N. Pivovarova, “Regular and chaotic dynamics in the rubber model of a chaplygin top”, Regul. Chaotic Dyn., 21:7-8 (2016), 885–901  mathnet  crossref  mathscinet  zmath  scopus
    31. Yury L. Karavaev, Alexander A. Kilin, Anton V. Klekovkin, “Experimental investigations of the controlled motion of a screwless underwater robot”, Regul. Chaotic Dyn., 21:7-8 (2016), 918–926  mathnet  crossref  mathscinet  zmath  scopus
    32. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral chaos in the nonholonomic model of a chaplygin top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref  mathscinet  zmath  scopus
    33. E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674  mathnet  crossref  mathscinet  zmath  elib  scopus
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    38. A. V. Borisov, E. V. Vetchanin, A. A. Kilin, “Control of the motion of a triaxial ellipsoid in a fluid using rotors”, Math. Notes, 102:4 (2017), 455–464  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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    40. E. V. Vetchanin, V. A. Tenenev, A. A. Kilin, “Optimalnoe upravlenie dvizheniem v idealnoi zhidkosti tela s vintovoi simmetriei s vnutrennimi rotorami”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 741–759  mathnet  crossref  scopus
    41. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref  mathscinet  isi  scopus
    42. E. V. Vetchanin, I. S. Mamaev, “Optimal control of the motion of a helical body in a liquid using rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411  crossref  mathscinet  zmath  isi  scopus
    43. E. V. Vetchanin, A. A. Kilin, “Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body”, J. Dyn. Control Syst., 23:2 (2017), 435–458  crossref  mathscinet  zmath  isi  scopus
    44. A. R. Chowdhury, G. S. Soh, S. H. Foong, K. L. Wood, “Experiments in second order sliding mode control of a cpg based spherical robot”, IFAC PAPERSONLINE, 50:1 (2017), 2365–2372  crossref  mathscinet  isi  scopus
    45. T. B. Ivanova, A. A. Kilin, E. N. Pivovarova, “Controlled motion of a spherical robot with feedback. i”, J. Dyn. Control Syst., 24:3 (2018), 497–510  crossref  mathscinet  zmath  isi  scopus
    46. A. R. Chowdhury, G. S. Soh, Sh. Foong, K. L. Wood, “Implementation of caterpillar inspired rolling gait and nonlinear control strategy in a spherical robot”, J. Bionic Eng., 15:2, SI (2018), 313–328  crossref  isi  scopus
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