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This article is cited in 51 scientific papers (total in 51 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 2012–2014 (State contract 1.1248.2011, 1.7734.2013, 1.7734.2013). |
DOI:
https://doi.org/10.1134/S1560354713010103
 References:
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Bibliographic databases:
  
MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Received: 12.12.2012
Accepted:16.02.2013
Language:
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.
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\issue 1-2
\pages 144--158
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http://mi.mathnet.ru/eng/rcd101 http://mi.mathnet.ru/eng/rcd/v18/i1/p144
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Comments
This publication is cited in the following articles:
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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
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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
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A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara Chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754
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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
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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
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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
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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), ed. N. Amato, IEEE, 2013, 2413–2418
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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
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A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213
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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
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A. Morinaga, M. Svinin, M. Yamamoto, “A motion planning strategy for a spherical rolling robot driven by two internal rotors”, IEEE Trans. Robot., 30:4 (2014), 993–1002
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J. Lee, W. Park, “Design and path planning for a spherical rolling robot”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition (2013), v. 4a, Amer. Soc. Mechanical Engineers, 2014, V04AT04A028
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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
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E. V. Vetchanin, Yu. L. Karavaev, A. A. Kalinkin, A. V. Klekovkin, E. N. Pivovarova, “Model bezvintovogo podvodnogo robota”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 544–553
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E. N. Pivovarova, A. V. Klekovkin, “Vliyanie treniya kacheniya na upravlyaemoe dvizhenie robota-kolesa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 583–592
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A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645
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A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734
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Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152
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Alexander P. Ivanov, “On the Control of a Robot Ball Using Two Omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448
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Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172
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V. V. Kozlov, “The dynamics of systems with servoconstraints. II”, Regular and Chaotic Dinamics, 20:4 (2015), 401–427
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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
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I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453
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S. Ferraro, F. Jimenez, D. Martin de Diego, “New developments on the geometric nonholonomic integrator”, Nonlinearity, 28:4 (2015), 871–900
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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 Computer Soc., 2015, 656–661
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Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204
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Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
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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
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Alexander P. Ivanov, “On Final Motions of a Chaplygin Ball on a Rough Plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810
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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
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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
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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
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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
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E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
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V. Kozlov, “The phenomenon of reversal in the Euler–Poincaré–Suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724
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A. P. Ivanov, “The ANAIS billiard experiment”, Dokl. Phys., 61:6 (2016), 285–287
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A. P. Ivanov, N. N. Erdakova, “On a mechanical lens”, Int. J. Non-Linear Mech., 79 (2016), 115–121
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Alexander A. Kilin, Elena N. Pivovarova, “The Rolling Motion of a Truncated Ball Without Slipping and Spinning on a Plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317
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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
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A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
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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
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Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975
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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
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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
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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
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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
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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
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