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

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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. Borisov^abc, Alexander A. Kilin^bac, Ivan S. Mamaev^cba

^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

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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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Comments

How to Control the Chaplygin Ball Using Rotors. II
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev
Regul. Chaotic Dyn., 2013, 18:1-2, 144–158
Comments on the Paper by A.V. Borisov, A.A. Kilin, I.S. Mamaev "How to Control the Chaplygin Ball Using Rotors. II"
Tatiana B. Ivanova, Elena N. Pivovarova
Regul. Chaotic Dyn., 2014, 19:1, 140–143

This publication is cited in the following articles:

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
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
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Problema dreifa i vozvraschaemosti pri kachenii shara chaplygina”, Nelineinaya dinam., 9:4 (2013), 721–754
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
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
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
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
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
A. A. Kilin, Yu. L. Karavaev, “Kinematicheskaya model upravleniya sferorobotom s neuravnoveshennoi omnikolesnoi platformoi”, Nelineinaya dinam., 10:4 (2014), 497–511
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
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
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
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
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
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
A. A. Kilin, E. V. Vetchanin, “Upravlenie dvizheniem tverdogo tela v zhidkosti s pomoschyu dvukh podvizhnykh mass”, Nelineinaya dinam., 11:4 (2015), 633–645
A. A. Kilin, Yu. L. Karavaev, “Eksperimentalnye issledovaniya dinamiki sfericheskogo robota kombinirovannogo tipa”, Nelineinaya dinam., 11:4 (2015), 721–734
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
P. Alexander , Ivanov, “On the control of a robot ball using two omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and control of an omniwheel vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172
V. V. Kozlov, “The dynamics of systems with servoconstraints. ii”, Regul. Chaotic Dyn., 20:4 (2015), 401–427
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
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453
S. Ferraro, F. Jimenez, D. Martin de Diego, “New developments on the geometric nonholonomic integrator”, Nonlinearity, 28:4 (2015), 871–900
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
Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic invariants, diffusion and acceleration in rigid body dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
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
P. Alexander , Ivanov, “On final motions of a chaplygin ball on a rough plane”, Regul. Chaotic Dyn., 21:7-8 (2016), 804–810
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
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
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
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
E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
V. Kozlov, “The phenomenon of reversal in the euler-poincar,-suslov nonholonomic systems”, J. Dyn. Control Syst., 22:4 (2016), 713–724
A. P. Ivanov, “The anais billiard experiment”, Dokl. Phys., 61:6 (2016), 285–287
A. P. Ivanov, N. N. Erdakova, “On a mechanical lens”, Int. J. Non-Linear Mech., 79 (2016), 115–121
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
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
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
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
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
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
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
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
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
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
F. L. Chernousko, “Locomotion of multibody robotic systems: dynamics and optimization”, Theor. Appl. Mech., 45:1 (2018), 17–33

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