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Regul. Chaotic Dyn., 2012, Volume 17, Issue 6, Pages 559–570 (Mi rcd268)  

This article is cited in 10 scientific papers (total in 10 papers)

The Problem of Optimal Control of a Chaplygin Ball by Internal Rotors

Sergey Bolotinab

a University of Wisconsin–Madison, 480 Linkoln Dr., Madison, WI 53706-1325, USA
b V. A. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, Moscow, 119991 Russia

Abstract: We study the problem of optimal control of a Chaplygin ball on a plane by means of 3 internal rotors. Using Pontryagin maximum principle, the equations of extremals are reduced to Hamiltonian equations in group variables. For a spherically symmetric ball, the solutions can be expressed in by elliptic functions.

Keywords: nonholonomic constraint, vaconomic mechanics, optimal control, maximum principle, Hamiltonian.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This research was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for state support of scientific research conducted under the supervision of leading scientists at Russian institutions of higher professional education (Contract No11.G34.31.0039). Also supported by the Programme “Mathematical Control Theory” of RAS.


Bibliographic databases:

MSC: 37J60, 37J35, 70E18, 70F25, 70H45
Received: 04.09.2012

Citation: Sergey Bolotin, “The Problem of Optimal Control of a Chaplygin Ball by Internal Rotors”, Regul. Chaotic Dyn., 17:6 (2012), 559–570

Citation in format AMSBIB
\by Sergey Bolotin
\paper The Problem of Optimal Control of a Chaplygin Ball by Internal Rotors
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 6
\pages 559--570

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    This publication is cited in the following articles:
    1. 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
    2. Vladimir Dragović, Borislav Gajić, “Four-Dimensional Generalization of the Grioli Precession”, Regul. Chaotic Dyn., 19:6 (2014), 656–662  mathnet  crossref  mathscinet  zmath
    3. V. V. Kozlov, “Dinamika sistem s servosvyazyami. II”, Nelineinaya dinam., 11:3 (2015), 579–611  mathnet
    4. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Kang H., Liu C., Jia Ya.-B., “Inverse Dynamics and Energy Optimal Trajectories For a Wheeled Mobile Robot”, Int. J. Mech. Sci., 134 (2017), 576–588  crossref  isi  scopus
    6. Putkaradze V. Rogers S., “On the Dynamics of a Rolling Ball Actuated By Internal Point Masses”, Meccanica, 53:15 (2018), 3839–3868  crossref  mathscinet  isi  scopus
    7. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582  mathnet  crossref  mathscinet
    8. Ivan S. Mamaev, Evgeny V. Vetchanin, “Dynamics of Rubber Chaplygin Sphere under Periodic Control”, Regul. Chaotic Dyn., 25:2 (2020), 215–236  mathnet  crossref
    9. A. V. Borisov, E. A. Mikishanina, “Dynamics of the Chaplygin Ball with Variable Parameters”, Rus. J. Nonlin. Dyn., 16:3 (2020), 453–462  mathnet  crossref  mathscinet
    10. Putkaradze V. Rogers S., “on the Optimal Control of a Rolling Ball Robot Actuated By Internal Point Masses”, J. Dyn. Syst. Meas. Control-Trans. ASME, 142:5 (2020)  crossref  isi  scopus
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