Abstract:
In the paper we study the control of a balanced dynamically non-symmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic controllability is shown and the control inputs that steer the ball along a given trajectory on the plane are found. For some simple trajectories explicit tracking algorithms are proposed.
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), by the Federal Target Program “Development of Scientific Potential
of Higher Schools” (2012–2014, 1.1248.2011 “Nonholonomic Dynamical Systems and Control
Problems”) and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of
Innovative Russia” (2009—2013, “Scientific-Educational Center “Regular and Chaotic Dynamics”
State Contract No 02.740.11.0195). The work of A. A.Kilin was subsidized by the Presidential Grant
of the Russian Federation for Support of young Candidates of Science MK-8428.2010.1.
Citation:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “How to Control Chaplygin’s Sphere Using Rotors”, Regul. Chaotic Dyn., 17:3-4 (2012), 258–272
\Bibitem{BorKilMam12}
\by Alexey V.~Borisov, Alexander A.~Kilin, Ivan S.~Mamaev
\paper How to Control Chaplygin’s Sphere Using Rotors
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 3-4
\pages 258--272
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\crossref{https://doi.org/10.1134/S1560354712030045}
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Linking options:
https://www.mathnet.ru/eng/rcd337
https://www.mathnet.ru/eng/rcd/v17/i3/p258
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Alexander A. Kilin, Elena N. Pivovarova, “Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base”, Regul. Chaotic Dyn., 25:6 (2020), 729–752
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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)
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