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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 6, Pages 888–905
DOI: https://doi.org/10.1134/S1560354723060060 (Mi rcd1240) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback

Alexander A. Kilina, Tatiana B. Ivanovab, Elena N. Pivovarovaa

a Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, 426034 Izhevsk, Russia
b Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, 426069 Izhevsk, Russia
Citations (1)
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DOI: https://doi.org/10.1134/S1560354723060060
Abstract: This paper treats the problem of a spherical robot with an axisymmetric pendulum drive rolling without slipping on a vibrating plane. The main purpose of the paper is to investigate the stabilization of the upper vertical rotations of the pendulum using feedback (additional control action). For the chosen type of feedback, regions of asymptotic stability of the upper vertical rotations of the pendulum are constructed and possible bifurcations are analyzed. Special attention is also given to the question of the stability of periodic solutions arising as the vertical rotations lose stability.
Keywords: spherical robot, vibration, feedback, stabilization, damped Mathieu equation.
Funding agency Grant number
Udmurt State University 075-02-2023-933
Ministry of Science and Higher Education of the Russian Federation FZZN-2020-0011
FEWS-2020-0009
The work of A.A.Kilin (Sections 4.3–4.5 and 5) was performed at the Ural Mathematical Center (Agreement no. 075-02-2023-933). The work of T. B. Ivanova (Sections 1 and 2) was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of Russia (FZZN-2020-0011). The work of E. N.Pivovarova (Sections 3, 4.1 and 4.2) was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of Russia (FEWS-2020-0009).
Received: 21.08.2023
Accepted: 16.11.2023
Document Type: Article
MSC: 70E18, 37J60, 70E50, 34H15, 93D15
Language: English
Citation: Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova, “Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback”, Regul. Chaotic Dyn., 28:6 (2023), 888–905
Citation in format AMSBIB
\Bibitem{KilIvaPiv23}
\by Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova
\paper Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 6
\pages 888--905
\mathnet{http://mi.mathnet.ru/rcd1240}
\crossref{https://doi.org/10.1134/S1560354723060060}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:23
     
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