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Russian Journal of Nonlinear Dynamics, 2021, Volume 17, Number 4, Pages 507–525
DOI: https://doi.org/10.20537/nd210411
(Mi nd774)
 

Nonlinear engineering and robotics

The Problem of Balancing an Inverted Spherical Pendulum on an Omniwheel Platform

A. S. Shauraa, V. A. Teneneva, E. V. Vetchaninb

a Udmurt Federal Research Center UB RAS, ul. Tatiany Baramzinoi 34, Izhevsk, 426067 Russia
b Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
References:
Abstract: This paper addresses the problem of balancing an inverted pendulum on an omnidirectional platform in a three-dimensional setting. Equations of motion of the platform – pendulum system in quasi-velocities are constructed. To solve the problem of balancing the pendulum by controlling the motion of the platform, a hybrid genetic algorithm is used. The behavior of the system is investigated under different initial conditions taking into account a necessary stop of the platform or the need for continuation of the motion at the end point of the trajectory. It is shown that the solution of the problem in a two-dimensional setting is a particular case of three-dimensional balancing.
Keywords: balancing of an inverted pendulum, omnidirectional platform, hybrid genetic algorithm, Poincaré equations in quasi-velocities.
Funding agency Grant number
Russian Science Foundation 21-71-10039
Ministry of Science and Higher Education of the Russian Federation AAAA-A19-119092690104-4
This work was performed as part of the research project of the Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences “Artificial Intelligence in the Development, Training, and Support of Expert Systems for Presentation and Use of Knowledge in Natural, Engineering, and Socio-Humanitarian Sciences” AAAA-A19-119092690104-4. The work of E.V.Vetchanin (Section 1) is supported by the Russian Science Foundation (project no. 21-71-10039).
Received: 18.11.2021
Accepted: 15.12.2021
Bibliographic databases:
Document Type: Article
Language: english
Citation: A. S. Shaura, V. A. Tenenev, E. V. Vetchanin, “The Problem of Balancing an Inverted Spherical Pendulum on an Omniwheel Platform”, Rus. J. Nonlin. Dyn., 17:4 (2021), 507–525
Citation in format AMSBIB
\Bibitem{ShaTenVet21}
\by A. S. Shaura, V. A. Tenenev, E. V. Vetchanin
\paper The Problem of Balancing an Inverted Spherical
Pendulum on an Omniwheel Platform
\jour Rus. J. Nonlin. Dyn.
\yr 2021
\vol 17
\issue 4
\pages 507--525
\mathnet{http://mi.mathnet.ru/nd774}
\crossref{https://doi.org/10.20537/nd210411}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85123513907}
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