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ЖУРНАЛЫ // Russian Journal of Nonlinear Dynamics // Архив

Rus. J. Nonlin. Dyn., 2021, том 17, номер 4, страницы 507–525 (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

Аннотация: 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.

Ключевые слова: balancing of an inverted pendulum, omnidirectional platform, hybrid genetic algorithm, Poincarй equations in quasi-velocities.

MSC: 70Q05, 70Exx, 49M37, 49K15

Поступила в редакцию: 18.11.2021
Принята в печать: 15.12.2021

Язык публикации: английский

DOI: 10.20537/nd210411



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