Geodesic
The Problem of Balancing an Inverted Spherical
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 4, pp. 507-525.

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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, Poincarй equations in quasi-velocities. 
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A. S. Shaura; V. A. Tenenev; E. V. Vetchanin. The Problem of Balancing an Inverted Spherical. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 4, pp. 507-525. http://geodesic.mathdoc.fr/item/ND_2021_17_4_a10/

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