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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ND_2021_17_4_a10,
     author = {A. S. Shaura and V. A. Tenenev and E. V. Vetchanin},
     title = {The {Problem} of {Balancing} an {Inverted} {Spherical}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {507--525},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_4_a10/}
}
TY  - JOUR
AU  - A. S. Shaura
AU  - V. A. Tenenev
AU  - E. V. Vetchanin
TI  - The Problem of Balancing an Inverted Spherical
JO  - Russian journal of nonlinear dynamics
PY  - 2021
SP  - 507
EP  - 525
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2021_17_4_a10/
LA  - en
ID  - ND_2021_17_4_a10
ER  - 
%0 Journal Article
%A A. S. Shaura
%A V. A. Tenenev
%A E. V. Vetchanin
%T The Problem of Balancing an Inverted Spherical
%J Russian journal of nonlinear dynamics
%D 2021
%P 507-525
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2021_17_4_a10/
%G en
%F ND_2021_17_4_a10
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/