Stability of the rectilinear motion of an omni vehicle with consideration of wheel roller inertia.

*(English. Russian original)*Zbl 1423.70022
Mosc. Univ. Mech. Bull. 73, No. 6, 145-148 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 6, 78-82 (2018).

Summary: The dynamics of a mobile vehicle with three omni wheels is considered for the case when the vehicle moves on a fixed perfectly rough plane by inertia. In order to study the effect of wheel roller inertia on the stability of the rectilinear motion of the vehicle, the fore wheel is modeled by the following rigid bodies: a wheel disk and a supporting roller such that the roller does not slip with respect to the plane. The rear wheels are modeled by disks slipping without friction in the direction perpendicular to their planes (an inertialess model of an omni wheel). We propose some dynamic equations of motion of the vehicle in the form of Tatarinov’s laconic equations for systems with differential constraints. These equations are related to the dynamic equations obtained for a vehicle with three inertialess omni wheels. The stability of rectilinear motions is analyzed.

##### MSC:

70E18 | Motion of a rigid body in contact with a solid surface |

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\textit{G. N. Moiseev} and \textit{A. A. Zobova}, Mosc. Univ. Mech. Bull. 73, No. 6, 145--148 (2018; Zbl 1423.70022); translation from Vestn. Mosk. Univ., Ser. I 73, No. 6, 78--82 (2018)

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##### References:

[1] | Martynenko, Yu. G.; Formalâ€™skii, A. M., On the Motion of a Mobile Robot with Roller-Carrying Wheels, Izv. Akad. Nauk SSSR, Teor. Sist. Upravl., 6, 142-149, (2007) · Zbl 1294.93060 |

[2] | Zobova, A. A.; Tatarinov, Ya. V., The Dynamics of an Omni-Mobile Vehicle, Prikl. Mat. Mekh, 73, 13-22, (2009) · Zbl 1189.70020 |

[3] | Kosenko, I. I.; Gerasimov, K. V., Physically Oriented Simulation of the Omnivehicle Dynamics, Nelin. Dinam, 12, 251-262, (2016) · Zbl 1372.70021 |

[4] | Ya. V. Tatarinov, Classical Mechanics Equations in Laconic Forms (Mosk. Gos. Univ., Moscow, 2005) [in Russian]. |

[5] | I. G. Malkin, Theory of Stability of Motion (Nauka, Moscow, 1996) [in Russian]. |

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