On the Motion of a Symmetrical Vehicle with Omniwheels with Massive Rollers

Abstract

The dynamics of a symmetrical vehicle with omniwheels, moving along a fixed, absolutely rough horizontal plane, is considered, making the following assumptions: the mass of each roller is nonzero, there is a point contact between the rollers and the plane, and there is no slip. The equations of motion composed with the use of the Maxima symbolic computation system, contain additional terms, proportional to the axial moment of inertia of the roller and depending on angles of rotation of the wheels. The mass of the rollers is taken into account in those phases of motion when there is no change of rollers at the contact. The mass of rollers is considered to be negligible when wheels change from one roller to another. It is shown that a set of motions, existing in the inertialess model (i.e., the model that does not take into account mass of rollers), disappears, as well as its linear first integral. The main types of motion for a symmetrical three-wheeled vehicle, obtained by a numerical integration of equations of motion, are compared with results obtained on the basis of the inertialess model.