Criteria of Motion Without Slipping for an Omnidirectional Mobile Robot

In this paper we present a study of the dynamics of a mobile robot with omnidirectional wheels taking into account the reaction forces acting from the plane. The dynamical equations are obtained in the form of Newton –Euler equations. In the course of the study, we formulate structural restrictions on the position and orientation of the omnidirectional wheels and their rollers taking into account the possibility of implementing the omnidirectional motion. We obtain the dependence of reaction forces acting on the wheel from the supporting surface on the parameters defining the trajectory of motion: linear and angular velocities and accelerations, and the curvature of the trajectory of motion. A striking feature of the system considered is that the results obtained can be formulated in terms of elementary geometry.