Аннотация:We consider the motion of a vehicle with omni-wheels that moves along a horizontal plane without slipping. The mass of the rollers is non-zero and influences the dynamics of the system. The system is a multibody system of rigid bodies with non-holonomic constraints. The angular speed of the roller that enters in contact with the plane does not obligatorily satisfy the conditions of non-slipping. We propose to consider the vanishing of this slippage as a tangent inelastic impact. We get the analytic formula for the velocities after impact. It allows simulating the motion as a piecewise smooth system with switches.