Theoretical and experimental investigations of the controlled motion of the Roller Racer

In this paper we address the problem of the motion of the Roller Racer. We assume that the angle φ(t) between the platforms is a prescribed function of time and that the no-slip condition (nonholonomic constraint) and viscous friction force act at the points of contact of the wheels. In this case, all trajectories of the reduced system asymptotically tend to a periodic solution. In this paper it is shown analytically and experimentally that the chosen control defines periodic trajectories of the attachment point of the platforms on an average along a straight line. We determine the conditions for optimal control when the system moves along a straight line depending on the mass and geometric characteristics of the system and control parameters.