Motion planning for the roller racer with a sticking/slipping switching model

Abstract — The roller racer, an undulatory locomotion system, is a toy which can be propelled forward by sitting on it and only oscillating the steering handle. A nonholonomic dynamic model and controllability analysis of the roller racer was first published by Krishnaprasad and Tsakiris in 1998. The model is derived from the usual assumption that all the wheels obey sticking (non-slipping) constraints, i.e., rolling without slipping. Controllability analysis shows that under these assumptions, the roller racer cannot be stopped once started. Yet physical prototypes do not exhibit this characteristic. In this paper, a high-fidelity model of the roller racer is presented by considering the finite static friction between the wheels and the ground, i.e., slipping will occur when constraint force exceeds the maximal allowable frictional force. It is proved that the system could be stopped from any state with only the steering angle control. Furthermore, based on group symmetry and motion primitives, a planner is designed to achieve motions between any two given positions and orientations with zero velocities. Experiments also show that front wheel slipping stops the system faster than joint frictions. I