Analysis and Experiments of the Dissipative Twistcar - Direction Reversal and Asymptotic Approximations

Underactuated wheeled vehicles are commonly studied as nonholonomic systems with periodic actuation. Twistcar is a classical example inspired by a riding toy, which has been analyzed using a planar model of a dynamical system with nonholonomic constraints. In this work, we study a theoretical two-link model of the Twistcar with rolling dissipation, and obtain asymptotic expressions for its small-amplitude steady-state periodic dynamics. The analysis reveals the possibility of reversing the direction of motion upon varying the geometric and mass properties of the vehicle. Next, we design and construct a robotic prototype of the Twistcar whose center-of-mass position can be shifted by adding and removing a massive block. This robot enables experimental demonstration of the Twistcar’s direction reversal phenomenon. We also consider models with wheels’ skidding dissipation, and conduct parameter fitting for the frictional resistances in order to improve agreement with experiments.