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arXiv · 2506.19112

Analysis and experiments of the dissipative Twistcar: direction reversal and asymptotic approximations

Rom Levy·Ari Dantus·Zitao Yu·Yizhar Or
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Abstract

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. Most of the previous analyses did not account for energy dissipation due to frictional resistance. In this work, we study a theoretical two-link model of the Twistcar while incorporating dissipation due to rolling resistance. We obtain asymptotic expressions for the system's small-amplitude steady-state periodic dynamics, which 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, enabling experimental demonstration of the Twistcar's direction reversal phenomenon. We also conduct parameter fitting for the frictional resistance in order to improve agreement with experiments.

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Rom Levy, Ari Dantus, Zitao Yu, Yizhar Or. 2026-08-09. Analysis and experiments of the dissipative Twistcar: direction reversal and asymptotic approximations. https://arxiv.org/abs/2506.19112

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