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

TL;DR

This paper analyzes a dissipative two-link Twistcar model, deriving asymptotic dynamics, demonstrating direction reversal through parameter variation, and validating findings with a robotic prototype and experimental data.

Contribution

It introduces a theoretical model incorporating frictional dissipation and experimentally verifies the direction reversal phenomenon in a robotic Twistcar.

Findings

Asymptotic expressions for steady-state dynamics derived.

Direction reversal achieved by changing geometric and mass parameters.

Experimental results confirm theoretical predictions.

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.