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

2025-06-23

AI Summary

This study investigates the direction-reversal mechanism in a nonholonomic two-wheel steered vehicle (Twistcar) model incorporating rolling friction dissipation. Method: A two-link dynamical model with energy dissipation is formulated; asymptotic analysis combined with parameter-fitted rolling resistance modeling enables theoretical analysis under small-amplitude periodic actuation. A reconfigurable robotic prototype with adjustable center-of-mass is designed for experimental validation. Contribution/Results: For the first time, direction reversal is theoretically demonstrated under dissipative conditions, and asymptotic analytical expressions for the steady-state periodic response are derived. Experiments confirm that geometric and inertial parameters—particularly center-of-mass position—actively regulate locomotion direction. Crucially, system behavior diverges markedly from conservative (dissipation-free) models, and quantitative agreement between theory and experiment is achieved. This work overcomes the restrictive dissipation-free assumption, establishing a new paradigm for motion control in nonholonomic dissipative systems.

Technology Category

Intelligent Robots: Motion and Path PlanningComputer Vision: Motion & TrackingCognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

Responsible Web: Machine-in-the-loop, human agency and autonomySystems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environmentsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 friction. 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 demonstration of the Twistcar's direction reversal phenomenon. We also conduct parameter fitting for the frictional resistance in order to improve agreement with experiments.

Problem

• Studying direction reversal in underactuated wheeled vehicles with friction
• Developing asymptotic approximations for small-amplitude periodic dynamics
• Designing a robotic prototype to demonstrate motion reversal

Innovation

• Incorporates rolling resistance in two-link model
• Demonstrates direction reversal via mass adjustment
• Fits frictional parameters for experimental accuracy