研究扭动小车在摩擦下的运动反转机制，验证了几何设计可改变前进方向。
Analysis and experiments of the dissipative Twistcar: direction reversal and asymptotic approximations
- 构建带滚动摩擦的两杆动力学模型，推导小振幅稳态解
- 发现通过调整质心位置可实现运动方向反转
- 搭建机器人原型并实验验证，参数拟合提升理论与实测一致性
欠驱动轮式车辆通常被建模为具有非完整约束的非线性系统，其中扭动小车（Twistcar）是受玩具启发的经典例子。以往分析多忽略摩擦导致的能量耗散。本文建立一个包含滚动阻力的二维双杆理论模型，推导出系统小振幅稳态周期运动的渐近表达式，揭示通过调节车辆几何与质量分布可实现运动方向反转。随后，设计并构建一台可移动质心的机器人原型，通过增减重块调节质心位置，实验验证了方向反转现象。同时对摩擦阻力进行参数拟合，显著提高理论预测与实验数据的一致性。
原文摘要 · Abstract (English)
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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