揭示无动力轮式行走的稳定性根源，阐明能量守恒与姿态约束的关系。
Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel
- 基于运动方程线性化分析步态稳定性
- 发现能量恢复与姿态约束共同保障渐近稳定
- 适合研究步行机器人动力学的学者参考
无轮辐轮是被动动态行走的最简模型。已知仅由重力驱动的被动步态始终具有渐近稳定性和1周期特性，因其自动满足保证渐近稳定的两个必要条件：冲击姿态约束和恢复机械能约束。该稳定性可通过动能递推公式轻松证明。然而，其内在稳定性原理仍有待深入探究。本文重新考虑支撑相的稳定性，基于运动方程的线性化方法，研究稳定性与能量守恒定律之间的关系。通过数学分析，深化了对内在稳定性机制的理解。
原文摘要 · Abstract (English)
Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.
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