Obayashi Ippei, Aoi Shinya, Tsuchiya Kazuo, Kokubu Hiroshi
Advanced Institute for Materials Research (AIMR) , Tohoku University , 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
Department of Aeronautics and Astronautics , Graduate School of Engineering, Kyoto University , Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan.
Proc Math Phys Eng Sci. 2016 Jun;472(2190):20160028. doi: 10.1098/rspa.2016.0028.
Passive dynamic walking is a useful model for investigating the mechanical functions of the body that produce energy-efficient walking. The basin of attraction is very small and thin, and it has a fractal-like shape; this explains the difficulty in producing stable passive dynamic walking. The underlying mechanism that produces these geometric characteristics was not known. In this paper, we consider this from the viewpoint of dynamical systems theory, and we use the simplest walking model to clarify the mechanism that forms the basin of attraction for passive dynamic walking. We show that the intrinsic saddle-type hyperbolicity of the upright equilibrium point in the governing dynamics plays an important role in the geometrical characteristics of the basin of attraction; this contributes to our understanding of the stability mechanism of bipedal walking.
被动动态行走是一种用于研究产生节能行走的身体机械功能的有用模型。吸引域非常小且薄，并且具有分形状；这解释了产生稳定的被动动态行走的困难。产生这些几何特征的潜在机制尚不清楚。在本文中，我们从动力系统理论的角度考虑这一问题，并使用最简单的行走模型来阐明形成被动动态行走吸引域的机制。我们表明，主导动力学中直立平衡点的固有鞍型双曲性在吸引域的几何特征中起着重要作用；这有助于我们理解双足行走的稳定性机制。
