Passive dynamic walking is a model that walks down a shallow slope without any control or input. This model has been widely used to investigate how humans walk with low energy consumption and provides design principles for energy-efficient biped robots. However, the basin of attraction is very small and thin and has a fractal-like complicated shape, which makes producing stable walking difficult. In our previous study, we used the simplest walking model and investigated the fractal-like basin of attraction based on dynamical systems theory by focusing on the hybrid dynamics of the model composed of the continuous dynamics with saddle hyperbolicity and the discontinuous dynamics caused by the impact upon foot contact. We clarified that the fractal-like basin of attraction is generated through iterative stretching and bending deformations of the domain of the Poincaré map by sequential inverse images. However, whether the fractal-like basin of attraction is actually fractal, i.e.,...

中文翻译：

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被动动态行走中吸引盆的分形机制。

被动动态行走是一种在没有任何控制或输入的情况下沿着浅坡行走的模型。该模型已被广泛用于研究人类如何以低能耗行走，并为节能双足机器人提供设计原则。然而，吸引盆很小很薄，而且形状复杂，很难产生稳定的行走。在我们之前的研究中，我们使用最简单的步行模型，并通过关注由具有鞍形双曲线的连续动力学和由撞击引起的不连续动力学组成的模型的混合动力学，基于动力系统理论研究了分形吸引力盆地脚接触时。我们澄清了分形状吸引力盆地是通过连续逆图像对 Poincaré 映射域的迭代拉伸和弯曲变形产生的。然而，分形般的吸引力盆地是否真的是分形的，即...