title: Formation mechanism of a basin of attraction for passive dynamic walking induced by intrinsic hyperbolicity.
abstract: 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.
authors.affiliation: Advanced Institute for Materials Research (AIMR) , Tohoku University , 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
authors.forename: Ippei
authors.identifier: 0000-0002-7207-7280
authors.initials: I
authors.lastname: Obayashi
authors.affiliation: Department of Aeronautics and Astronautics , Graduate School of Engineering, Kyoto University , Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan.
authors.forename: Shinya
authors.initials: S
authors.lastname: Aoi
authors.affiliation: Department of Aeronautics and Astronautics , Graduate School of Engineering, Kyoto University , Kyoto daigaku-Katsura, Nishikyo-ku, Kyoto 615-8540, Japan.
authors.forename: Kazuo
authors.initials: K
authors.lastname: Tsuchiya
authors.affiliation: Department of Mathematics , Graduate School of Science, Kyoto University , Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kokubu
keywords: bipedal walking; saddle; simplest walking model; stable/unstable manifolds; theory of dynamical systems