Fractal mechanism of basin of attraction in passive dynamic walking.

Abstract:

: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., whether infinitely many self-similar patterns are embedded in the basin of attraction, is dependent on the slope angle, and the mechanism remains unclear. In the present study, we improved our previous analysis in order to clarify this mechanism. In particular, we newly focused on the range of the Poincaré map and specified the regions that are stretched and bent by the sequential inverse images of the Poincaré map. Through the analysis of the specified regions, we clarified the conditions and mechanism required for the basin of attraction to be fractal.

journal_name

Bioinspir Biomim

authors

Okamoto K,Aoi S,Obayashi I,Kokubu H,Senda K,Tsuchiya K

doi

10.1088/1748-3190/ab9283

subject

Has Abstract

pub_date

2020-07-15 00:00:00

pages

055002

issue

5

eissn

1748-3182

issn

1748-3190

journal_volume

15

pub_type

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