Common formation mechanism of basin of attraction for bipedal walking models by saddle hyperbolicity and hybrid dynamics

Ippei Obayashi, Shinya Aoi, Kazuo Tsuchiya, Hiroshi Kokubu

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we investigate the mathematical structures and mechanisms of bipedal walking from a dynamical viewpoint. Especially, we focus on the basin of attraction since it determines the stability of bipedal walking. We treat two similar but different bipedal walking models (passive and active dynamic walking models) and examine common mathematical structure between these models. We find that the saddle hyperbolicity and hybrid system play important roles for the shape of the basin of attraction in both models, which are quite common for more general bipedal models and important for understanding the stability mechanism of bipedal walking.

Original languageEnglish
Pages (from-to)315-332
Number of pages18
JournalJapan Journal of Industrial and Applied Mathematics
Volume32
Issue number2
DOIs
Publication statusPublished - 2015 Jul 28

Keywords

  • Basin of attraction
  • Bipedal walking
  • Dynamical system
  • Hybrid system
  • Hyperbolicity

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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