Formation Mechanism of a Basin of Attraction for Passive Dynamic Walking   Induced by Intrinsic Hyperbolicity
  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. 
Ippei Obayashi, Shinya Aoi, Kazuo Tsuchiya, Hiroshi Kokubu
math.DS math-ph math.MP