  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.
