文档介绍：The Simplest Walking Model: Stability, Complexity, and Scaling
Mariano Garcia Anindya Chatterjee Andy Ruina Michael Coleman
Department of Theoretical and Applied Mechanics
212 Kimball Hall, Cornell University
Ithaca, New York 14853
Submitted to: ASME Journal of Biomechanical Engineering
Accepted (subject to revisions): April 16, 1997
FINAL VERSION
February 10, 1998
Abstract
We demonstrate that an irreducibly simple, uncontrolled, 2D, two-link model, vaguely resembling
human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special
case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at
the hip, a point-mass at the hip, and in
nitesimal point-masses at the feet. The feet have plastic (no-slip,
no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference
(foot scu
ng) is ignored. After nondimensionalizing the governing equations, the model has only one free
parameter, the ramp slope
. This model shows stable walking modes similar to more elaborate models,
but allows some use of analytic methods to study its dynamics. The analytic calculations
nd initial
conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one
gait cycles, one of which is stable when 0 <
< rad. With increasing
, stable cycles of higher
periods appear, and the walking-like motions apparently e chaotic through a sequence of period
doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance
angle is proportional to
1/3, and that the gravitational power used is proportional to v4 where v is the
velocity along the slope.
1
1 Introduction
How much of coordination is purely mechanics? Human motion is controlled by the neuro-muscular system.
But bipedal walking, an example of a basic human motion, might be largely understood as a p