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The simplest walking model: Stability, complexity, and scaling (1998)
| Venue: | ASME Journal of Biomechanical Engineering |
| Citations: | 160 - 8 self |
BibTeX
@ARTICLE{Garcia98thesimplest,
author = {Mariano Garcia and Anindya Chatterjee and Andy Ruina and Michael Coleman},
title = {The simplest walking model: Stability, complexity, and scaling},
journal = {ASME Journal of Biomechanical Engineering},
year = {1998},
volume = {120},
pages = {281--288}
}
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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 infinitesimal 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 scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope γ. 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 find 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 <γ<0.015 rad. With increasing γ, stable cycles of higher periods appear, and the walking-like motions apparently become 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 γ 1/3, and that the gravitational power used is proportional to v 4 where v is the velocity along the slope. 1 1
Keyphrases
walking model shallow slope walking-like motion stance angle free parameter special case passive-dynamic model human leg period-one gait limit cycle ramp slope stable cycle gravitational power two-link model model predict geometric interference initial condition infinitesimal point-masses period-one gait cycle stability estimate elaborate model analytic calculation period doubling forward swinging foot scuffing rigid massless leg analytic method slope surface
