The simplest walking model: Stability, complexity, and scaling
The simplest walking model: Stability, complexity, and scaling
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DOI：
10.1115/1.2798313
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发表时间：
1998-04-01
影响因子：
1.7
通讯作者：
Coleman, M
中科院分区：
文献类型：
--
作者：
Garcia, M;Chatterjee, A;Coleman, M
我们证明了一个不可约的简单的，不受控制的二维双链接模型，隐约类似于人类的腿，可以走下一个浅坡，仅由重力驱动。该模型是由McGeer（1990 a）开创的被动-动态模型中最简单的特例。它有两个刚性的无质量的腿铰接在臀部，一个点质量在臀部，和无穷小的点质量在脚。除了向前摆动时忽略几何干涉（脚擦伤）外，脚与坡面发生塑性（无滑动、无反弹）碰撞。在对控制方程进行无量纲化后，模型中只有一个自由参数：斜坡坡度γ。该模型显示了类似于更精细模型的稳定行走模式，但允许使用一些分析方法来研究IFS动力学。分析计算发现初始条件和稳定性估计周期一步态极限环。该模型表现出两个周期-一个步态周期，其中一个是稳定的，当0 <γ < 0.015拉德。随着γ的增加，出现了更高周期的稳定循环，并且类似行走的运动显然通过一系列的周期doughs而变得混沌。模型的比例定律预测步行速度与站立角度成比例，站立角度与γ（1/3）成比例，并且所使用的重力功率与上升率（4）成比例，其中上升率是沿着斜坡的速度沿着。
We demonstrate that an irreducibly simple, uncontrolled two-dimensional 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 gamma. This model shows stable walking modes similar to more elaborate models, bur allows some use of analytic methods to study ifs 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 < gamma < 0.015 rad. With increasing gamma, 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 gamma(1/3), and that the gravitational power used is proportional to upsilon(4) where upsilon is the velocity along the slope.