双足模型步行中的倍周期步态和混沌步态现象

被动行走模型只依赖重力可以在斜坡上形成自然的周期步态.当模型参数改变时，步态随之改变.应用胞映射方法与Newton-Raphson迭代结合来获取被动行走模型周期步态的不动点，消除了迭代方法在初值选取上的随机性，并获得了模型的吸引盆.通过对不同参数的模型的仿真，讨论了参数变化对步态的影响.结果表明，转动惯量增大会导致倍周期步态到混沌步态的产生，足半径减小和质心位置降低也会导致分岔的出现. 关键词： 胞映射 双足步行 倍周期 混沌

Period-doubling gait and chaotic gait of biped walking model

Passive walking model can exhibit natural gait on a slope， depending only on the gravity. The gait changes with the changing of parameters. The fixed point of the periodical gait can be obtained by the combination of cell mapping method and Newton-Raphson iteration. By the aid of cell mapping method，periodical cells can be used as the initial value of iteration，and the basins of attraction can be obtained. Simulations of models with different parameters show that the increasing of moment of inertia will result in the appearance of period-doubling and chaotic gaits. The same effect can be obtained by the decreasing of foot radius or position of center of mass.