中文摘要：

在双足机器人沿小斜坡向下被动行走的问题中，考虑了双足和刚性双腿的质量对运动状态的影响。根据第二类拉格朗日方程，建立了行走的动力学模型。通过数值仿真得到系统的Lyapunov指数和Poincare映射图。比较发现：如果不考虑双足和刚性双腿的质量，模型可以稳定行走的斜面倾斜角范围最大；考虑了双足和双腿的质量，模型可以稳定行走的斜面倾斜角范围变小；在同样倾斜角的斜面上，模型的运动状态可随着双足和双腿质量的增加而由周期变成混沌，最后变成不能稳定行走。

英文摘要：

The influence of the mass of two feet and two rigid legs on motion state is considered in a passive-walking of a biped robot. The dynamic model of the system is established according to Lagrange method. The Lyapunov exponents and Poincare maps are obtained according to simulating calculations. Compared with those original results, it is shown that the model can walk in a large ramp slope if the mass of feet and legs are ignored. At the same ramp slope, the state of motion changes from period to chaos and finally to unstable walking with the increase of the mass of feet and legs.