When bipedal robots walk, the compliance of local contact zone and whole structure usually causes high amplitude contact force and wave propagation excited by impact. The object of this paper is to analyze the transient contact-impact behavior during the walking of compliant bipedal robots (CBR) using a completely flexible body model (CFBM) and obtain its fine contact modes. The applicability of the traditional method based on completely rigid body model (CRBM) to the compliant bipedal robots is also discussed. In CFBM, the structural deformation field and inertial field are discretized by finite element theory, and the penalty function method is adopted to account for the unilateral contact constraint. The dynamic equations, strain and stress equations for the CFBM are derived. The contact forces, impact-induced wave propagation and total mechanical energy of the CBR are calculated. The results show that the relative contact motions between the foot and the slope experience two phases: (1) macroscopic oblique impact phase (duration time is 0.1$\sim$0.2 s) and (2) rolling phase (duration time is 0.6$\sim$0.7 s). Phase 1 consists of a series of fast normal contact-separation switches and tangential stick–slip switches. Phase 2 means there are continuous normal compression and tangential stick. Since the traditional method neglects the first phase, it is not comprehensive for investigating the CBR with impact-induced waves and vibration, especially for the case of lower coefficient of friction (COF) $\mu$. In addition, a ‘dynamic self-locking’ phenomenon is found as $\mu >0.9$, which will lead to the walking unstable.

当双足机器人行走时，局部接触区和整个结构的顺应性通常会导致高振幅接触力和冲击引起的波传播。本文的目的是使用完全柔性的人体模型（CFBM）分析顺应性双足机器人（CBR）在行走过程中的瞬态接触碰撞行为，并获得其精细的接触模式。还讨论了基于完全刚体模型（CRBM）的传统方法对顺应性双足机器人的适用性。在CFBM中，通过有限元理论离散结构变形场和惯性场，并采用罚函数法解决单边接触约束。推导了CFBM的动力学方程，应变方程和应力方程。接触力 计算了CBR的冲击波传播和总机械能。结果表明，脚与斜坡之间的相对接触运动经历了两个阶段：（1）宏观倾斜冲击阶段（持续时间为0.1$〜$0.2 s）和（2）轧制阶段（持续时间为0.6$〜$0.7秒）。第1阶段包括一系列快速的法向接触分离开关和切向粘滑开关。第2阶段表示存在连续的法向压缩和切线棒。由于传统方法忽略了第一阶段，因此对于冲击波和振动研究CBR并不全面，尤其是在摩擦系数（COF）较低的情况下$\mu$。另外，发现“动态自锁”现象为$\mu >0。9$，这会导致行走不稳定。