Template models are frequently used to simplify the control dynamics for robot hopping or running. Passive limit cycles can emerge for such systems and be exploited for energy-efficient control. A grand challenge in locomotion is trunk stabilization when the hip is offset from the center of mass (CoM). The swing phase plays a major role in this process due to the moment of inertia of the leg; however, many template models ignore the leg mass. In this work, the authors consider a robot hopper model (RHM) with a rigid trunk and leg plus a hip that is displaced from the CoM. It has been previously shown that no passive limit cycle exists for such a model given a linear hip spring. In this work, we show that passive limit cycles can be found when a nonlinear hip spring is used instead. To the authors' knowledge, this is the first time that a passive limit cycle has been found for this type of system.

翻译：模板模型常用于简化机器人跳跃或跑步的控制动态。此类系统可能出现被动极限环，并可被利用以实现节能控制。运动控制中的一个重大挑战是当髋关节偏移质心时的躯干稳定问题。由于腿部转动惯量的存在，摆动相在此过程中起主要作用；然而，许多模板模型忽略了腿部质量。本工作中，作者考虑了一种具有刚性躯干和腿部以及偏离质心髋关节的机器人跳跃模型（RHM）。先前研究表明，在具有线性髋关节弹簧的情况下，此类模型不存在被动极限环。在本工作中，我们证明当采用非线性髋关节弹簧时，可以找到被动极限环。据作者所知，这是首次在此类系统中发现被动极限环。