标题： 如何在崎岖地形上运行 显示英文标题

标题： How to run on rough terrains

摘要： 在崎岖地形上奔跑的稳定性取决于由于地面引起的扰动传播。 我们考虑矢状面内的稳定性，并将跑步的动力学建模为一个二维身体，具有交替的空中阶段和支撑阶段。 支撑阶段被建模为被动的冲击碰撞，随后是主动的冲击蹬地，以补偿碰撞损失。 这样的跑者在平坦地面上有无限多种保持周期步态的策略。 然而，这些策略在如何传播由于地形不平引起的扰动方面有所不同。 不稳定性表现为翻滚（方向不稳定）或无法保持稳定速度（平移不稳定）。 我们发现，避免感官反馈的开环策略足以在具有分段平坦表面且高度随机变化的台阶状地形上保持稳定性。 然而，这些开环跑者在坡度和高度随机变化的崎岖地形上会失去方向稳定性。 只有通过避免切向碰撞才能恢复方向稳定性。 可以通过腿后缩来避免切向碰撞，以在触地时匹配脚和地面的速度。 通过分析扰动的传播，我们推导出一个无量纲参数，该参数决定了稳定性，并指导生物和机器人跑者的的设计和控制。 显示英文摘要

摘要： Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with an alternating aerial and stance phase. Stance is modeled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope and height vary randomly. Only by avoiding tangential collisions is orientational stability recovered. Tangential collisions may be avoided through leg-retraction to match foot and ground speed at touch down. By analyzing the propagation of perturbations, we derive a single dimensionless parameter that governs stability and guides the design and control of both biological and robotic runners.