Snakes can traverse almost all types of environments by bending their elongate bodies in 3-D to interact with the terrain. Similarly, a snake robot is a promising platform to perform critical tasks in various environments. Understanding how 3-D body bending effectively interacts with the terrain for propulsion and stability can not only inform how snakes traverse natural environments, but also allow snake robots to achieve similar performance. How snakes and snake robots move on flat surfaces has been understood well. However, such ideal terrain is rare in natural environments and little was understood about how to generate propulsion and maintain stability in 3-D terrain, except for some studies on arboreal snake locomotion and on robots using geometric planning. To bridge the knowledge gap, we integrated animal experiments and robotic studies in three representative environments: a large smooth step, an uneven arena of blocks of large height variation, and large bumps. We discovered that vertical body bending induces stability challenges but can generate large propulsion. When traversing a large smooth step, a snake robot is challenged by roll instability that increases with the amplitude of vertical bending. The instability can be reduced by body compliance that statistically improves body-terrain contact. Despite this, vertical body bending can potentially allow snakes to push against terrain for propulsion, as demonstrated by corn snakes traversing an uneven arena. A snake robot can generate large propulsion like this if contact is well maintained. Contact feedback control can help accommodate perturbations such as novel terrain geometry or excessive external forces by improving contact. Our findings provide insights into how snakes and snake robots can use vertical body bending for efficient and versatile traversal of the 3-D world stably.

翻译：蛇类通过三维空间中的身体弯曲与地形交互，几乎能够穿越所有类型的环境。同样地，蛇形机器人也是在各类环境中执行关键任务的有前景的平台。理解三维身体弯曲如何有效与地形相互作用以实现推进和稳定性，不仅能揭示蛇类在自然环境中穿行的机制，还能使蛇形机器人达到类似的性能。目前，蛇类和蛇形机器人在平坦表面上的运动已得到充分理解。然而，此类理想地形在自然环境中极为罕见，除了一些关于树栖蛇类运动和基于几何规划的机器人研究外，对于如何在三维地形中产生推进力并保持稳定性知之甚少。为填补这一知识空白，我们整合了动物实验和机器人研究，在三种代表性环境中进行探索：大型光滑台阶、石块高度变化大的不平整场地以及大型凸起地形。我们发现，纵向身体弯曲会引发稳定性挑战，但能产生较大的推进力。当穿越大型光滑台阶时，蛇形机器人面临滚转不稳定性问题，且该不稳定性随纵向弯曲幅度增大而加剧。通过身体柔顺性可以降低不稳定性，这种柔顺性在统计上能改善身体与地形的接触。尽管如此，纵向身体弯曲可能使蛇类能够通过推抵地形产生推进力——这一点在穿越不平整场地的玉米蛇实验中得到了证实。若接触得以良好维持，蛇形机器人也能产生类似的巨大推进力。接触反馈控制可通过改善接触来适应新型地形几何结构或过强外力等扰动。我们的研究揭示了蛇类和蛇形机器人如何利用纵向身体弯曲在三维世界中实现稳定、高效且多功能的穿越。