Computations and Analysis of Efficient Snake Locomotion

几十年来，生物学家和工程师一直在研究蛇的运动，但对蛇如何弯曲身体以有效地移动缺乏一般的定量了解。 已经描述和研究了少数典型的蛇运动（例如，侧向波动和侧旋），但是生物学和机械学上可以发生更广泛的运动。该项目将使用数学分析和模拟来研究各种蛇的运动，确定最有效地移动蛇身的运动，并了解它们如何依赖于物理参数和约束。蛇没有四肢，但仍然可以在陆地上有效地移动。该研究将开发在摩擦力和接触力存在下的蛇动力学的精确模拟。在实验中，测量真实的蛇在进行各种运动时所受的力是很困难的，因此数学模型和模拟是必不可少的。该研究将对正在进行的强大的蛇形机器人的开发产生更广泛的影响，以探索，执行检查和搜索和救援行动，并协助内部医疗程序，通常在密闭和/或危险的环境中。基本的物理原理将适用于一系列陆地生物和机器人的有效运动。该项目将包括对本科生和一名研究生进行跨学科研究培训。改进的计算和分析的二维蛇运动的目标是准确地表征最佳有效的运动，在制度的中度和小的横向摩擦，这是重要的生物学和机器人。目前对这种最佳状态知之甚少，以及为什么横向波动在这种状态下是无效的。最佳的运动将被确定的约束下，包括零时间平均的身体旋转和固定的能量消耗。最佳的运动中存在的墙壁和障碍物将计算使用惩罚力防止穿透的固体障碍物，并提供额外的摩擦相互作用。这种急剧变化的力将使用接触附近的摩擦力和障碍力的自适应求积来精确计算。被动弹性的好处，众所周知的水生生物，将研究在蛇。精确计算与地面的接触力将允许在三维空间中研究最佳的蛇形运动，考虑到克服重力所做的工作。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Snake locomotion has been studied for several decades by biologists and engineers, but a general quantitative understanding of how snakes bend their bodies to move efficiently is lacking. A small number of typical snake motions (for example, lateral undulation and sidewinding) have been described and studied, but a much wider range of motions can occur biologically and mechanically. This project will use mathematical analysis and simulations to study a wide range of snake motions, identify those that move the snake body most efficiently, and understand how they depend on physical parameters and constraints. Snakes lack limbs but can nonetheless move efficiently on land. The research will develop accurate simulations of snake dynamics in the presence of friction and contact forces. Measuring the forces on real snakes performing a wide range of movements is difficult in experiments, so mathematical models and simulations are essential. The research will have broader impacts in the ongoing development of robust snake robots to explore, perform inspections and search-and-rescue operations, and assist internal medical procedures, often in confined and/or hazardous environments. The underlying physical principles will apply to efficient locomotion by a range of terrestrial organisms and robots. The project will involve interdisciplinary research training of undergraduates and a graduate student. Improvements in computations and analysis of two-dimensional snake locomotion will aim to accurately characterize optimally efficient motions in the regimes of moderate and small transverse friction, which are important biologically and for robotics. Little is known about such optima at present, and why transverse undulation is ineffective in this regime. Optimal motions will be identified under constraints including zero time-averaged body rotation and fixed energy consumption. Optimal motions in the presence of walls and obstacles will be computed using penalty forces preventing penetration of the solid barriers and giving additional frictional interactions. Such sharply varying forces will be computed accurately using adaptive quadrature of frictional and barrier forces in the vicinity of contact. The benefits of passive elasticity, well known for aquatic organisms, will be studied in snakes. Accurate computations of contact forces with the ground will allow for the study of optimal snake motions in three dimensions, accounting for the work done against gravity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.