Computations and Analysis of Efficient Snake Locomotion

生物学家和工程师对蛇的运动进行了几十年的研究，但对蛇如何弯曲身体以有效移动的总体定量理解尚缺乏。少数典型的蛇运动（例如，横向波动和侧绕）已经被描述和研究，但更广泛的运动可以发生在生物学和机械上。该项目将使用数学分析和模拟来研究蛇的各种运动，确定那些最有效地移动蛇体的运动，并了解它们如何依赖于物理参数和约束。蛇虽然没有四肢，但却能在陆地上高效地移动。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，测量真正的蛇进行大范围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。这项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，这些机器人通常在受限和/或危险的环境中进行探索、执行检查和搜救行动，并协助内部医疗程序。潜在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。该项目将包括本科生和一名研究生的跨学科研究培训。二维蛇运动的计算和分析的改进将旨在准确地描述中等和小横向摩擦状态下的最佳有效运动，这在生物学和机器人技术中是重要的。目前对这种最佳状态知之甚少，也不知道为什么横向波动在这种状态下是无效的。在时间平均为零的身体旋转和固定的能量消耗约束下，确定最优运动。在存在墙壁和障碍物的情况下，将使用惩罚力来计算最佳运动，以防止穿透固体障碍物并给予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阻力的自适应正交来精确计算。被动弹性的好处，众所周知的水生生物，将研究蛇。与地面接触力的精确计算将允许在三维空间中研究蛇的最佳运动，考虑到对重力所做的功。该奖项反映了美国国家科学基金会的法定使命，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.