Collaborative Research: Geometric Mechanics for Locomoting Systems

这项工作旨在了解和制定在生物和合成运动系统中有效移动的战略。步态是动物运动的一个基本方面；例如马的行走、鱼的划水和蛇的滑行。在这些运动中，动物经历了与周围环境相互作用的循环运动，以在每个循环中获得净位移。这种步态的有效性表明，它们形成了机械系统运动的核心能力。了解基于步态的运动原理提供了两个机会：深入了解生物过程和创造复杂的合成运动器，将机械系统送到危险和肮脏的环境中。为了获得这一认识，出现了一些问题：如何对运动进行建模，以及如何使用该模型来评估和设计步态以实现所需的机车性能？在这个项目中，重点将放在无腿运动器上，包括蛇、细长蜥蜴、细菌、精子和线虫。将开发用于有限空间应用的无腿运动控制器，如在倒塌的建筑和山体滑坡瓦砾中进行搜索和救援。研究人员的初步工作表明，几何力学可以直观地理解步态如何以及为什么会产生成功的运动。然而，以前的许多几何工具都提供了计算繁琐的步态设计方法：为步态选择参数化基函数，模拟系统的运动，然后优化输入参数以找到满足设计要求的步态。这种用正向模拟进行的优化在计算上是昂贵的。此外，现有的几何方法忽略了现实世界的考虑，如机构和环境之间的身体形状和颗粒状(例如，污垢)相互作用。因此，这项工作的智力价值是通过将复杂形状表示为曲率函数的基础来推进复杂系统步态的设计和评估，同时一直从生物观察中经验地推导出这些参数与颗粒介质中产生的位移之间的线性关系。然后，计算将花费几分钟而不是多粒子离散元方法(DEM)模拟所需的几天，从而减轻了在真实机械系统上执行许多实验所固有的挑战。这项工作将有助于对生物运动机的新理解，并有助于在机械系统中创造生命运动。

This effort seeks to understand and develop strategies for effective movement in biological and synthetic locomoting systems. Gaits are a fundamental aspect of animal locomotion; examples include a horse's walking, a fish's strokes, and a snake's slithering. In these motions, the animals undergo cyclic motions which interact with the surrounding environment to gain a net displacement over each cycle. The efficacy of such gaits suggests they form a core capability in locomotion of mechanical systems. Understanding the principles of gait-based locomotion offers two opportunities: to gain deep insight into biological processes and to create sophisticated synthetic locomotors to send mechanical systems into dangerous and dirty environments. To gain this insight, questions arise: how to model locomotion, and with this model, how to both evaluate and design gaits to achieve desired locomotive capabilities? In this project, the focus will be on limbless locomotors, including snakes, slender lizards, bacteria, spermatozoa and nematode worms. Limbless locomotor controllers for confined space applications, such as search and rescue in collapsed buildings and landslide debris, will be developed.The investigators' preliminary work reveals that geometric mechanics allows intuitive understanding of how and why gaits, produce successful locomotion. Much of the prior work with geometric tools, however, provided computationally burdensome approaches to design gaits: choose parameterized basis functions for gaits, simulate the motion of the system and then optimize the input parameters to find gaits that meet the design requirements. Such optimization with forward simulation is computationally expensive. Moreover, existing geometric approaches ignore real world considerations such as body-shape and granular (e.g., dirt) interaction between the mechanism and the environment. Therefore, the intellectual merit of this work is to advance the design and evaluation of gaits for complex systems by representing complex shapes as a basis of curvature functions, while all along empirically deriving from biological observation linear relationships between these parameters and the resulting displacement in granular media. Calculations will then take minutes rather than the days needed for multi-particle discrete element method (DEM) simulation, mitigating the challenges inherent in performing many experiments on real mechanical systems. This work will contribute to a new understanding of biological locomotors as well as help create life-life locomotion in mechanical systems.