Collaborative Research: Geometric Mechanics for Locomoting Systems

这一努力旨在理解和发展生物和合成运动系统中有效运动的策略。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，动物经历与周围环境相互作用的循环运动，在每个循环中获得净位移。这种步态的功效表明它们形成了机械系统运动的核心能力。理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，创造复杂的合成运动装置，将机械系统送入危险和肮脏的环境。为了获得这一见解，问题出现了：如何建模运动，并与此模型，如何评估和设计步态，以实现所需的机车性能？在这个项目中，重点将放在无肢运动动物上，包括蛇、细长的蜥蜴、细菌、精子和线虫。将开发用于密闭空间应用的无肢运动控制器，例如在倒塌的建筑物和滑坡碎片中进行搜索和救援。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，先前使用几何工具的许多工作提供了计算负担的方法来设计步态：为步态选择参数化的基函数，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。这种正演模拟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因素，如身体形状和颗粒（如污垢）之间的机制和环境的相互作用。因此，这项工作的智力价值在于通过将复杂形状表示为曲率函数的基础来推进复杂系统的步态设计和评估，同时从生物学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。计算只需几分钟，而不是多粒子离散元法（DEM）模拟所需的几天，从而减轻了在真实机械系统上进行许多实验所固有的挑战。这项工作将有助于对生物运动的新理解，并有助于在机械系统中创造生命-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.