Collaborative Research: Geometric Mechanics for Locomoting Systems

这项工作旨在了解和发展战略，在生物和合成的移动系统的有效移动。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，以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。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，并创造复杂的合成运动，将机械系统送入危险和肮脏的环境。为了获得这种洞察力，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，以实现所需的机车能力？在这个项目中，重点将放在无肢运动，包括蛇，细长蜥蜴，细菌，精子和蠕虫。将开发用于受限空间应用的无肢运动控制器，例如在倒塌建筑物和滑坡碎片中的搜索和救援。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产生成功的运动。然而，许多先前的工作与几何工具，提供计算负担的方法来设计步态：选择参数化的基函数的步态，模拟系统的运动，然后优化输入参数，以找到步态，满足设计要求。这样的优化与正向模拟是计算昂贵的。此外，现有的几何方法忽略了真实的世界的考虑，例如身体形状和颗粒（例如，污垢）机构与环境之间的相互作用。因此，这项工作的智力价值是推进复杂系统的步态的设计和评价，通过表示复杂的形状作为曲率函数的基础，而所有沿着经验性地从生物观察中得出这些参数之间的线性关系，并在粒状介质中产生的位移。计算将需要几分钟的时间，而不是多粒子离散元法（DEM）模拟所需的几天，减轻了在真实的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.