Analysis and Optimal Design of Aquatic and Atmospheric Vehicles That Use Biologically Inspired Propulsion and Control Methods

生物运动指的是生物在流体中或在地形上移动的方法。对于生命科学家来说，研究生物运动可以澄清生物的生理和控制其运动的物理规律之间的关系。对于工程师来说，研究生物运动可以改进用于制造先进车辆和移动机器人的建模和设计工具。对于汽车设计师来说，一个长期的挑战是在尺寸、重量和动力之间进行基本的权衡，这是自然界以无数迷人的方式解决的一个权衡。除了非常有效地利用储存的能量外，许多生物还表现出惊人的控制力和可操作性。该奖项支持基础研究，以发现生物启发的水生和大气飞行器的几何和运动的综合优化设计的新方法。这些工程系统的民用和商业应用范围从平凡的（如不起眼的交通监控）到未来的（如水产养殖、授粉或害虫控制）。此外，在此努力下开发的建模和设计工具可用于更好地了解天然游泳者和飞行者，从而在生命科学和工程科学之间形成知识流动的良性循环。该教育计划将通过正式课程和非正式的公开教程来支持对生物运动的兴趣，这些课程将直观地展示数学的生物物理应用。几何控制和广义平均理论可以实现仿生水生和大气飞行器形态和步态的综合优化设计。这种方法需要足够通用的动力系统模型，以代表一个大的系统类别，但具有易于分析的结构。研究小组将研究欠驱动机械系统模型在生物和仿生运动中的应用，并通过与生物学中不同例子的比较来验证这些模型。然后，该团队将构建仿生运动设计优化问题的分类，并解决一系列引人注目的问题，作为可视化和教程中使用的说明性示例。研究重点将放在生物或仿生系统中控制权威的起源和性质上，这些系统通过周期性地调节其内部形状来移动。对于一类大的系统模型，可以用一阶或高阶平均理论简化非线性时间周期动力学。然后可以从定义给定系统时均动力学的对称积向量场推断出控制权限。对这些矢量场的分析揭示了形态和输入波形在决定系统整体运动中的作用。因此，在本研究计划下开发的分析和设计工具将能够优化仿生或生物运动的几何和控制参数，其中移动代理被建模为欠驱动的机械系统。

Biolocomotion refers to the methods that creatures use to move through fluids or across terrain. For life scientists, studying biolocomotion can clarify the relationship between the physiology of a creature and the physical laws that govern its movement. For engineers, studying biolocomotion can improve modeling and design tools that are used to create advanced vehicles and mobile robots. A perennial challenge for vehicle designers is the fundamental tradeoff among size, weight, and power, a tradeoff that the natural world has resolved in myriad, fascinating ways. Besides being extremely efficient in their use of stored energy, many creatures exhibit astonishing degrees of control authority and maneuverability. This award supports fundamental research to discover new methods for integrated optimal design of both the geometry and movement of biologically inspired aquatic and atmospheric vehicles. Civil and commercial applications of these engineered systems range from the mundane (such as unobtrusive traffic monitoring) to the futuristic (such as aquaculture, pollination, or pest control). Moreover, the modeling and design tools developed under this effort can be used to better understand natural swimmers and flyers, feeding a virtuous cycle of knowledge flow between the life and engineering sciences. The educational program will support interest in biolocomotion with formal courses and informal, publicly available tutorials that visually demonstrate biophysical applications of mathematics.Geometric control and generalized averaging theory can enable integrated optimal design of the morphology and gaits of biologically inspired aquatic and atmospheric vehicles. The approach requires dynamical system models that are general enough to represent a large class of systems but have a structure that is amenable to analysis. The research team will investigate the use of underactuated mechanical system models for biological and biomimetic motion, validating these models through comparisons with diverse examples from biology. The team will then construct a taxonomy of design optimization problems for biomimetic locomotion and address a selection of compelling problems as illustrative examples for use in visualizations and tutorials. The research focus will be on the origin and nature of control authority in biological or biomimetic systems that move by periodically modulating their internal shape. For a large class of system models, one may simplify the nonlinear, time-periodic dynamics using first or higher order averaging theory. Control authority may then be inferred from the symmetric product vector fields that define the given system's time-averaged dynamics. Analysis of these vector fields reveals the role that morphology and input waveforms play in determining the system's overall motion. The analysis and design tools developed under this research program will therefore enable the optimization of geometric and control parameters for biomimetic or biological motion, where the moving agent is modeled as an underactuated mechanical system.