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

生物移动指的是生物在流体中或在地形中移动的方法。对于生命科学家来说，研究生物运动可以澄清生物的生理学和支配其运动的物理规律之间的关系。对于工程师来说，研究生物移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。汽车设计师面临的一个长期挑战是尺寸、重量和动力之间的基本权衡，自然界已经以无数有趣的方式解决了这个权衡。除了极其高效地利用储存的能量外，许多生物还表现出惊人的控制权威和机动性。该奖项支持基础研究，以发现以生物为灵感的水上和大气交通工具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普通的(如不显眼的交通监测)到未来的(如水产养殖、授粉或病虫害防治)。此外，在这一努力下开发的建模和设计工具可以用来更好地理解自然游泳运动员和飞行运动员，从而促进生命科学和工程科学之间的知识流动的良性循环。该教育计划将通过正规课程和非正式的公开教程支持人们对生物运动的兴趣，这些课程和非正式的公开教程直观地演示了数学的生物物理应用。几何控制和广义平均理论可以实现生物启发的水上和大气交通工具的形态和步态的综合优化设计。这种方法要求动力系统模型足够通用，可以代表一大类系统，但具有易于分析的结构。研究小组将研究生物和仿生运动的欠驱动机械系统模型的使用，通过与生物学的不同例子进行比较来验证这些模型。然后，该团队将构建用于仿生运动的设计优化问题的分类，并选择一些引人注目的问题作为可视化和教程中使用的说明性例子。研究重点将放在生物或仿生系统中控制权力的起源和性质上，这些系统通过周期性地调节其内部形状来移动。对于一大类系统模型，可以使用一阶或更高阶平均理论来简化非线性的时间周期动力学。然后，可以从定义给定系统的时间平均动态的对称乘积向量场推断控制权限。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所起的作用。因此，根据该研究计划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参数和控制参数，其中运动剂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.