Mechanics of Locomotion with Nonholonomic Constraints in a Fluid

该奖项支持对鱼类身体与周围流体相互作用的基础研究，以及身体运动如何传递能量和动量以实现推进力和机动性。这项研究建立在最近的结果，显示了某些类型的鱼状体的复杂动力学如何可以捕获的形式，一个相对容易处理的非完整约束，即系统的不同部分的速度之间的代数关系。这个项目将概括和扩展这一结果的后果，并澄清这类流体-结构相互作用的变量。机器人平台将被建造来实验验证理论见解。精确操纵小型水下机器人的能力有许多重要的应用，包括水下结构的检查，环境监测和水下探索。该项目的结果将导致改进具有不同形状，大小和推进机制的水上机器人的设计。鱼类机器人的自然吸引力将被用来招募代表性不足的群体进入工程领域，为本科生开发有吸引力的独立研究项目，并在本科课程中展示和激励流体力学的关键方面。该项目提供了丰富的多学科研究教育和培训环境，展示了流体力学，非线性动力学，几何力学和控制理论等学科之间的协同作用，这些学科在本科阶段很少连接。鱼状物体在水中的运动受其形状变化，涡量的产生以及物体与涡量的相互作用的控制。涡量的产生对物体的运动施加了非完整约束。该奖项支持的研究的主要目的是创建一个数学框架，可以阐明抽象形状变量和非完整约束对水中物体运动的相互作用。形状变量将采用内部质量和转子的形式。将使用离散涡近似法对涡量产生形式的约束进行建模。这种模型与新的解释旋涡脱落作为一个非完整约束非常适合理解和仿真的效率和机动性的鱼，调查步态和设计控制算法的水上机器人。将设计完全通过内部转子或移动质量推进和减速的水上机器人，并提供一个平台来验证理论结果。

This award supports fundamental research into the interactions of a fish-like body with a surrounding fluid, and the ways in which motion of the body can transfer energy and momentum for propulsion and maneuverability. The research builds upon recent results that show how the complex dynamics of certain types of fish-like bodies can be captured in the form of a relatively tractable nonholonomic constraint, that is, an algebraic relationship between the velocities of different parts of the system. This project will generalize and extend the consequences of this result, and clarify the variables that govern this class of fluid-structure interaction. Robotic platforms will be built to experimentally validate the theoretical insights. The ability to precisely maneuver small aquatic robots has many important applications, including the inspection of underwater structures, environmental monitoring, and underwater exploration. The results of this project will lead to improved design of aquatic robots with different shapes, sizes and propulsion mechanisms. The natural appeal of fish-like robots will be leveraged to recruit members of underrepresented groups into engineering, to develop attractive independent research projects for undergraduate students, and to demonstrate and motivate key aspects of fluid mechanics in undergraduate courses. The project provides a rich multidisciplinary research education and training environment, demonstrating synergy between subjects, including fluid mechanics, nonlinear dynamics, geometric mechanics, and control theory, which are rarely connected at the undergraduate level.The motion of a fish-like body in water is governed by the changes in its shape, the creation of vorticity and the interaction of the body with such vorticity. The creation of vorticity imposes a nonholonomic constraint on the motion of the body. The primary aim of the research supported by this award is to create a mathematical framework that can illuminate the interplay of abstract shape variables and nonholonomic constraints on the motion of a body in water. Shape variables will take form of internal masses and rotors. The constraints in the form of vorticity creation will be modeled using discrete vortex approximations. Such models with the novel interpretation of vortex shedding as a nonholonomic constraint are well suited to understand and emulate the efficiency and maneuverability of fish, to investigate gaits and to design control algorithms for an aquatic robot. Aquatic robots propelled and maneuvered entirely via internal rotors or moving masses will be designed and provide a platform to validate the theoretical results.