Mechanics of Locomotion with Nonholonomic Constraints in a Fluid

该奖项支持对鱼形物体与周围流体相互作用的基础研究，以及身体运动为推进和机动性传递能量和动量的方式。这项研究建立在最近的结果基础上，这些结果表明，如何以相对容易处理的非完整约束的形式来捕获某些类型的类鱼物体的复杂动力学，即系统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结果，并阐明支配这类流体-结构相互作用的变量。将建造机器人平台，以实验验证理论见解。精确操纵小型水上机器人的能力有许多重要的应用，包括水下结构检测、环境监测和水下探测。该项目的结果将导致不同形状、大小和推进机构的水上机器人的改进设计。像鱼一样的机器人的自然吸引力将被用来招募代表不足的群体的成员进入工程学，为本科生开发有吸引力的独立研究项目，并在本科课程中演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，这些学科在本科生水平上很少联系在一起。鱼形物体在水中的运动受其形状变化、涡度的产生以及物体与涡度的相互作用的支配。涡度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建立一个数学框架，能够阐明抽象形状变量和非完整约束对物体在水中运动的相互作用。形状变量将采用内部质量和转子的形式。涡度产生形式的约束将使用离散涡旋近似来建模。这类模型将涡流脱落作为非完整约束进行了新的解释，非常适合于理解和仿真鱼类的效率和机动性，研究步态和设计水上机器人的控制算法。将设计完全通过内部转子或移动质量推进和操纵的水上机器人，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.