DynSyst Special Topics: Coupled Inertial Navigation System

该项目的目标是发展群理论技术来建模、分析和制造复杂系统，特别强调由耦合振动陀螺仪组成的耦合惯性导航传感器（CINS）系统。目前的原型微机电系统陀螺仪结构紧凑，生产成本低，但其性能特点，特别是漂移速率，不能满足惯性制导系统的要求。该项目的基本原理是研究每个陀螺仪的传感模式之间同步状态存在和稳定性的条件，初步结果表明，这种状态可以通过最小化相位漂移和对干扰和其他干扰的敏感性来产生更好的鲁棒性。所采用的方法将直接利用系统的对称性：制定适当的模型；动态分析；概述了一个系统的程序，用于推导既能保持CINS系统的大规模特征，又能便于分析的简化模型；并且能够在系统制造之前预测其行为。上述研究目标将有助于推进具有陀螺仪力的复杂工程系统的设计和制造，例如导航系统、水弹性和旋转系统、单列火车和船/船。从数学的角度来看，该项目将有助于推进具有对称性的耦合机械系统的分岔领域。从教育的角度来看，该项目将直接影响未来的计算科学家，工程师和应用数学家的准备。特别是，招募和培训未被充分代表的少数民族从事科学和工程职业将通过大学的既定渠道进行，这所大学已经有40%的学生来自传统上未被充分代表的群体。外联活动包括在当地博物馆举办展览和在国家和国际会议上发表正式报告。此外，研究生将与当地海军实验室的合作者一起参加暑期实习，从事制造CINS设备的转化研究任务。

The goal of this project is to develop group-theoretical techniques to model, analyze, and fabricate complex systems, with particular emphasis in a Coupled Inertial Navigation Sensor (CINS) system made up of coupled vibratory gyroscopes. Current prototype Micro-Electro-Mechanical Systems gyroscopes are compact and inexpensive to produce but their performance characteristics, in particular drift rate, fail to meet the requirements for an inertial guidance system. The underlying principle of the project is to investigate the conditions for the existence and stability of synchronization states among the sensing modes of each of the individual gyroscopes, which preliminary results suggest that such states can produce better robustness by minimizing phase drift and susceptibility to jamming and other interferences. The approach to be used will exploit the symmetry of the system directly to: formulate appropriate models; analyze the dynamics; outline a systematic procedure for deriving reduced models that can preserve the large-scale features of a CINS system while being amenable to analysis; and be able to predict behavior before the system can be fabricated.The research objectives outline above will help advance the design and fabrication of complex engineered systems with gyroscopic forces, such as navigational systems, hydroelastic and rotating systems, mono-trains and boats/ships. From a mathematical point of view, the project will help advance the field of bifurcations of coupled mechanical systems with symmetries. From the educational point of view, the project will directly impact the preparation of future computational scientists, engineers, and applied mathematicians. In particular, recruiting and training of underrepresented minorities for careers in science and engineering will be pursued through established channels at the university, which already has a 40% population of students from traditionally underrepresented groups. Outreach activities include exhibits at a local museum and formal presentations at national and international conferences. Additionally, graduate students will participate in summer internships with collaborators from a local Navy laboratory to work on translational research tasks to fabricate the CINS device.