Topological Methods for Distributed Coverage Problems in Mobile Sensing Networks

传感器网络领域正在经历一场革命性的变革，从一个学术好奇的主题转变为许多工业和工程解决方案中的成熟使能技术。主要挑战之一是开发用于预测和控制大规模网络中出现的复杂性的分析工具。这导致了移动动态代理网络分析和设计的工具、方法和算法的开发中出现了理论挑战。智能优势：提出了一项专注于开发用于移动感知网络覆盖控制和验证的分布式算法分析和设计的工具和方法的研究计划。该方法基于不同学科的工具，如代数拓扑学、控制论、并行和分布式计算以及图论。提议的活动的主要论点是使用单纯复形而不是图作为主要的建模抽象。通过研究这种复合体的拓扑结构，人们可以在不使用任何几何数据和/或定位的情况下推断出关于移动感知网络覆盖特性的丰富信息集。通过构造基于组合拉普拉斯算子的分布式动态系统，我们提出了一种健壮的、可扩展的动态覆盖验证机制。这样的动态系统将能够以最小的感知和局部计算来检测和定位覆盖空洞，即使在传感器是移动的并且网络动态变化的情况下也是如此。此外，我们建议将谱图理论扩展到单纯复形的谱理论，从而更好地理解传感器网络覆盖方案的健壮性和脆弱性。广泛影响：该研究将影响动态传感网络在国土安全、国防、交通、无线通信、环境监测等领域的新兴应用，这些应用要求代理网络能够进行多用户通信、协作信息处理以及分布式计算、驱动和控制。研究计划还伴随着一项积极的教育和推广计划，包括本科生和研究生水平的课程和课程开发。

The field of sensor networks is undergoing a revolutionary transformation from a subject of academic curiosity to a mature enabling technology in many industrial and engineering solutions. One of the main challenges is in the development of analytical tools for predicting and controlling the complexities arising in large-scale networks. This has resulted in the emergence of theoretical challenges in the development of tools, methods, and algorithms for analysis and design of networks of mobile dynamic agents.Intellectual Merit:A research plan focused on development of tools and methods for analysis and design of distributed algorithms for coverage control and verification in mobile sensing networks is proposed. The approach is based on utilizing tools from diverse disciplines such as algebraic topology, control theory, parallel and distributed computation and graph theory. The main thesis of the proposed activity is the use of simplicial complexes instead of graphs as the main modeling abstraction. By studying the topology of such complexes, one can infer a surprisingly rich set of information about coverage properties of mobile sensing networks without the use of any geometrical data and or localization. We propose to develop a robust, scalable mechanism for dynamic coverage verification by constructing distributed dynamical systems based on combinatorial Laplacians. Such dynamical systems will enable detection and localization of coverage holes with minimal sensing and local computation, even when the sensors are mobile and the network changes dynamically. Furthermore, we propose to expand spectral graph theory to a spectral theory of simplicial complexes, resulting in a better understanding of robustness and fragilities of coverage schemes in sensor networks.Broader Impact: The research will impact emerging applications of dynamic sensing networks in homeland security, defense, transportation, wireless communication, environmental monitoring, which require networks of agents to be capable of multi-user communication, collaborative information processing, and distributed computation, actuation, and control. The research plan is also accompanied by an active education and outreach plan consisting of undergraduate and graduate level curriculum and course development.