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转变，从学术好奇心的主题到许多工业和工程解决方案中的成熟技术。主要挑战之一是开发分析工具，以预测和控制大规模网络中出现的复杂性。这就导致了出现在理论上的挑战，在开发的工具，方法和算法的分析和设计网络的移动的dynamic agents.Intellectual Merit：一个研究计划，重点是开发的工具和方法的分布式算法的覆盖控制和验证在移动的传感网络的分析和设计。该方法是基于利用不同学科的工具，如代数拓扑，控制理论，并行和分布式计算和图论。所提出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。通过研究这种复杂的拓扑结构，人们可以推断出一个令人惊讶的丰富的信息集覆盖性能的移动的传感网络，而不使用任何几何数据和/或本地化。我们建议开发一个强大的，可扩展的动态覆盖验证机制，通过构建分布式动态系统的基础上组合拉普拉斯算子。这样的动态系统将使检测和定位的覆盖漏洞与最小的传感和本地计算，即使当传感器是移动的和网络动态变化。此外，我们建议将谱图理论扩展为单纯复形的谱理论，从而更好地理解传感器网络中覆盖方案的鲁棒性和脆弱性。这项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，这些领域需要智能体网络能够进行多用户通信，协同信息处理和分布式计算、驱动和控制。该研究计划还伴随着一个积极的教育和推广计划，包括本科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.