Topological Methods for Distributed Coverage Problems in Mobile Sensing Networks

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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.