Robotics: Science and Systems III

Dynamic Coverage Verification in Mobile Sensor Networks Via Switched Higher Order Laplacians

Abubakr Muhammad and Ali Jadbabaie

Abstract: In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on time-evolving simplicial complexes. The simplicial complexes model the connectivity of agents in the network, whereas the homology groups of the simplicial complexes lets one infer about the coverage properties of the network. Our main result states that the asymptotic stability of the switched linear system implies that every point of the domain covered by the mobile sensor nodes is visited infinitely often. The enabling mathematical technique for this result is the theory of higher order Laplacian operators, which is a generalization of the graph Laplacian used in consensus problems.

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Bibtex:

@INPROCEEDINGS{ Muhammad-RSS-07,
    AUTHOR    = {A. Muhammad and A. Jadbabaie},
    TITLE     = {Dynamic Coverage Verification in Mobile Sensor Networks Via Switched Higher Order Laplacians},
    BOOKTITLE = {Proceedings of Robotics: Science and Systems},
    YEAR      = {2007},
    ADDRESS   = {Atlanta, GA, USA},
    MONTH     = {June},
    DOI       = {10.15607/RSS.2007.III.039} 
}