Nonuniform Coverage and Cartograms

Francois Lekien and Naomi Ehrich Leonard

Proceedings of the IEEE Conference on Decision and Control, Atlanta, GA, 2010.

This paper is a shortened version of this paper which appeared in SIAM Journal on Control and Optimization in 2009.
In this paper, we summarize our investigation of nonuniform coverage of a planar region by a network of autonomous, mobile agents. We derive centralized nonuniform coverage control laws from uniform coverage algorithms using cartograms, transformations that map nonuniform metrics to a near Euclidean metric. We also investigate time-varying coverage metrics and the design of control algorithms to cover regions with slowly varying, nonuniform metrics. Our results are applicable to the design of mobile sensor networks, notably when the coverage metric varies as data is collected such as in the case of an information metric. The results apply also to the study of animal groups foraging for food that is nonuniformly distributed and possibly changing.

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