Nonuniform Coverage and Cartograms

Francois Lekien and Naomi Ehrich Leonard

SIAM J. Control and Optimization, Special issue on "Control and Optimization in Cooperative Networks," Vol. 48, No. 1, 351-372, 2009.
In this paper, we investigate 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.
See the following links for animations and follow-up results:
Animations
Cartograms for Belgian Election

(Paper 1.6 MB, pdf)
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