  This paper presents an algorithm for a team of mobile robots to
simultaneously learn a spatial field over a domain and spatially distribute
themselves to optimally cover it. Drawing from previous approaches that
estimate the spatial field through a centralized Gaussian process, this work
leverages the spatial structure of the coverage problem and presents a
decentralized strategy where samples are aggregated locally by establishing
communications through the boundaries of a Voronoi partition. We present an
algorithm whereby each robot runs a local Gaussian process calculated from its
own measurements and those provided by its Voronoi neighbors, which are
incorporated into the individual robot's Gaussian process only if they provide
sufficiently novel information. The performance of the algorithm is evaluated
in simulation and compared with centralized approaches.
