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In this work, we present a novel distributed method for constructing an occupancy grid map of an unknown environment using a swarm of robots with global localization capabilities and limited inter-robot communication. The robots explore the domain by performing L\'evy walks in which their headings are defined by maximizing the mutual information between the robot's estimate of its environment in the form of an occupancy grid map and the distance measurements that it is likely to obtain when itarXiv:1903.04836v2 fatcat:rvyzqnzm35b27dfx2fqf3iu6pe