  In this paper, we present a consensus-based decentralized multi-robot
approach to reconstruct a discrete distribution of features, modeled as an
occupancy grid map, that represent information contained in a bounded planar 2D
environment, such as visual cues used for navigation or semantic labels
associated with object detection. The robots explore the environment according
to a random walk modeled by a discrete-time discrete-state (DTDS) Markov chain
and estimate the feature distribution from their own measurements and the
estimates communicated by neighboring robots, using a distributed Chernoff
fusion protocol. We prove that under this decentralized fusion protocol, each
robot's feature distribution converges to the ground truth distribution in an
almost sure sense. We verify this result in numerical simulations that show
that the Hellinger distance between the estimated and ground truth feature
distributions converges to zero over time for each robot. We also validate our
strategy through Software-In-The-Loop (SITL) simulations of quadrotors that
search a bounded square grid for a set of visual features distributed on a
discretized circle.
