In this work, we present a novel automated procedure for constructing a metric map of an unknown domain with obstacles using uncertain position data collected by a swarm of resource-constrained robots. The robots obtain this data during random exploration of the domain by combining onboard odometry information with noisy measurements of signals received from transmitters located outside the domain. This data is processed offline to compute a density function of the free space over a discretization of the domain. We use persistent homology techniques from topological data analysis to estimate a value for thresholding the density function, thereby segmenting the obstacle-occupied region in the unknown domain. Our approach is substantiated with theoretical results to prove its completeness and to analyze its time complexity. The effectiveness of the procedure is illustrated with numerical simulations conducted on six different domains, each with two signal transmitters.
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