  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.
