  Two types of probabilistic maps are popular in the mobile robotics
literature: occupancy grids and geometric maps. Occupancy grids have the
advantages of simplicity and speed, but they represent only a restricted class
of maps and they make incorrect independence assumptions. On the other hand,
current geometric approaches, which characterize the environment by features
such as line segments, can represent complex environments compactly. However,
they do not reason explicitly about occupancy, a necessity for motion planning;
and, they lack a complete probability model over environmental structures. In
this paper we present a probabilistic mapping technique based on polygonal
random fields (PRF), which combines the advantages of both approaches. Our
approach explicitly represents occupancy using a geometric representation, and
it is based upon a consistent probability distribution over environments which
avoids the incorrect independence assumptions made by occupancy grids. We show
how sampling techniques for PRFs can be applied to localized laser and sonar
data, and we demonstrate significant improvements in mapping performance over
occupancy grids.
