Title:
Bayesian Inference in the Space of Topological Maps
Bayesian Inference in the Space of Topological Maps
Author(s)
Ranganathan, Ananth
Menegatti, Emanuele
Dellaert, Frank
Menegatti, Emanuele
Dellaert, Frank
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Abstract
While probabilistic techniques have previously been
investigated extensively for performing inference over the space
of metric maps, no corresponding general purpose methods exist
for topological maps. We present the concept of Probabilistic
Topological Maps (PTMs), a sample-based representation that
approximates the posterior distribution over topologies given
available sensor measurements. We show that the space of
topologies is equivalent to the intractably large space of set
partitions on the set of available measurements. The combinatorial
nature of the problem is overcome by computing an
approximate, sample-based representation of the posterior. The
PTM is obtained by performing Bayesian inference over the space
of all possible topologies and provides a systematic solution to
the problem of perceptual aliasing in the domain of topological
mapping. In this paper, we describe a general framework for
modeling measurements, and the use of a Markov chain Monte
Carlo (MCMC) algorithm that uses specific instances of these
models for odometry and appearance measurements to estimate
the posterior distribution. We present experimental results that
validate our technique and generate good maps when using
odometry and appearance, derived from panoramic images, as
sensor measurements.
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Date Issued
2006-02
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Text
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Post-print