Bayesian inference in the space of topological maps

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 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.