Bayesian inference in the space of topological maps

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 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

Incremental Topological Mapping Using Omnidirectional Vision

“…The approach does not eliminate the need for multi-hypothesis tracking; on the contrary, our approach is intended to be incorporated into such a framework (e.g. [16]). However, because the method has been shown to be quite insensitive to perceptual aliasing, the computational explosion associated with multi-hypothesis algorithms could possibly be mitigated to a great extent.…”

Autonomous legged hill and stairwell ascent

“…Navigation behaviors have been dominated over the last decade by interest in learning [13,14] and, more specifically, applications of Bayesian map-building [15]. Even in their more relaxed topological representations [16], such methods are committed to repeated measurements as a necessary means of discovery, even when used on legged platforms [11]. However, the dynamics of locomotion inherent to dexterous machines such as the legged robot used in this work complicate considerably the task of accurately estimating state or building a world model [17,18].…”

Robust Vision-only Mobile Robot Navigation with Topological Maps

“…Very popular are various probabilistic approaches of the topological map building problem. (Ranganathan et al, 2005) for instance use Bayesian inference to find the topological structure that explains best a set of panoramic observations, while (Shatkay & Kaelbling, 1997) fit hidden Markov models to the data. If the state transition model of this HMM is extended with robot action data, the latter can be modeled using a partially observable Markov decision process or POMDP, as in (Koenig & Simmons, 1996;Tapus & Siegwart, 2005).…”