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Dellaert, Frank

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    Probabilistic Topological Mapping for Mobile Robots using Urn Models
    (Georgia Institute of Technology, 2007) Ranganathan, Ananth ; Dellaert, Frank
    We present an application of Bayesian modeling and inference to topological mapping in robotics. This is a potentially difficult problem due to (a) the combinatorial nature of the state space, and (b) perceptual aliasing by which two different landmarks in the environment can appear similar to the robot's sensors. Hence, this presents a challenging approximate inference problem, complicated by the fact that the form of the prior on topologies is far from obvious. We deal with the latter problem by introducing the use of urn models, which very naturally encode prior assumptions in the domain of topological mapping. Secondly, we advance simulated tempering as the basis of two rapidly mixing approximate inference algorithms, based on Markov chain Monte Carlo (MCMC) and Sequential Importance Sampling (SIS), respectively. These algorithms converge quickly even though the posterior being estimated is highly peaked and multimodal. Experiments on real robots and in simulation demonstrate the efficiency and robustness of our technique.
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    A Variational inference method for Switching Linear Dynamic Systems
    (Georgia Institute of Technology, 2005) Oh, Sang Min ; Ranganathan, Ananth ; Rehg, James M. ; Dellaert, Frank
    This paper aims to present a structured variational inference algorithm for switching linear dynamical systems (SLDSs) which was initially introduced by Pavlovic and Rehg. Starting with the need for the variational approach, we proceed to the derivation of the generic (model-independent) variational update formulas which are obtained under the mean field assumption. This leads us to the derivation of an approximate variational inference algorithm for an SLDS. The details of deriving the SLDS-specific variational update equations are presented.
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    Data Driven MCMC for Appearance-based Topological Mapping
    (Georgia Institute of Technology, 2005) Dellaert, Frank ; Ranganathan, Ananth
    Probabilistic techniques have become the mainstay of robotic mapping, particularly for generating metric maps. In previous work, we have presented a hitherto nonexistent general purpose probabilistic framework for dealing with topological mapping. This involves the creation of Probabilistic Topological Maps (PTMs), a sample-based representation that approximates the posterior distribution over topologies given available sensor measurements. The PTM is inferred using Markov Chain Monte Carlo (MCMC) that overcomes the combinatorial nature of the problem. In this paper, we address the problem of integrating appearance measurements into the PTM framework. Specifically, we consider appearance measurements in the form of panoramic images obtained from a camera rig mounted on a robot. We also propose improvements to the efficiency of the MCMC algorithm through the use of an intelligent data-driven proposal distribution. We present experiments t hat illustrate the robustness and wide applicability of our algorithm.
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    Dirichlet Process based Bayesian Partition Models for Robot Topological Mapping
    (Georgia Institute of Technology, 2004) Ranganathan, Ananth ; Dellaert, Frank
    Robotic mapping involves finding a solution to the correspondence problem. A general purpose solution to this problem is as yet unavailable due to the combinatorial nature of the state space. We present a framework for computing the posterior distribution over the space of topological maps that solves the correspondence problem in the context of topological mapping. Since exact inference in this space is intractable, we present two sampling algorithms that compute sample-based representations of the posterior. Both the algorithms are built on a Bayesian product partition model that is derived from the mixture of Dirichlet processes model. Robot experiments demonstrate the applicability of the algorithms.