A Multifrontal QR Factorization Approach to Distributed Inference Applied to Multirobot Localization and Mapping

Abstract

QR factorization is most often used as a black box algo-rithm, but is in fact an elegant computation on a factor graph. By computing a rooted clique tree on this graph, the com-putation can be parallelized across subtrees, which forms the basis of so-called multifrontal QR methods. By judiciously choosing the order in which variables are eliminated in the clique tree computation, we show that one straightforwardly obtains a method for performing inference in distributed sen-sor networks. One obvious application is distributed localiza-tion and mapping with a team of robots. We phrase the prob-lem as inference on a large-scale Gaussian Markov Random Field induced by the measurement factor graph, and show how multifrontal QR on this graph solves for the global map and all the robot poses in a distributed fashion. The method is illustrated using both small and large-scale simulations, and validated in practice through actual robot experiments.