The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping

Michael Kaess, Viorela Ila, Richard Roberts and Frank Dellaert
Workshop Paper, Intl. Workshop on the Algorithmic Foundations of Robotics, WAFR, pp. 157-173, December, 2010

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We present a novel data structure, the Bayes tree, that provides an al- gorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root in- formation matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of batch matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a ma- trix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, that combines incremental updates with fluid relinearization of a reduced set of variables for efficiency, combined with fast convergence to the exact solution. We also present a novel strategy for incremental variable reordering to retain sparsity. We evaluate our algorithm on standard datasets in both landmark and pose SLAM settings.

author = {Michael Kaess and Viorela Ila and Richard Roberts and Frank Dellaert},
title = {The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping},
booktitle = {Intl. Workshop on the Algorithmic Foundations of Robotics, WAFR},
year = {2010},
month = {December},
pages = {157-173},
keywords = {graphical models, clique tree, probabilistic inference, sparse linear algebra, nonlinear optimization, smoothing and mapping, SLAM, iSAM},
} 2019-06-27T16:48:32-04:00