The journal version on our latest magic, iSAM 2, is now slated for publication. You can download the preprint here:

iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree, Michael Kaess, Hordur Johannsson, Richard Roberts, Viorela Ila, John Leonard, and Frank Dellaert, International Journal of Robotics Research, 2012

Abstract

We present a novel data structure, the Bayes tree, that provides an algorithmic 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 information 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 the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix 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, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.

Also see our earlier conference papers:

1. •iSAM2: Incremental Smoothing and Mapping with Fluid Relinearization and Incremental Variable Reordering, Michael Kaess, Hordur Johannsson, Richard Roberts, Viorela Ila, John Leonard, and Frank Dellaert, IEEE International Conference on Robotics and Automation (ICRA), 2011
   

2. •The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping, Michael Kaess, Viorela Ila, Richard Roberts, and Frank Dellaert, Intl. Workshop on the Algorithmic Foundations of Robotics, 2010