“Loopy SAM”
by
A. Ranganathan,
M. Kaess,
and
F. Dellaert.
In Intl. Joint Conf. on Artificial Intelligence, IJCAI,
(Hyderabad, India), Jan. 2007, pp. 2191-2196. Oral presentation
acceptance ratio 15.7% (212 of 1353).

Abstract

Smoothing approaches to the Simultaneous Localization and Mapping (SLAM)
problem in robotics are superior to the more common filtering approaches
in being exact, better equipped to deal with non-linearities, and
computing the entire robot trajectory. However, while filtering algorithms
that perform map updates in constant time exist, no analogous smoothing
method is available. We aim to rectify this situation by presenting a
smoothingbased solution to SLAM using Loopy Belief Propagation (LBP) that
can perform the trajectory and map updates in constant time except when a
loop is closed in the environment. The SLAM problem is represented as a
Gaussian Markov Random Field (GMRF) over which LBP is performed. We prove
that LBP, in this case, is equivalent to Gauss-Seidel relaxation of a
linear system. The inability to compute marginal covariances efficiently
in a smoothing algorithm has previously been a stumbling block to their
widespread use. LBP enables the efficient recovery of the marginal
covariances, albeit approximately, of landmarks and poses. While the final
covariances are overconfident, the ones obtained from a spanning tree of
the GMRF are conservative, making them useful for data association.
Experiments in simulation and using real data are presented.