A convex relaxation for approximate global optimization in simultaneous localization and mapping
David M. Rosen, Charles DuHadway, John J. Leonard
Abstract
Modern approaches to simultaneous localization and mapping (SLAM) formulate the inference problem as a high-dimensional but sparse nonconvex M-estimation, and then apply general first- or second-order smooth optimization methods to recover a local minimizer of the objective function. The performance of any such approach depends crucially upon initializing the optimization algorithm near a good solution for the inference problem, a condition that is often difficult or impossible to guarantee in practice. To address this limitation, in this paper we present a formulation of the SLAM M-estimation with the property that, by expanding the feasible set of the estimation program, we obtain a convex relaxation whose solution approximates the globally optimal solution of the SLAM inference problem and can be recovered using a smooth optimization method initialized at any feasible point. Our formulation thus provides a means to obtain a high-quality solution to the SLAM problem without requiring high-quality initialization.
BibTeX
@inproceedings{icra2015_aconvexrelaxatio,
title = {A convex relaxation for approximate global optimization in simultaneous localization and mapping},
author = {David M. Rosen and Charles DuHadway and John J. Leonard},
booktitle = {ICRA 2015},
year = {2015}
}