Delayed optimisation for robust and linear pose-graph SLAM

This paper addresses a robust and efficient solution to eliminate false loop-closures in a posegraph linear SLAM problem. Linear SLAM was recently demonstrated based on submap joining techniques in which a nonlinear coordinate transformation was performed separately out of the optimisation loop, resulting in a convex optimisation problem. This however introduces added complexity in dealing with any false loop-closures, which mostly stems from two factors: a) the limited local observations in submap-joining stages and b) the non blockdiagonal nature of the information matrix of each submap. To address these problems, we propose a Robust Linear SLAM (RL-SLAM) by 1) developing a delayed optimisation for outlier candidates and 2) utilising a Schur complement to efficiently eliminate corrupted information block. Based on this new strategy, we prove that the spread of outlier information does not compromise the optimisation performance of inliers and can be fully filtered out from the corrupted information matrix. Experimental results based on public synthetic and real-world datasets in 2D and 3D environments show that this robust approach can cope with the incorrect loop-closures robustly and effectively.