# Fast Loop Closure Selection Method with Spatiotemporal Consistency for Multi-Robot Map Fusion
###### Abstract  
This paper presents a robust method based on graph topology to find the topologically correct and consistent subset of inter-robot relative pose measurements for multi-robot map fusion. However, the absence of good prior on relative pose gives a severe challenge to distinguish the inliers and outliers, and once the wrong inter-robot loop closures are used to optimize the pose graph, which can seriously corrupt the fused global map. Existing works mainly rely on the consistency of spatial dimension to select inter-robot measurements, while it does not always hold. In this paper, we propose a fast inter-robot loop closure selection method that integrates the consistency and topology relationship of inter-robot measurements, which both conform to the continuity characteristics of similar scenes and spatiotemporal consistency. Firstly, a clustering method integrating topology correctness of inter-robot loop closures is proposed to split the entire measurement set into multiple clusters. Then, our method decomposes the traditional high-dimensional consistency matrix into the sub-matrix blocks corresponding to the overlapping trajectory regions. Finally, we define the weight function to find the topologically correct and consistent subset with the maximum cardinality, then convert the weight function to the maximum clique problem from graph theory and solve it. We evaluate the performance of our method in a simulation and in a real-world experiment. Compared to state-of-the-art methods, the results show that our method can achieve competitive performance in accuracy while reducing computation time by 75%. SLAM; multi-robot; map fusion; maximum clique problem +
Footnote †: journal: Applied  
0000-0001-999-22000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-  
measurements. It is a troublesome issue in appearance-based place recognition systems, where two scenes are wrongly recognized as the same position even if they are far apart in the environment. Multi-robot SLAM system usually uses the inter-robot loop closures to optimize the pose graph and then fuse the local maps into a global map, while the false positive inter-robot loop closures may corrupt the back-end optimization results. Following pose graph SLAM formulation, wrong inter-robot loop closures are called outliers. In [6], outliers are more commonly defined as \"any observation in a set of data that is inconsistent with the remainder of the observations in that dataset\". Therefore, effectively identifying outliers and choosing a consistent subset of measurements is the key to fusing the local maps into a global map. Existing methods follow the idea of building a high-dimensional consistency matrix at the level of the entire measurement set to find consistent subsets with high cardinality. Unfortunately, on the one hand, solving the maximum clique problem directly in the constructed high-dimensional consistency matrix takes a long time, which is not conducive to real-time performance. On the other hand, this method considers the consistency in the spatial dimension but not in the temporal dimension, while the neighboring constraints in the region where the trajectories overlap are also consistent in the temporal dimension. The topology relationship in the time dimension is a meaningful factor that should be considered for the inter-robot loop closure selection method. As we know, the accurate inter-robot measurements show that robots repeatedly visit the same position at different times, meaning that the two trajectories are coincident within the regions. This is the case when the appearance-based SLAM front-end generates constraints. Once a constraint is detected, it is certain that other constraints will also be generated in its neighboring regions or adjacent time intervals due to the continuity characteristics of similar scenes.