# Fast Loop Closure Selection Method with Spatiotemporal Consistency for Multi-Robot Map Fusion
## 2 Related Works  
SLAM has made significant development in the past 30 years [7; 8; 9]. As one of the indispensable modules, various typical SLAM frameworks (e.g., VINS [10], ORB-SLAM2 [11], LeGO-LOAM [12], Gr-LOAM [13]) have integrated loop closures modules to enhance the robustness of the system.  
Nevertheless, the robots performing long tasks are prone to perceptual aliasing and generate incorrect loop closures, posing severe challenges for graph SLAM sensitive to outliers. Regarding the susceptibility of graph SLAM to wrong loop closures, many works try to establish a robust back-end optimizer to detect and filter outliers introduced by the front-end algorithms [14; 15]. Realizing, reversing, and recovering algorithm [16] can realize that the appearance-based place recognition system has generated wrong constraints, remove them if required, and re-optimize the state estimation. A robust solver is proposed in [17] to address heavy-tailed measurement noise and develops convex relaxations for pose graph optimization that approximately solve nonconvex optimization problems via semidefinite programming. In order to build a globally consistent map, a robust back-end solver is proposed in [18], which disables inaccurate loop closures and changes part of the graph topology during optimization. The relative pose measurements are easy to estimate, for intra-robot loop closures, because they can be obtained by odometry or estimated from a visual frame or lidar frame matching algorithm [19; 20; 21]. In comparison, these methods for outliers rejection are not suitable for multi-robot SLAM.  
The vital issue of multi-robot SLAM is relative pose estimation, and most existing works deal with this issue by analyzing the inter-robot loop closures and then detecting and filtering the outliers. Researchers present a comprehensive review to illustrate the challenges for multi-robot SLAM map fusion [22; 23], many of which attempt to propose a robust loop closure method to address the problem of outliers introduced by perceptual aliasing and perform map fusion. For initialization problems, the concept of \"anchor nodes\" is proposed to convert individual nodes of each pose graph into a global frame [24]. The pairwise consistency maximization (PCM) method [25] applies the binary switch variables as weights to distinguish whether each pair of measurements is consistent. It then utilizes the maximum clique problem derived from graph theory to determine the largest pairwise internally consistent set. Following the solution of PCM, the definition of proposes the maximum edge weight clique (MEWC) integrating consistency and data similarity is proposed and then applies them as the weight for the objective function [26]. The expectation maximization algorithm is an effective solution for multi-robot pose graph localization [27]. It is capable of inferring the initial relative pose of the robot and solving the problem of multi-robot data association, in the absence of prior knowledge about the initial relative pose measurements. When there is overlap between two maps, those landmarks that appear repeatedly can provide additional information that is added to the optimization process in the form of constraints to improve alignment accuracy [28]. Some researchers propose to construct a semantic map in the unknown environment based on the rich features of visual images for map fusion between robots [29; 30]. DOOR-SLAM [31] is a typical distributed SLAM solution with low communication bandwidth, which integrates the PCM module at the back-end and includes a distributed SLAM front-end to detect inter-robot loop closures. Distributed systems often rely on additional communication channels to exchange maps for feature data, making it more challenging to implement. The mentioned solutions do not consider the temporal dimension making it impossible to determine the topology relationship of the measurements. In addition, as the definition of consistency only involves the spatial dimension, this case does not conform to the spatiotemporal consistency.