# Fast Loop Closure Selection Method with Spatiotemporal Consistency for Multi-Robot Map Fusion
## 5 Experiments Evaluation
### Real-World Experiments  
The primary sensor of the front-end place recognition system was a 3D lidar, where the iterative closest point (ICP) [21] algorithm was performed to calculate the inter-robot loop closures. For MEWC, the residual generated by ICP was used to represent the degree of data similarity between two frames. In this experiment, one of the challenges comes from the lack of ground truth, so we collected a complete dataset in the same scene, as a reference metric, to provide a global trajectory for the local maps. The metric has no other practical meaning, as this section aims to verify the algorithm's performance for outlier rejection of inter-robot loop closures, not navigation. We collected multiple local maps of this scene at different moments for each robot, where every pair of local maps contained repeatedly visited areas to generate potential inter-robot measurements. In addition, the end position of robot 1 is the starting position of the trajectory of robot 2, which is convenient for quantitative analysis because, theoretically, these two positions should be coincident in the fused map. We took the deviation between these two positions in the fused map as a new evaluation metric. The complete datasets were run multiple times to determine the number of loop closures within the overlapping region of the two maps. Figure 8 represents two independent local robot trajectories, and solid green lines represent inter-robot loop closures. From the local maps, the starting positions of two trajectories are coincident due to the lack of prior information on relative measurements. Figure 7: Results of ATE between the ground truth of the manhattan dataset and the map estimated by our method. The color changes from blue to red, and the error gradually increases. The self-collected dataset is not as large as the synthetic dataset, so we reset the threshold \(t_{g}\) to 15 to define the clusters, making it more suitable for real situations. Likewise, to increase the difficulty of outlier rejection, we added 30 outliers generated randomly with random mean and covariance to the measurement set. Figures 9 and 10 shows example plots of the map fusion results. For convenience, the dataset corresponding to robot 1 is abbreviated as session 1, and robot 2 is referred to as session 2. Figures 9a and 10a represent the complete trajectories of the two experimental scenarios, respectively, as global references. Figure 9 shows the test results of the different algorithms in scene 1, where the red and blue lines indicate the local pose graphs of the two robots, and the thick green lines represent the inter-robot measurements corresponding to the selected subset. Then, the subset of inter-robot measurements selected by each algorithm can be inserted into the existing SLAM back-end optimizer for map fusion. The maps estimated by MEWC, PCM, and our method are shown in Figure 9b-d. Although there is a certain deviation between the red square and blue triangle in the fused map, it can be intuitively seen that the three methods are succeeded in map fusion, and the fused  
Figure 8: The local trajectories of robots in different scenes. The trajectories of robot 1 and robot 2 are shown in red and blue, respectively. Figure 9: The fused global map corresponding to scene 1 shown in Figure 8a. The red square and blue triangle represent the end position of session 1 and the start position of the trajectory of session 2, respectively. Correctly accepted inlier constraints are green, disabled outliers in gray. map approximately conforms to the reference trajectory. This case indicates that all three methods consider and apply the concept of consistency to select measurement subset. Next, we quantitatively analyze the performance of the algorithm by evaluating the experimental results. Due to the lack of ground truth in the experiments, ATE cannot be used as an available evaluation metric.