## 4 Experiments and Analysis
### Experiment 2: FiMa-Reader System Positioning Accuracy  
In the second experiment, we evaluated the positioning accuracy of an autonomous mobile robot (AMR) equipped with the proposed FiMa-Reader system. The AMR used in this experiment, shown in Figure 6a, is called the Trans and features a differential mobile chassis with two 2D LiDARs mounted on opposite corners. It uses wheel encoders and an IMU for odometry and a 2D LiDAR point cloud for observation to navigate. To evaluate the position accuracy, we used a PGV100 Pepperl-Fuchs sensor to record the relative position between a DM placed on the ground and the PGV100, which has a measurement resolution of 0.1 mm and 0.1 degrees. We installed the FiMa-Reader system and the PGV100 on top of the Trans.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Fiducial Marker**} & \multirow{2}{*}{**Data Capacity**} & \multicolumn{2}{c}{**Origin (100 per Group)**} & \multicolumn{2}{c}{**Occlusion (100 per Group)**} \\ \cline{3-6}  & & **Detection Rate** & \begin{tabular}{c} **Average (Success)** \\ **Detection Time (ms)** \\ \end{tabular} & **Detection Rate** & \
\begin{tabular}{c} **Average (Success)** \\ **Detection Time (ms)** \\ \end{tabular} \\ \hline DAH pattern & maximum 1556 & 97\% & 11.06 & 67.3\% & 23.56 \\ ArUco &
\begin{tabular}{c} origin dictionary \\ size: 1000 ids \\ maximum 1556 \\ bytes (ECC200) \\ maximum 1556 \\ bytes (ECC200) \\ maximum 1556 \\ bytes (ECC200) \\ \end{tabular} & 70\% & 24.58 & 4.5\% & 27.61 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of the data capacity, detection rate, and average detection time of the DAH pattern, ArUco, DM, and DM with Box in the original and occlusion image datasets.  
Figure 6: Experimental setup. (**a**) The Trans experimental AMR. (**b**) The experimental scenarios simulating an industrial environment, human–robot coexistence and highly dynamic environment.  
As shown in Figure 6b, we conducted two independent missions for the Trans: one for pure navigation and the other for navigation with docking. Both missions had the same navigation goal. In the pure navigation process, we used only LiDAR and odometry to determine the robot's position. In the docking process, the FiMa-Reader system outputted the relative pose between the DAH pattern and the Trans and transmitted this information to the chassis to update the robot self-localization. When the chassis determined that the current position was close enough to the navigation goal, the mission was completed, and the PGV100 recorded the current relative pose according to the DM placed on the ground. After each mission was completed, the chassis returned to the navigation starting point and repeated each task 1500 times.  
Figure 7 illustrates the positioning distribution of the pure navigation task and the navigation with docking task. Figure 7a shows the x-y distribution of the two tasks, with a green \"x\" representing the completed positions of the pure navigation task and a red \"+\" representing the positions of the navigation with docking task. The group of red points is significantly more centralized than the green points, indicating that the navigation with docking task has a more precise positioning ability. Figure 7b shows the x-direction, y-direction and theta angle position distributions, respectively. The x range of the docking process is 8.4 mm, while the x range of the pure navigation is 61.9 mm. Using the FiMa-Reader system improved the accuracy by 86.42%. The y range of the docking process is 4.7 mm, while the y range of the pure navigation is 8.5 mm, with the FiMa-Reader system improving the accuracy by 44.7%. The theta angle of the docking process is 0.30 degrees, while the theta angle of pure navigation is 1.9 degrees, with the FiMa-Reader system improving the accuracy by 84.21%.