## 4 Experimental Validation
### Improved AMCL Algorithm Simulation Comparison Experiment  
A raster map is generated using SLAM laser navigation, and AMCL localization particles are tiled over the raster map until the whole map is tiled. The AMCL algorithm and the improved AMCL algorithm are introduced separately, and the different situations among the two are observed and data is collected for analysis. The size of the map is 10 m \(\times\) 10 m, and travelling one lap is recorded as one complete distance. Figure 17: Simulation test: (**a**) convergence to true value; (**b**) the estimated value is near the true value. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Number** \\ \hline Maximum linear speed & 1 m/s \\ Maximum angular velocity & 1 rad/s \\ Maximum linear acceleration & 0.5 m/s\({}^{2}\) \\ Maximum angular acceleration & 0.5 rad/s\({}^{2}\) \\ Radar scanning angle & 320\({}^{\circ}\) \\ Radar scanning frequency & 10 Hz \\ Maximum measurement distance of radar & 10 m \\ Improved AMCL algorithm particle initial value & 1000 \\ Resampling measurement & Low variance resampling \\ \hline \hline \end{tabular}
\end{table} 
Table 3: AGV setup parameters. Navigation was tested using different algorithms in the same environment, and Figure 18 show the different scenarios in which the particles behaved separately. Photoelectric sensors were set up on both sides of the laying of the QR code and at the start-end position to detect the number of corrections and the maximum distance of error when different algorithms were used for tracking the trajectory, in order to record a week's navigation time as well as the maximum distance from the set point of the target error. It can be learnt from the distribution of the particles that the distribution of the improved algorithm particles performs better compared to the previous algorithm, distributing on the real trajectory with less error, and the rest of the particles of the regions not involved by the AGVs disappear, only in the aggregation of the labels. From Figure 19 it can be seen that during approximately the first 30 messages released by the AMCL, the localization error is small; once 30 messages are released, the AGV is abducted to produce a large error. As the AGV moves, the positioning error gradually decreases, and after multiple messages, the error tends to 0, restoring the original positioning accuracy. Although the improved AMCL algorithm also encounters kidnapping, the adjustment time is improved by 68.73% compared to the unimproved algorithm. Figure 18: AMCL algorithm with improved AMCL algorithm particle changes: (**a**) AMCL algorithm for particle changes at the starting point; (**b**) AMCL algorithm changes of particles at the end point; (**c**) improved AMCL algorithm for particle changes at the starting point; (**d**) improved AMCL algorithm for particle changes at endpoints. The maximum data for the offset recorded by the photoelectric sensor in Figure 20a is (\(-18.79\), \(22.38\)) when using the AMCL algorithm, while the improved AMCL algorithm is (\(-4.79\), \(6.82\)). That is to say, adjusting the trajectory to the left exceeds the set trajectory line by a maximum of \(22.83\) cm and \(6.82\) cm, and adjusting the trajectory to the right exceeds the distance by a maximum of \(18.79\) cm and \(4.79\) cm, from which the comparison can be significantly concluded that the improved algorithm is superior. Figure 20b with the increase in the running time, the error gradually increases and reaches a peak at a certain point, and then the error gradually decreases, but the adjustment time also gradually increases. In contrast, because of the addition of the algorithm to eliminate the cumulative error link, in the improved algorithm, the error will be adjusted quickly with a slight difference between the scan data and the simulation algorithm.