## 5 Simulation Analysis
### Simulation Results and Analysis of Improved A* Algorithm  
To validate the viability of the enhanced A* algorithm, the subsequent experiment employs a 20 \(\times\) 20 raster map for simulation purposes. The outcomes of this experiment are visually depicted in Figure 6 while the accompanying numerical data are presented in Table 2. Furthermore, to bolster the credibility of the improved A* algorithm, additional experiments are conducted within randomly generated 50 \(\times\) 50 raster maps. The results of these experiments are illustrated in Figure 7, while the corresponding quantitative findings are tabulated in Table 3. In Figures 6 and 7, the blue triangle represents the starting point, the blue circle represents the endpoint, and the red solid line represents the planned path. (a) represents the traditional A* algorithm, (b) represents the improved A* algorithm from reference [21], (c) represents the improved ant colony algorithm from reference [8], (d) represents the improved A* algorithm in this study.  
Figure 6: 20 \(\times\) 20 raster maps to compare experimental results.  
Figure 7: 50 \(\times\) 50 raster maps to compare experimental results.  
In the above experiments, the results from Figure 6a show that the path planned by the traditional A* algorithm not only disregards the vehicle's size but also involves a higher number of turns. From the results in Figure 6b, it can be observed that the improved A* algorithm takes into account the vehicle's size but the path still has too many turns, resulting in non-smoothness. On the other hand, as indicated by the results in Figure 6c, the improved ant colony algorithm plans a very smooth path but does not consider the vehicle's size. However, from Figure 6d, it can be seen that in this study, the modified A* algorithm takes both the vehicle's size and the issue of path smoothness into consideration. According to the data in Table 3, in the 20 \(\times\) 20 raster maps, compared with the traditional A* algorithm, the improved A* algorithm reduces the path by 1.3%, the turning times by 62.5%, and the total turning angle by 77.8%; compared with the improved A* algorithm in the literature [21], the path is reduced by 5.6%, the turning times are reduced by 70%, and the total turning angle is reduced by 82.3%; compared with the improved ant colony algorithm in the literature [8], the path is reduced by 0.2% and the total turning angle is reduced by 29.0%. From the results in Figure 7 and Table 3, in the 50 \(\times\) 50 raster maps, the improved A* algorithm in this study is better than the traditional A*, study [8], and study [21] in terms of path length, turning times, and total turning angle.  
In comparison to both the traditional A* algorithm and the enhanced ant colony algorithm discussed in [8], the improved A* algorithm introduced in this study encompasses a comprehensive consideration of obstacle distances, thereby ensuring path safety is a paramount priority. Moreover, juxtaposed against the enhanced A* algorithm featured in [21], the current implementation not only reduces the number of turns but also achieves a smoother path, resulting in heightened operational efficiency for the AGV. These distinctions underscore the unique advantages and advancements in the proposed improved A* algorithm, positioning it as a compelling solution that amalgamates safety, path optimization, and operational effectiveness for AGV navigation.