# Research on the A* Algorithm for Automatic Guided Vehicles in Large-Scale Maps
## 3 Improved A* Algorithm Based on Local Obstacle Rate and Dynamic Neighbourhood
### Modifications to the Evaluation Function
#### 3.4.3 Adding Direction Change Penalty
When we make a side-by-side comparison between the PA*F algorithm (the improved algorithm in this article adds Floyd smoothing) and the improved algorithm proposed by [PERSON] [26], as shown in Figure 12(b), it is not difficult to find that although [PERSON]'s algorithm [26] shortens the path length to a certain extent by eliminating redundant nodes in the paths, the PA*F algorithm still maintains an average advantage of 0.5% in terms of path length. More significantly, in terms of the number of expansion nodes and running time, [PERSON]'s algorithm is up to 11 times and 6 times higher than the PA*F algorithm, respectively. This is mainly attributed to the inadequacy of [PERSON]'s algorithm in the dynamic weight allocation strategy, with relatively conservative weight settings, which fails to adequately guide the algorithm towards a more efficient and optimised search path. Figure 13: Comparison chart with existing algorithms. On the other hand, although [PERSON]'s algorithm achieves a further reduction in path length by adjusting the distance function in the heuristic function, this improvement is at the expense of search efficiency. The large number of unnecessary node extensions significantly drags down the overall performance of the algorithm, making it ineffective in facing complex path planning tasks. In summary, the PA*F algorithm shows strong competitiveness and broad application prospects in the field of path planning by virtue of its comprehensive optimisation strategy and efficient execution efficiency. Although A*JPS is designed to efficiently find the optimal path by directly locating and searching for \"jump points\", its core jump point determination mechanism is extremely time-consuming, which directly leads to a significant increase in the running time of the algorithm, specifically, its average running time is about a hundred times that of the PA*F algorithm. Although in terms of path length, the A*JPS and PA*F algorithms are almost the same, by comparing the search results in Figure 13a,d, it is not difficult to find that A*JPS firstly focuses on identifying and locating the \"jump points\" during the search process, which are mostly distributed diagonally. These \"jump points\" are mostly distributed diagonally, and then paths are constructed in the subsequent steps. However, this strategy results in a relatively more convoluted and complex path. In contrast, as shown in Figure 13c, another improved algorithm achieved a significant reduction in the algorithm's response time as well as a reduction in the number of expansion nodes by introducing an innovative e-based weight design scheme (A*Yu). However, despite the progress in efficiency achieved by this improvement, the number of expansion nodes still increased somewhat compared to the PA* algorithm. The average increase was 5.5%. It is worth noting that this weighting design approach, while pursuing speedups, also has a side effect, namely, it sacrifices some quality attributes of the paths through the amplification of the estimated cost. Specifically, it leads to a slight increase in the final path length compared to the PA* algorithm, by about 1.1%, thus seeking a balance between path optimisation and algorithmic efficiency. In summary, the reason why the fusion algorithm can outperform the traditional algorithm and other improved algorithms in terms of performance lies in the reasonableness of the strategy combination, the scientificity of the weight design, and the flexibility of the search mechanism. These features work together in all aspects of the algorithm to achieve the double improvement of search efficiency and path quality. ## 5 Conclusions

In this paper, the performance of the A* algorithm was significantly enhanced through a series of refined improvements.