# Research on Path Planning Based on the Integrated Artificial Potential Field-Ant Colony Algorithm
## 5 Algorithm Simulation and Analysis
### A 30 \(\times\) 30 Grid Map  
To conduct a comparison of the performance differences between the improved ACA and the traditional ACA, this paper sets up a more complex grid environment for further experiments. The map size is set to 30 \(\times\) 30, and the obstacles are more densely distributed. The starting node is set as the grid with the number 1, with coordinates (0.5, 29.5), and the target node is set as the grid with the number 900, with coordinates (29.5, 0.5). In this study, to comprehensively evaluate the algorithm performance, simulation experiments are conducted, respectively, for the classic ACA, the GA-ACA algorithm proposed in the literature [25] and the optimized ACA. The experiments precisely simulate the robot's operation under the guidance of different algorithms through specific simulation environments and parameter settings. Each algorithm was run 100 times and the optimal result was taken. Ultimately, the robot path trajectory diagrams and convergence curve diagrams obtained from the experiments are uniformly organized and presented in Figure 10 for intuitive comparison and analysis of the performance of the three algorithms in PP.  
As can be seen from Figure 10, when the environmental complexity continuously increases, the path trajectory planned by the traditional ACA shows more pronounced zigzag patterns, which greatly affect the smoothness and rationality of the path. However, GA-ACA and the improved ACA still prefer to take the diagonal paths of the grids. Meanwhile, the path obtained by the improved ACA has fewer corners compared to GA-ACA. In more complex grid environments, the algorithm proposed in this study demonstrates significant advantages, being able to find shorter and smoother paths. At the same time, the convergence speed of the algorithm is also faster, and the PP task is effectively completed.  
By improving the HF, pheromone evaporation factor, and pheromone updating mechanism, Table 3 shows that the improved ACA reduces the shortest path length by 12.58%, the number of convergence iterations by 87.97%, the number of path turning points by 20%, and the runtime by 79.98% compared to the conventional ACA. Compared to GA-ACA, the improved ACA reduces the path length by 3.21%, the number of convergence iterations by 81.40%, the path turning points by 5.88%, and the running time by 69.84%.  
As shown in Figure 11, after path optimization, unnecessary direction adjustment points in the original trajectory are effectively eliminated. After optimization, the system records show that the optimal moving distance is shortened from 43.35 units to 41.99 units, and the trajectory turning point is shortened from the initial 16 points to 9 points. The improved effect is reflected in the movement efficiency increased by 3.13%, and the direction adjustment frequency decreased significantly by 43.75%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Shortest Path Length** & **Convergent Iteration Times** & **Path Turning Points** & **Running Time** \\ \hline Traditional ACA & 49.60 & 133 & 20 & 124.73 \\ ACA fused with AG & 44.80 & 86 & 17 & 24.97 \\ ACA fused with APF & 43.36 & 16 & 16 & 7.53 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the results of simulation experiments in a 30 \(\times\) 30 grid environment.  
Figure 10: _Cont._  
Figure 10: Cont.  
Figure 10: Comparative simulation experiment results in a 30 \(\times\) 30 grid environment: **(a)** simulation movement trajectory of traditional ACA (30 \(\times\) 30); **(b)** simulation convergence curve of traditional ACA (30 \(\times\) 30); **(c)** simulation of motion trajectories using ACA integrated with AG (30 \(\times\) 30); **(d)** convergence curve of ACA integrated with AG (30 \(\times\) 30); **(e)** simulation of motion trajectories using ACA integrated with APF (30 \(\times\) 30); **(f)** convergence curve of ACA integrated with APF (30 \(\times\) 30).