# Research on Path Planning Based on the Integrated Artificial Potential Field-Ant Colony Algorithm
## 5 Algorithm Simulation and Analysis
### A 20 \(\times\) 20 Grid Map  
Firstly, a 20-order grid matrix was simulated, with the obstacle distribution randomly set. The starting node was set as the grid with the serial number 1, with coordinates (0.5, 19.5), and the target node was set as the grid with the serial number 400, with coordinates (19.5, 0.5). In order to verify the validity of the algorithm proposed in this paper, this study conducted simulation experiments on the traditional ACA, the GA-ACA proposed in the literature [25] and the improved ACA after optimizing the HF, the pheromone evaporation factor and the pheromone updating mechanism. The robot path trajectory graphs and convergence curve graphs were obtained by simulating the experimental process of the three algorithms with rigorous parameter settings and operations, and each algorithm was run 100 times to find the optimal path. These experimental results are shown in Figure 8, which visualizes the performance of different algorithms in PP.  
In Figure 8, the conventional ACA forms a zigzag path trajectory, whereas the GA-ACA and the improved ACA proposed in the literature [25] tend to  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Letter Code** & **Value** \\ \hline Ant population & \(M\) & 50 \\ Iteration times & \(K\) & 200 \\ Importance factor of PC & \(\alpha\) & 1 \\ Importance factor of HF & \(\beta\) & 4 \\ Pheromone evaporation degree factor & \(\rho\) & 0.7 \\ Total pheromone amount & \(Q\) & 10 \\ Influence factor of APF attraction & \(a\) & 0.3 \\ Gravity gain coefficient & \(k\) & 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Configuration of basic parameters for simulation experiments.  
Figure 7: Effect of parameter \(\rho\) on path length.  
the grid. Meanwhile, the path obtained by the improved ACA has fewer corners compared to GA-CA. Therefore, the algorithm proposed in this study can find shorter, smoother and faster converging paths.  
HF improvement, pheromone evaporation factor, and pheromone update mechanisms, as detailed in Table 2, are evidenced by comparing them with a conventional ACA and GA-ACA when resolving path problems that the upgraded performance ACA has successfully surpassed. Compared with the traditional algorithm, the advanced path optimization method reduces the path length by 8.14%, the number of convergence iterations by 91.36%, the path turning points by 15.38%, and the running time by 61.34%. Compared to GA-ACA, the advanced path optimization method reduces the path length by 3.85%, the number of convergence iterations by 22.22%, the path turning points by 8.33%, and the runtime by 47.35  
Figure 8: Cont.  
Figure 8: Comparative simulation experiment results in a \(20\times 20\) grid environment: **(a)** simulation movement trajectory of traditional ACA (\(20\times 20\)); **(b)** simulation convergence curve of traditional ACA (\(20\times 20\)); **(c)** simulation of motion trajectories using ACA integrated with GA (\(20\times 20\)); **(d)** convergence curve of ACA integrated with GA (\(20\times 20\)); **(e)** simulation of motion trajectories using ACA integrated with APF (\(20\times 20\)); **(f)** convergence curve of ACA integrated with APF (\(20\times 20\)).  
Figure 9: Results of pruning processing in a \(20\times 20\) grid environment.