## 3 Algorithm Design: Hybrid Voronoi-A* Framework and Pseudocode
The planned path in the Voronoi-A* fusion algorithm simulation environment is shown in Figure 8:4 It can be observed that the aircraft only requires three key waypoints to successfully navigate over obstacles at the same flight altitude, realizing successful path planning. 2. The APF algorithm's planned path in the simulation environment is shown in Figure 8:5 The parameter settings are consistent with those of the previous scene's setup. As the middle portion of the canyon terrain is relatively open, the APF computes the gravitational field to guide obstacle avoidance. Path planning is successful. The planned path is short, and time costs are relatively low. Therefore, the APF algorithm is also applicable in certain open environments. Figure 8:6 Two-dimensional path planning using four algorithms for hilly terrain. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Collision** & **Number of Waypoints** & **Length (500 m)** & **Time (S)** \\ \hline
**Voronoi–A*** & No & **4** & 159.72 & **0.81 \(\pm\) 0.18** \\
**A*** & No & 151 & 155.37 & 3.42 \(\pm\) 3.22 \\
**APF** & Yes & 193 & **138.61** & 1.51 \(\pm\) 1.16 \\
**RRT** & No & 62 \(\pm\) 21 & 201.69 \(\pm\) 23 & 75.96 \(\pm\) 55.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hilly terrain test comparison chart. * The path planning of the RRT algorithm in the simulation environment is shown in Figure 19. Compared to the Voronoi-A* fusion algorithm, the path is noticeably more winding and complex, resulting in higher computational complexity and longer computation times for real-world applications. * The planned path for the A* algorithm simulation environment is shown in Figure 20. The traditional A* algorithm can successfully navigate around obstacles. Compared to Figure 17, the number of planned path points increases, resulting in longer computation times. Figure 19: Simulation diagram of the RRT algorithm for scene 3. Figure 17: Simulation of the Voronoi–A* fusion algorithm for scene 3. Figure 18: APF algorithm simulation diagram for scene 3. The test results of the four algorithms in this scenario with start point \((10,74)\) and end point \((128,170)\) are compared, with data summarized in Table 4. \(\pm\) represents the average value of the statistical results of the 20 tests carried out on each algorithm. From the simulation results of the canyon terrain, it can be observed that the Voronoi-A* fusion algorithm for path planning has the advantage of producing extremely simplified paths. Voronoi-A* enables horizontal obstacle avoidance using only three key points, and its planning time is 13.8% of that of the RRT algorithm (0.81 s vs. 5.88 \(\pm\) 3.47 s), demonstrating its efficiency in open scenarios. The APF algorithm is sporadically applicable, successfully navigating only in canyon scenes with sparse obstacles, but the number of path points is 63 times greater than that of Voronoi-A* (190 vs. 3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Collision** &
\begin{tabular}{c} **Number of** \\ **Waypoints** \\ \end{tabular} & **Length (500 m)** & **Time (S)** \\ \hline
**Voronoi–A*** & No & **3** & **132.12** & **0.81 \(\pm\) 0.24** \\
**A*** & No & 120 & 134.28 & 3.64 \(\pm\) 2.13 \\
**APF** & No & 190 & 139.54 & 2.41 \(\pm\) 1.56 \\
**RRT** & No & 51 \(\pm\) 11 & 164.46 \(\pm\) 25 & 5.88 \(\pm\) 3.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Canyon terrain test comparison chart. Figure 21: Two-dimensional path planning using four algorithms for canyon terrain. Figure 20: A* algorithm simulation diagram for scene 3. ### Analysis of Simulation Results in Multiple Scenarios

The comprehensive performance comparison of the simulation results across multiple scenarios is shown in Table 5.

The summary in Table 5 indicates that the Voronoi-A* fusion algorithm significantly outperforms traditional algorithms in path planning performance within complex mountainous environments, as evidenced in the following aspects.