## 3 Algorithm Design: Hybrid Voronoi-A* Framework and Pseudocode
The red * above the magenta line indicates the position where the obstacle was hit. The simulation results of the mountainous terrain clearly show that the Voronoi-A* fusion algorithm has significant advantages in path planning. By combining Voronoi layering with A* search, inter-layer flights are enabled. The number of path points is only 4.9% of that of the A* algorithm (17 vs. 349), and the planning time is reduced by 96.1% (3.36 s vs. 85.14 s). This is the only method that fully implements three-dimensional obstacle avoidance. Limitations of Traditional Algorithms: APF causes collisions with mountains due to the imbalance of the potential field; RRT has high path complexity and unstable path costs. ### Scene 2: Hilly Terrain

The same starting and ending points are set with a map scale of 1:0.2. The simulation results of the four algorithms under this terrain are as follows. 1. The planned path in the Voronoi-A* fusion algorithm simulation environment is shown in Figure 12. It can be observed that the aircraft's flight path includes an alternate flight level after climbing, enabling it to cross mountainous terrain and successfully avoid obstacles. 2. The APF algorithm's planned path in the simulation environment is shown in Figure 13. The algorithm sets initial parameters with a gravity coefficient of 15, a repulsion coefficient of 5, and an influence of 10 pixels. In a complex environment

Figure 11: Two-dimensional path planning using five algorithms for mountainous terrain. Figure 12: Simulation diagram of the Voronoi–A* fusion algorithm for scene 2.

with mountainous terrain and numerous obstacles, it is clearly evident that the aircraft's flight path directly passes through the mountains, causing the plane to crash. Moreover, the algorithm is sensitive to parameter settings. Therefore, the simulation results in this scenario indicate that the APF method is not feasible. 3. The RRT algorithm's planned path in the simulation environment is shown in Figure 14. In comparison to the self-developed Voronoi-A* fusion algorithm, the path is noticeably more convoluted and complex. Moreover, across multiple simulation scenarios, the outcome of planning--success or failure--is uncertain. In cases of successful planning, the path is complex, and computational efficiency is relatively low. 4. The planned path of the A* algorithm's simulation environment is shown in Figure 15. In this scenario, the A* algorithm has an advantage over the Voronoi-A* fusion algorithm in terms of the total path length. However, the number of planned path points and the computation time are both inferior to those of the Voronoi-A* fusion algorithm. In practical engineering applications, in terrain with relatively more obstacles, the flight complexity of the A* algorithm increases. Figure 8:0 Simulation diagram of the RRT algorithm for scene 2. Figure 8:1 Simulation diagram of the APF algorithm for scene 2. Figure 8:2 Simulation diagram of the A* algorithm for scene 2. The test results of the four algorithms in this scenario with start point (50, 55) and end point (200, 120) are compared, with statistical data shown in Figure 8:3 \(\pm\) represents the average value of the statistical results of the 20 tests carried out on each algorithm. From the hilly terrain simulation results, it is evident that the path planning efficiency of the Voronoi-A* hybrid algorithm is significantly superior, with the number of path points being only 2.6% of that in the A* algorithm (4 vs. 151), and the planning time is reduced by 76.3% (0.81 vs. 3.42 s). Additionally, the path length is nearly optimal (159.72 vs. 155.37). The failure of the APF is due to its sensitivity to parameters (gravitational coefficient of 15/repulsive coefficient of 5), which results in the flight path's collision with obstacles, rendering it ineffective in a complex scenario. ### Scene 3: Canyon Terrain

The same starting and ending points are set with a map scale of 1:0.2, and the test results of the four algorithms are as follows. 1.