## 4 Experiment
### Randomized-Map Experiment  
In this paper, maps consisting of 125 grids, 343 grids, 1000 grids, 2179 grids, 3375 grids, 4913 grids, and 8000 grids are used in the design of the randomness maps, and the percentage of obstacles in each map is 20% to 40%. The computation time, space occupation rate, number of path nodes, path length, and total path-turning angle of the 3D JPS algorithm, 3D A* algorithm, RRT algorithm, and Theta* algorithm are summarized and analyzed, respectively. In the simulation experiments, the Euclidean distance formula is uniformly chosen as the distance calculation of the heuristic function in this paper. The experimental results were taken from the average of 10 experiments. The simulation results are partially shown in Figure 15 below. Figure 15: _Cont._  
As can be seen in Figure 15, the 3D JPS algorithm can complete the global path planning in 3D space with different sizes and different obstacle occupancy of the map. The data of the four algorithms involved in the experimental comparison process are further presented and explained. In terms of the time complexity of the algorithm, the 3D JPS algorithm had a better performance in the comparison of the four spatial-pathfinding algorithms, as shown in Figure 16. However, it is very obvious that as the number of map grids and the percentage of obstacles increased, all four algorithms used in the experimental process invariably showed an increase in algorithm computation time. In the same map environment, the 3D JPS algorithm had the lowest computation time and the Theta* algorithm had the highest computation time. The 3D JPS algorithm reduced the computation time by 88.45% to 30.18% compared to the 3D A* algorithm and by 34.83% to 4.75% compared to the RRT algorithm. Analyzing the average growth rate of the algorithm's computation time, we can find that the 3D JPS algorithm will improve the computation time by 0.45% to 1.18% for every 10% increase in the number of grids with the same percentage of obstacles. With the same number of grids in the map, the computation time of the 3D JPS algorithm will be improved by 46.98% to 153.31% for every 10% increase in obstacle percentage. It can be seen that the percentage of the number of obstacles has a large impact on the computation time of the 3D JPS algorithm. Figure 15: Experimental comparison of algorithms based on randomness maps. (**a**) Obstacles accounted for 20%. (**b**) Obstacles accounted for 30%. (**c**) Obstacles accounted for 40%. (**d**) Obstacles accounted for 20%. (**e**) Obstacles accounted for 30%. (**f**) Obstacles accounted for 40%. (**g**) Obstacles accounted for 20%. (**h**) Obstacles accounted for 30%. (**i**) Obstacles accounted for 40%. (**j**) Obstacles accounted for 20%. (**k**) Obstacles accounted for 30%. (**l**) Obstacles accounted for 40%. The analysis was performed in terms of the memory usage of the algorithm, as shown in Figure 17. The RRT algorithm had the lowest memory usage among the four algorithms, followed by the 3D JPS algorithm, while the Theta* algorithm had the highest memory usage. The memory usage of the 3D JPS algorithm was 28.72% to 48.32% higher compared to the RRT algorithm and 2.72% to 37.78% lower compared to the A* algorithm. The memory footprint of all four algorithms increased as the map size and obstacle percentage increased. The number of grids was increased by 10% at a time for a map with the same percentage of obstacles. The RRT algorithm had the highest average growth rate of 4.89% in memory usage. The Theta* algorithm had the lowest growth rate of 1.31%. The 3D JPS algorithm had an average growth ratio of 2.26% in the middle region of memory occupation. Figure 16: Experimental comparison of algorithms based on randomness maps. (**a**) Obstacles accounted for 20%. (**b**) Obstacles accounted for 30%. (**c**) Obstacles accounted for 40%. Figure 17: Algorithm memory usage comparison. (**a**) Obstacles accounted for 20%. (**b**) Obstacles accounted for 30%. (**c**) Obstacles accounted for 40%.