## 4 Experiment
### 3D JPS Algorithm Trajectory Optimization Experiment Based on Open Dataset  
In this paper, we use the maps of London, Boston, and New York City Center from the public database of Moving AI Lab and the mountain areas from the GIS map database to compare the resultant paths of the 3D JPS algorithm, the parent node transfer rule, and the polynomial interpolation optimization, respectively. This is to verify the effectiveness and realism of trajectory optimization based on path generation by the 3D JPS algorithm. In this paper, the path after parent node optimization is abbreviated as PNP-JPS; then, the path after the polynomial-interpolation optimization is abbreviated as OP-PNP-JPS for the convenience of presentation. The experimental results are shown below. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Map Name** & **Algorithm Type** & **Path Length (m)** & \begin{tabular}{c} **Total Turning Angle** \\ **of the Path (°)** \\ \end{tabular} & \begin{tabular}{c} **Calculation** \\ **Time (s)** \\ \end{tabular} & \
\begin{tabular}{c} **Memory Usage** \\ **(kb)** \\ \end{tabular} &
\begin{tabular}{c} **Number of Nodes** \\ \end{tabular} \\ \hline \multirow{2}{*}{mountain region 1} & JPS3d & 156.385 & 1976.610 & 9.848 & 12,678.968 & 108 \\  & PNP-JPS3d & 144.965 & 421.465 & 10.029 & 12,679.540 & 14 \\  & OP-PNP-JPS3d & 144.966 & NULL & 10.384 & 12,681.331 & 501 \\ \hline \multirow{2}{*}{mountain region 2} & JPS3d & 125.187 & 1011.851 & 12.120 & 14,137.523 & 91 \\  & PNP-JPS3d & 115.041 & 183.576 & 12.302 & 14,138.243 & 11 \\  & OP-PNP-JPS3d & 115.148 & NULL & 12.421 & 14,138.492 & 495 \\ \hline \multirow{2}{*}{mountain region 3} & JPS3d & 137.329 & 1515.288 & 8.795 & 14,991.102 & 94 \\  & PNP-JPS3d & 130.699 & 732.246 & 9.035 & 14,991.821 & 25 \\  & OP-PNP-JPS3d & 130.700 & NULL & 9.506 & 14,992.329 & 507 \\ \hline \multirow{2}{*}{London} & JPS3d & 82.332 & 546.057 & 5.503 & 9217.221 & 16 \\  & PNP-JPS3d & 78.036 & 143.024 & 5.580 & 9218.319 & 10 \\  & OP-PNP-JPS3d & 78.038 & NULL & 5.739 & 9218.970 & 477 \\ \hline \multirow{2}{*}{New York} & JPS3d & 93.629 & 1195.529 & 6.946 & 9679.211 & 33 \\  & PNP-JPS3d & 87.548 & 255.291 & 7.171 & 9680.490 & 11 \\  & OP-PNP-JPS3d & 87.550 & NULL & 7.233 & 9680.992 & 483 \\ \hline \multirow{2}{*}{Boston} & JPS3d & 113.470 & 520.528 & 9.603 & 10,149.380 & 25 \\  & PNP-JPS3d & 107.483 & 35.567 & 9.787 & 10,150.194 & 4 \\ \cline{1-1}  & OP-PNP-JPS3d & 107.284 & NULL & 9.871 & 10,150.870 & 499 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Map information selected for the dataset. Figure 19: Three-dimensional JPS algorithm generates paths and its trajectory optimization path comparison experiment. (**a**) Map of the mountain region 1. (**b**) Map of London. (**c**) Map of the mountain region 2. (**d**) Map of New York. (**e**) Map of the mountain region 3. (**f**) Map of Boston. As shown in Figure 19, the optimized 3D JPS algorithm based on the parent node transfer law cuts out a large number of unnecessary turnaround nodes and further reduces the total length of the generated paths. The seventh-order polynomial-interpolation optimization based on the minimum snap again smooths the path to ensure the continuity and smoothness of the position, velocity, acceleration, and jerk of the generated path at each interpolation node, while using the snap as the optimization goal further ensures that the final generated path is the path with the least energy consumption by the drone. In this paper, the experimental results are presented as shown in Table 1.  
From Table 1, it can be seen that the optimized path based on the parent node transfer law removes unnecessary redundant turning points from the path generated by the 3D JPS algorithm, making the optimized path length and smoothness better than the original path.