## 2 Research on UAV Post-Disaster Path Planning Problem  
### Problem Description  
During emergency rescue missions, UAVs need to determine the optimal flight path, through path planning, in order to reach the accident site quickly and efficiently. Due to the limitations of UAV performance, it is necessary to plan the UAV's path to ensure the avoidance of obstacles and flight risks. Additionally, suitable landing areas need to be selected based on the specific conditions of the accident site to facilitate safe landing and provide rescue services [32].  
This study utilizes a digital elevation model (DEM) to construct the simulation environment. The elevation refers to the description of the ups and downs of the terrain. The elevation model is commonly used in three-dimensional environments and is also known as a three-dimensional elevation model. The digital elevation model represents the digitalized representation of the terrain undulations using corresponding terrain data. It is a collection of plane environment coordinates \((x,y)\) and elevation data, describing the environmental distribution in the area. Real-world terrain models are a part of the digital elevation model, from which the environmental distribution can be derived [33]. Through the digital elevation model, we can obtain more relevant factors such as terrain, landforms, and spatial distribution, including altitude, central coordinates, slope, and slope variation rate, compared to a general digital terrain model.  
The information required for UAV path planning needs to be extracted from the terrain model, and effective terrain modeling can significantly improve the efficiency of path planning. This paper considers factors such as the original terrain and obstacle areas and models the environment based on mountainous terrain. The primary flight mission of the UAV is to avoid mountainous obstacles and find the optimal path to reach the target for rescue purposes. The established baseline terrain model [34] is as follows:  
\[\left\{\begin{array}{l}\mathit{center}=[x_{i},y_{i}]\\ \mathit{height}=z_{i}\\ \mathit{range}=[a_{i},b_{i},c_{i}]\end{array}\right. \tag{1}\]  
\[Z(x,y)=\sum_{i=1}^{n}h_{i}\exp\left[-\left(\frac{x-x_{i}}{x_{si}}\right)^{2}- \left(\frac{y-y_{i}}{y_{si}}\right)^{2}\right] \tag{2}\]  
\[\left\{\begin{array}{l}x_{si}=a_{i}\\ y_{si}=b_{i}\end{array}\right. \tag{3}\]  
In the equation: \(x_{i},y_{i}\) represent the point coordinates of the center of obstacle peaks in the three-dimensional environment, \(z_{i}\) represents the height of the obstacle, \(\mathit{range}\) represents the extent of the peak's expansion, \(a,b,c\) are user-defined constants that control the range and steepness of the mountain peaks. By adjusting the values of various parameters, different terrain morphologies can be obtained; \(h_{i}\) is a terrain parameter that controls the height, \(x_{si}\) and \(y_{si}\) correspond to the attenuation along the \(x\) and \(y\) axes, respectively, for the \(i\) peak, controlling the slope, \(n\) represents the total number of peaks. The environmental model is shown in Figure 1.  
The path planning nodes for the UAV in this three-dimensional environment can be represented by coordinates \((x_{i},y_{i},z_{i})\). The starting and ending points of the path are set as point (0, 0, 0) and point (100, 100, 100), respectively. Multiple obstacles are placed in the UAV operating environment, and the detailed parameter information is provided in Table 2. Therefore, the UAV path planning task can be described as finding the optimal route from the takeoff point that avoids all obstacles and reaches the target point.  
Figure 1: The environmental model.