## 4 Experimental Results and Discussion of IHSSAO Performance Verification
### UAV Path Planning Modeling  
In order to plan a high-quality flight trajectory that satisfies the constraints, it is necessary to establish a suitable fitness function and consider various constraints. The major indicators that affect the performance of UAVs include trajectory length, flight altitude, minimum step length, turning angle cost, maximum climb angle, etc. According to the above UAV flight trajectory constraint, the expression of the cost function is as follows [2]:  
\[J_{cost}=\omega_{1}I_{path}+\omega_{2}I_{height}+\omega_{3}I_{turn},(\omega_{1}+ \omega_{2}+\omega_{3}=1;\;\omega_{i}\geq 0) \tag{29}\]  
where \(J_{cost}\) is the total cost function and the parameters \(\omega_{i},\;i=1,2,3\) represent the weights of each cost function and satisfy \(\omega_{1}+\omega_{2}+\omega_{3}=1\) and \(\omega_{i}\geq 0\). \(J_{path}\), \(J_{height}\), and \(I_{turn}\) represent the path length cost, flight altitude cost, and corner cost of UAV, respectively.  
The length of the trajectory is also very significant for most flight missions in the UAV path planning process. As we all know, shorter paths save more fuel and more time, and have a lower chance of finding unknown threats. Assuming that there are \(n\) waypoints in a complete path, the path cost expression is as follows:  
\[J_{path}=\left\{\begin{array}{l}\infty,\;\text{{pass the obstacles}}\\ \sum\limits_{i=1}^{n-1}l_{i},\;\text{otherwise}\\ l_{i}=\left\|(x_{i+1},y_{i+1},z_{i+1})-(x_{i},y_{i},z_{i})\right\|_{2}\end{array}\right. \tag{30}\]  
where \(l_{i}\) denotes the distance between the \(i\)th waypoint and the \(i+1\)th waypoint. Furthermore, \((x_{i},\;y_{i},\;z_{i})\) and \((x_{i+1},\;y_{i+1},\;z_{i+1})\) are the coordinates of the \(i\)th waypoint and \(i+1\)th waypoint, respectively.  
In general, if the UAV is flying at a low altitude in complex mountain terrain, it will easily collide with the grounds and mountains. However, if the UAV flight height is too high, it will also increase fuel costs and the risk of being detected by radar. Therefore, it is very essential for the UAV to keep a stable flight altitude. In order to have a safe UAV flight, we give the following flight height cost \(J_{height}\) model.  
\[J_{height}=\sqrt{\frac{1}{n}\sum\limits_{i=0}^{n-1}(z(i)^{2}- \overline{z})^{2}} \tag{31}\] \[\overline{z}=\frac{1}{n}\sum\limits_{i=0}^{n-1}z(i)\]  
Furthermore, the maneuverability of UAVs is also limited by their turning angle cost function. During the UAV's mission, its turning angle should be less than or equal to the pre-set maximum turning angle \(\phi\), because the size of the turning angle affects the stability of its flight. The cost function model of turning angle is described as follows.  
\[J_{turn}=\left\{\begin{array}{l}\infty,\;if\;\phi<\theta_{i}\\ \sum\limits_{i=1}^{n}\left(\cos\phi-\cos\theta_{i}\right),\;otherwise\\ \cos\theta=\frac{a_{i}^{T}a_{i+1}}{|a_{i}||a_{i+1}|}\end{array}\right. \tag{32}\]  
where \(\theta_{i}\) represents the \(i\)th turning angle and \(a_{i}\) denotes a vector of the \(i\)th part of the whole path.  
By efficiently processing the total cost function, we can obtain the trajectory consisting of line segments. It is undeniable that the obtained paths are often only theoretically feasible, but for practical flyability, it is necessary to smooth the paths Smoothing. In this paper, we apply cubic spline interpolation to smooth the flight trajectory of UAVs.