## 5 Simulation Experiment and Analysis
### Path Planning Analysis
#### 5.1.2 Multi-UAV Cooperative Search Trajectories Planning Based on KD-SAC Scenario 2  
This section establishes a 1000 m \(\times\) 1000 m task area. It is assumed that within this designated area, multiple water and underwater targets are traveling in an unknown direction and same velocity but maintaining a certain distance between each other. The initial information setting for the movable targets can be found in Table 3. Furthermore, we have represented variations in the mission area's environmental complexity by setting obstacles and threat areas, which are detailed in Table 4. The experiment was conducted across two scenarios, with each scenario repeated a total of 1000 times using four algorithms. Subsequently, the path generated by each algorithm was thoroughly analyzed. Scenario 2 satisfies event attribute \(\mathcal{A}\) in knowledge base \(\alpha_{1}\) (threat areas within mission area), \(\alpha_{2}\) (obstacles within mission area), \(\alpha_{3}\) (search for underwater targets), \(\alpha_{4}\) (considered height of obstacles in the task area), and \(\alpha_{3}\) (considered number of obstacles in the task area). Furthermore, relationship condition \(\mathcal{B}\) satisfies \(\beta_{1}\) (detection). The optional action templates remain \(\chi_{1}\) (select LiDAR sensor), \(\chi_{2}\) (select underwater target detection sensor),  
Figure 5: Two UAVs searching trajectories in a barrier-free environment. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Serial Number**} & \multirow{2}{*}{**Start Point (m)**} & \multicolumn{2}{c}{**Initial Relative**} & \multirow{2}{*}{**Velocity (km/h)**} \\  & & **Angle (\({}^{\circ}\))** & \\ \hline
1 & (180, 420) & 45 & 3 \\
2 & (350, 180) & \(-\)35 & 3 \\
3 & (750, 650) & 30 & 3 \\
4 & (850, 350) & \(-\)60 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Moving target information. and \(\chi_{3}\) (perform search Rule 1). To navigate through more complex environments, all four algorithms require real-time adjustments of the UAV's attitude. Figure 6 illustrates the planned path for the UAV by these algorithms. Additionally, Table 5 presents the initial information of the UAV in this particular scenario. The complexity of the search environment increases as the number of obstacles is increased, as shown in Figure 6. Similar to Scenario 1, all UAVs select action templates \(\chi_{3}\) and execute search Rule 1. Due to the increased number of obstacles, the KD-SAC algorithm is employed to learn and adapt to the new environment, resulting in a new search rule formation. Ultimately, the paths through areas with nine obstacles (represented by black circles in the top view of Figure 6) and two threats (indicated by hemispheres in Figure 6) successfully reach the predicted target location from the start point. The peak depicted in Figure 6 represents the actual target location. Furthermore, as evident from the smoothness of pink lines in Figure 5(c),d, KD-SAC demonstrates superior path planning capabilities compared to SAC. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial Number** & **Attribution** & **Center Coordinates** & **Radius Size (m)** \\  & & **(m)** & **Radius Size (m)** \\ \hline
1 & Obstacle 1 & (350, 500, 40) & 60 \\
2 & Obstacle 2 & (600, 200, 50) & 70 \\
3 & Obstacle 3 & (500, 350, 50) & 50 \\
4 & Obstacle 4 & (300, 280, 50) & 30 \\
5 & Obstacle 5 & (700, 550, 50) & 50 \\
6 & Obstacle 6 & (650, 750, 50) & 40 \\
7 & Obstacle 7 & (800, 400, 50) & 50 \\
8 & Obstacle 8 & (300, 650, 50) & 50 \\
9 & Obstacle 9 & (500, 600, 50) & 60 \\
10 & Threat area 10 & (450, 650, 70) & 20 \\
11 & Threat area 11 & (580, 400, 80) & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Obstacle and threat location information settings.