## 4 Simulation Experiment and Result Analysis
### The Impact of the Yav Cost on Search Effectiveness  
The analysis of the yaw cost \(Cost_{turn}\) follows the same methodology used to examine the impact of \(D_{wp,1}\) on search effectiveness, focusing on the effects of incorporating \(Cost_{turn}\) into the UAV decision-making algorithm. As shown in Figures 13 and 14, similar to the case without \(Cost_{turn}\), the influence of \(D_{wp,1}\) on the indicators is significantly smaller than that of \(N_{UAAV}\). However, Figures 14b and 15b reveal that increasing \(Cost_{turn}\) slightly reduces the target capture rate while increasing the average capture time. As shown in Figures 15 and 16, the trend of the influence of \(N_{UAAV}\) and \(D_{wp,1}\) on the average capture time and average decision frequency with \(Cost_{turn}\) is consistent with that without \(Cost_{turn}\). Table 1 lists the average coverage rate \(\overline{r}_{cover}\), average capture rate \(\overline{r}_{capture}\), average capture time \(\overline{r}_{capture}\), and average decision frequency \(\overline{N}_{D,\overline{J}}\) for all combinations of \(N_{UAAV}\) and \(D_{wp,1}\) values, both with and without \(Cost_{turn}\). Considering these four indicators collectively, the swarm's collaborative search effectiveness is improved when UAV decision-making incorporates \(Cost_{turn}\), albeit at the cost of increased communication and decision-making consumption per UAV. Figure 11: Comparison of average capture time trends: (**a**) \(N_{UAAV}\); (**b**) \(D_{wp,1}\). Figure 12: Average number of decision frequencies per UAV under different \(N_{UAAV}\) and \(D_{wp,1}\). Figure 17a,b illustrate the ratio of average turning time to total flight duration \(r_{turn}\) without and with \(Cost_{turn}\) respectively. The average values of \(r_{turn}\) are 0.574 and 0.481, demonstrating that incorporating \(Cost_{turn}\) into the path-planning algorithm significantly reduces \(r_{turn}\). Figure 14: When considering \(Cost_{turn}\), a comparison of target capture rate trends: (**a**) \(N_{UAV}\); (**b**) \(D_{up,1}\). Figure 13: When considering \(Cost_{turn}\), a comparison of coverage rate trends: (**a**) \(N_{UAV}\); (**b**) \(D_{up,1}\). Figure 15: When considering \(Cost_{turn}\), a comparison of average capture time trends: (**a**) \(N_{UAV}\); (**b**) \(D_{up,1}\). The difference in \(r_{turn}\) explains the variation in search effectiveness with and without \(Cost_{turn}\). First, while the path grid determination algorithm extracts situation information from distant paths to calculate path costs, it does not limit the time UAVs spend circling near the previous waypoint. Incorporating \(Cost_{turn}\) into the cost function effectively mitigates this issue, reducing redundant searches caused by excessive circling. Second, as observed in Table 1, \(\overline{N}_{D\tilde{I}}\) is higher with \(Cost_{turn}\) than without it. This is because minimizing the circling time near the previous waypoint allows the UAVs to reach the next waypoint more quickly via straight-line flight, facilitating faster information exchange and decision making, thereby accelerating the OODA cycle and improving search effectiveness. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Conditions** & **Effectiveness Indicators** & **Result** \\ \hline \multirow{4}{*}{Without \(Cost_{turn}\)} & \(\overline{r}_{cover}\) & 0.811 \\  & \(\overline{r}_{capture}\) & 0.875 \\  & \(\overline{t}_{capture}\) & 135.32 \\  & \(\overline{N}_{D\tilde{I}}\) & 1.303 \\ \hline \multirow{4}{*}{With \(Cost_{turn}\)} & \(\overline{r}_{cover}\) & 0.827 \\  & \(\overline{r}_{capture}\) & 0.898 \\  & \(\overline{t}_{capture}\) & 126.65 \\  & \(\overline{N}_{D\tilde{I}}\) & 1.407 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of various indicators without and with \(Cost_{turn}\). Figure 16: Average number of decision frequencies per UAV under different with \(Cost_{turn}\) under different \(N_{UAAV}\) and \(D_{up,1}\). Figure 17: Comparison of \(r_{turn}\): (**a**) without \(Cost_{turn}\); (**b**) with \(Cost_{turn}\).