# Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory
## 4 Simulation Results
### Variation in Exploration Time  
In order to investigate the effect of exploration time on the performance, other simulations were conducted with the simulation parameters provided in Table 2. Since most of the simulation parameters for this case are identical to the parameters for the previous scenario, only the parameters different from the previous ones are provided in Table 2. The parameters \(f_{X}\), \(f_{Y}\) and \(d_{v}\) for LM (TI-Uni) are adjusted such that the UAVs can explore most of the regions within the corresponding exploration time. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Parameter Values** \\ \hline Exploration strategies & 3 (OT (TV-Gauss), LM (TI-Uni), OT (TI-Uni)) \\ \hline Exploration time & 900, 1800, 3600 s (for each strategy) \\ \hline No. of UAVs & 3 \\ \hline Time delay & 600 \\ \hline No. of simulations & 30 (for each strategy with a specific exploration time \\ \hline Initial UAV positions (m) (OT(TV-Gauss) and OT(TI-Uni)) & \([-100,900]^{T}\) \\ \([200,600]^{T}\) \\  & \([500,150]^{T}\) \\ \hline \multirow{6}{*}{Parameters varied with exploration time} & **Exploration Time** \\ \cline{2-3}  & **900** \\ \cline{2-3}  & **900** \\ \cline{2-3}  & Exploration domain size(m\({}^{2}\)) & 2500 \(\times\) 2500 \\ \cline{2-3}  & \(2500\times\) 2500 \\ \cline{2-3}  & Number of UAV steps for each agent \\ \cline{2-3}  & for exploration, \(M_{a}\) (OT(TV-Gauss)) \\ \cline{2-3}  & Horizontal and vertical expansion \\ \cline{2-3}  & factors, \(f_{X}\), \(f_{Y}\) (LM(TI-Uni)) \\ \cline{2-3}  & Spacing between adjacent vertical \\ \cline{2-3}  & lines \(d_{v}(m)\) (LM(TI-Uni)) \\ \hline \multirow{6}{*}{Simulation output} & **Exploration Strategy** \\ \cline{2-3}  & **900** \\ \cline{2-3}  & OT (TV-Gauss) \\ \cline{2-3}  & LM (TI-Uni) \\ \cline{2-3}  & OT (TI-Uni) \\ \cline{2-3}  & OT (TI-Uni) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters for simulations performed for variation of exploration time. Figure 7: Statistical data for the performance comparison among OT (TV-Gauss), OT (TI-Uni), and LM (TI-Uni) with the variation in the number of UAVs: (**a**) \(n_{a}=2\); (**b**) \(n_{a}=3\); and (**c**) \(n_{a}=3\). Mean values for the boxplots are indicated by the asterisk symbols. Similar to the simulation for the variation in the number of agents, there are total of 9 tracked animals and 12 Gaussian sample point distributions are generated at the estimated herd centers and then, propagated in every time step. If an animal is detected by the UAVs, a sample distribution is assigned to the detected animal herd and the center of that distribution is relocated to the detected animal's location. The snapshots of one particular simulation result (when the exploration time is 1800 s with a time delay of 600 s) are provided in Figure 8, to illustrate the UAV trajectories. For OT (TV-Gauss) in Figure 8a-c, the three UAVs detected a total of 93 animals out of 142 (detection rate: 65.49%), whereas the detection rate for LM (TI-Uni) and OT (TI-Uni) were 28.87% and 10.56%, respectively. Figure 8: Snapshots of different monitoring strategies when the exploration time is given by 1800 s: (**a–c**) OT (TV-Gauss); (**d–f**) LM (TI-Uni); (**g–i**) OT (TI-Uni). The negative time indicates the time to travel from the base station to the pre-specified location before the initiation of the monitoring mission. The monitoring mission starts at \(T=1\) s and continues until 1800 s.  
The statistical data for a total of 30 simulation runs are presented in Figure 9 for three different exploration times (900, 1800, and 3600 s). Also, the average detection rates for different exploration times are provided in Table 2. These results show that increasing the exploration time resulted in the decrease of the average detection rate for all monitoring strategies, which is because the domain size has increased as well with the exploration time increase.