# Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory
## 4 Simulation Results
### Variation in the Number of Agents
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Parameter Values** \\ \hline Exploration domain size & 2500 m \(\times\) 3000 m \\ \hline Maximum velocity of the UAVs & 30 m/s \\ \hline Minimum velocity of the UAVs & 10 m/s \\ \hline Angular velocity limit & 30 deg/\(s\) \\ \hline Positional error gain, \(K_{x}\) & 0.4 \\ \hline Angular error gain, \(K_{\theta}\) & 1 \\ \hline UAV sensor range to detect animals, \(r_{\text{sensing}}\) & 15 m \\ \hline \multicolumn{2}{l}{Number of sample points, \(N\)} & 3600 \\ \cline{2-3}  & Number of UAV steps for each agent for exploration, \(M_{a}\) \\ \cline{2-3}  & Initial covariance for the sample point \\ \cline{2-3}  & clusters \\ \cline{2-3}  & Herd threshold & 50 m \\ \cline{2-3}  & Horizon length, \(h\) & 5 \\ \cline{2-3}  & Search radius, \(r\) & 0.1 m \\ \cline{2-3}  & Radius increment, \(\delta\) & 0.05 m \\ \cline{2-3}  & Initial robot positions & [100 m, 400 m]\({}^{T}\) \\  & [200 m, 600 m]\({}^{T}\) \\  & Initial robot positions & [200 m, 150 m]\({}^{T}\) \\  & [150 m, 400 m]\({}^{T}\) \\  & [400 m, 750 m]\({}^{T}\) \\ \cline{2-3}  & Distribution parameters for the sample point \\ \cline{2-3}  & propagation & \(r_{j,T+1}\sim\Gamma(\mu_{\gamma}=0.6\) m/s, \(\sigma_{\gamma}=0.05\) m/s) \\ \cline{2-3}  & Distribution parameters for the sample point \\ \cline{2-3}  & propagation & \(v_{j,T+1}\sim V(\mu_{\
u m}=0,k_{cm}=150)\) \\ \cline{2-3}  & \(\theta_{j,0}=v_{j,0}\sim V(\mu_{\
u m}=0,k_{cm}=0)\) \\ \hline \multirow{4}{*}{Specific parameters for LM (TI-Uni)} & Horizontal and vertical expansion factors, \(f_{X},f_{Y}\) \\ \cline{2-3}  & Distance between adjacent waypoints, \(d_{w}\) & 10 m \\ \cline{2-3}  & Spacing between adjacent vertical lines \(d_{v}\) & 120 m, 70 m, 40 m for \(n_{a}=2\), 3, 5, respectively \\ \hline \multirow{4}{*}{Simulation output} & \multirow{2}{*}{**No. of UAVs**} & **Average Detection Rate (\%)** \\ \cline{2-3}  & & **OT(TV-Gauss)** & **LM(TI-Uni)** \\ \cline{2-3}  & 2 & 40.45 & 21.08 & 19.86 \\ \cline{2-3}  & 3 & 57.72 & 27.86 & 25.85 \\ \cline{2-3}  & 5 & 74.34 & 40.31 & 36.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._monitoring area as a team, unlike the Lawn Mower method, where each agent is assigned to a pre-partitioned monitoring area. The spacing between adjacent vertical line segments \(d_{v}\) for LM (TI-Uni) varies with the number of agents such that the agents can cover most of their assigned monitoring regions within the given amount of time for exploration. With a higher number of agents, the area can be monitored thoroughly and therefore, \(d_{v}\) decreases. The discrete-time interval \(\Delta t\) is assumed to be 1 s for all simulation scenarios. Hence, 900 s exploration time corresponds to 900 robot steps for all exploration strategies, meaning that the robot positions are updated using the implemented unicycle robot dynamics in every second. For OT (TI-Uni), the initial UAV positions, the number of sample points \(N\), the total number of UAV steps for each agent for exploration \(M_{a}\), \(h\), \(r_{0}\) and \(\delta\) are the same as that for OT (TV-Gauss). Additionally, the parameters \(f_{X},f_{Y}\) to determine the monitoring area for OT (TI-Uni) is identical to \(f_{X},f_{Y}\) for LM (TI-Uni). As the initially detected animal locations can be a critical factor affecting the performance (detection rate), a total of 30 simulations were carried out by randomly generating their detected locations in the beginning. The snapshots of one specific simulation for three different monitoring strategies are presented in Figure 6 as examples. This result illustrates how different the UAV trajectories are from each other. The following scenario is considered for all the simulation cases. Among a total of 142 animals in 9 herds, only 9 animals are being tracked via the GPS trackers at time \(T=-600\) (600 s before the start of the monitoring mission).