# Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory
## 4 Simulation Results
### Variation in the Number of Agents  
Since one of the parameters that significantly affect the monitoring performance (detection rate) is the number of agents, we test how the different number of UAVs results in the performance variation. The simulations were carried out with the following simulation parameters presented in Table 1, which also includes the major outputs of the simulations. \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 No. of agents & 2, 3, 5 (for each strategy) \\ \hline No. of simulations & 30 (for each strategy with a specific no. of agents) \\ \hline Exploration time & 900 s \\ \hline Time delay & 600 s \\ \hline No. of animal herds & 9 \\ \hline Initial locations (m) of the animal herds and populations in each herd & 3: \([150,750]^{T}\), \(15\), \(6\): \([150,750]^{T}\), \(15\), \(6\): \([150,750]^{T}\), \(15\), \(6\): \([150,750]^{T}\), \(15\), \(8\): \([700,300]^{T}\), \(13\) \\ \hline \multirow{4}{*}{Initial GPS tracker information for 9 tracked animals (m)} & 1: \([-0.58,402.60]^{T}\), \(2\): \([402.11,651.83]^{T}\) \\  & 3: \([296.22,398.91]^{T}\), \(4\): \([297.10,396.19]^{T}\) \\ \cline{1-1}  & 5: \([151.90,747.73]^{T}\), \(6\): \([199.65,205.11]^{T}\) \\ \cline{1-1}  & 7: \([503.16,496.32]^{T}\), \(8\): \([404.92,648.39]^{T}\) \\ \cline{1-1}  & 9: \([305.28,403.58]^{T}\) \\ \hline \multirow{4}{*}{Estimated herd center (m) from Section 3.3 with tracked animal no.} & 1: \([299.53,399.56]^{T}\), \(3.49,\) \(2\): \([151.90,747.73]^{T}\), \(5\) \\ \cline{1-1}  & 3: \([-0.58,402.60]^{T}\), \(1\), \(4\): \([503.16,496.32]^{T}\), \(7\) \\ \cline{1-1}  & 5: \([403.52,650.11]^{T}\), \(2.8\), \(6\): \([199.65,205.11]^{T}\), \(6\) \\ \hline \multirow{4}{*}{Distribution parameters for animal herd movement} & \(r_{u,T+1}\), \(r_{k,T+1}\sim\Gamma(\mu_{T}=0.4\) m/s, \(\sigma_{\gamma}=1\) m/s) \\ \cline{1-1}  & \(v_{u,T+1}\sim\Gamma(\mu_{em}=0,\)\(k_{em}=100)\) \\ \cline{1-1}  & \(v_{k,T+1}\sim V(\mu_{em}=0,\)\(k_{em}=2)\) \\ \cline{1-1}  & \(-90^{\circ}\leq v_{u,T+1}\leq 90^{\circ}\) \\ \cline{1-1}  & \(\theta_{u,0}=v_{u,0}\sim V(\mu_{em}=0,\)\(k_{em}=0)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for simulation performed for variation of number of UAVs. The time delay (or equivalently the traveling time) in this context indicates the total time for the UAVs to travel from the base station to the monitoring region. The UAVs are regarded as having a monitoring mission when they arrived at the predefined initial positions for the monitoring. OT (TI-Uni) is implemented to compare the performance with the proposed scheme, OT (TV-Gauss). Similar to the Lawn Mower method, an initial rectangular exploration area for OT (TI-Uni) method is determined from the animal locations obtained from the GPS trackers by (11). Next, the total exploration area is determined from the initial search area using (12). Then, this area is filled with randomly generated sample points with uniform distribution. Based on this uniform sample point representation, multiple UAVs carry out the monitoring mission using the three-stage approach. All agents explore the