# Connectivity Maintenance Based on Multiple Relay UAVs Selection Scheme in Cooperative Surveillance
## 5 Numerical Results
The instantaneous UAVs network topologies are depicted in Figure 6, where the ground station is expressed by red diamond, and the triangles with different colors represent three relevant roles in cooperative surveillance. The Figure 6a represents that the most of UAVs can directly communicate with ground station at the beginning of simulation, and relay UAV is unnecessary. With some UAVs beyond effective communication range of ground station, some UAVs are chosen as relays to establish communication links at 20 s depicted in Figure 6b, and the relay UAV alternatives sequence \(V_{seq}\) is calculated by ground station as \(\{3,2,1,5,4,6\}\). Combined with the current relay UAVs number \(N_{R}=1\), UAV3 is selected as relay to provide communication linking service, and UAV2 serves as AUAV connecting remote SUAVs swarm and UAV3. While SUAVs swarm is away from ground station, UAV2 subsequently converts role to RUAV and UAV1 serves as AUAV for surveillance range expansion at 30 s as Figure 6c. With the surveillance scope expansion, the communication links gradually increase with multiple relay UAVs selection scheme, and more unknown regions can be detected at 50 s, which is described in Figure 6d. Comparing with the last two subfigures, the relay UAVs number is dynamically adjusted by the relationship among UAVs with surveillance scope change. According to the instantaneous network topologies, it is concluded that some UAVs gradually transform roles to stretch communication links and expand search scope based on multiple relay UAVs selection scheme, and all potential target existence regions are detected by UAVs over time. In cooperative surveillance, multiple relay UAVs are appropriately chosen by fuzzy optimum selection,  
Figure 6: Network topologies in multiple UAVs cooperative surveillance at different instants: (**a**) 5 s; (**b**) 20 s; (**c**) 30 s; (**d**) 50 s; (**e**) 100 s; (**f**) 150 s. The red triangle means RUAV and the blank represents AUAV, and the remaining cyan one is SUAV. and communication links are dynamically adjusted by relationship among UAVs with surveillance scope change. It is concluded that balance between surveillance payoff and network connectivity can be guaranteed by the proposed multiple relay UAVs selection scheme. The cooperative surveillance payoff curve is depicted in Figure 7. One can see that the payoff curve is growing quickly with surveillance scope expansion over time. All unknown and potential target existence regions are searched and detected by multiple UAVs in a short time, and maximum surveillance payoff can be obtained, which represents that the effectiveness of the proposed method. Due to the dispersed target distributions and network connectivity with ground station, the payoff curve slowly grows in some periods. Figure 8 shows the topology connectivity and minimum distance between UAVs. The network connectivity depicted in the above subfigure is described by the second smallest eigenvalue of the Laplacian matrices, namely \(\lambda_{2}\) The value of \(\lambda_{2}\) gradually decreases over time, which means that the communication links extension with the surveillance UAVs swarm is far away from ground station over time. Moreover, \(\lambda_{2}\) is always larger than zero, and network connectivity is guaranteed in entire simulation based on multiple relay UAVs selection scheme, meanwhile multiple UAVs cooperative surveillance mission is commendably completed. The minimum distance between pair of UAVs is  
Figure 8: Topology connectivity and minimum distance between UAVs. Figure 7: Surveillance payoff in multi UAVs cooperative surveillance. depicted in the bottom subfigure, which is always larger than the minimum safe distance. Figure 8 indicates the validity of penalty function for connectivity maintenance and collision avoidance.