# A Coalition Formation Game Approach for Efficient Cooperative Multi-UAV Deployment
## 2 System Model and Problem Formulation  
We consider a UAV-assisted sensor network employing \(N\) distributed UAVs and one central control UAV, where UAV groups perform reconnaissance and data collection tasks under disaster scenarios. UAVs communicate with each other through radio frequency (RF) signals of wireless sensors. The sensor devices are equipped on UAV's fuselage. Sensor devices have limited battery power and data processing capabilities. They can also acquire the location of other sensor nodes (UAV). The UAV groups need to collect data information by covering the ground. Here, UAV's coverage capability is determined by observation thresholds. Then, the data traffic collected by distributed UAVs is sent to the central UAV for processing. Due to the huge energy consumption caused by long distance transmission, it requires forming groups and utilizes some UAV sensor nodes as relays to carry out data transmission. For the cooperative multi-UAV deployment example showed in Figure 1, there are seven UAVs performing coverage mission and uploading the collected information data to the upper central UAV. Due to the limited energy of sensor devices, UAVs need to form groups to cooperate. In this case, some UAVs are used as relays to optimize the energy consumption of data transmission. In particular, the high transmission energy consumption between UAVs that are too far apart (such as UAV 1 and UAV 7) prevents the formation of the grand coalition. Therefore, it makes sense to consider the coalition formation by optimizing the coverage utility of the UAV network. To facilitate computation, we discretize the continuous area \(I\in R^{2}\), which is uniformly meshed and divided into cells, and each cell \(i\)'s width is \(l_{w}\) and is identified by the position of its center \(g_{i}^{*}=\{x_{i},y_{i},h_{i}\}\). Denote the number of available coalitions as \(M,1\leq M\leq N\), and the set of UAVs as \(\mathcal{N}\), i.e., \(\mathcal{N}=\{1,2,\ldots,N\}\), and the set of available coalition as \(\mathcal{M}\), i.e., \(\mathcal{M}=\{1,2,\ldots,M\}\). The serial number of the central UAV is set to 0. For each \(n\in\mathcal{N}\), let \(c_{n}\) denote UAV \(n\)'s coalition selections, \(g_{n}=\{x_{n},y_{n},h_{n}\}\) denotes UAV \(n\)'s three-dimensional position. Hence, the UAV \(n\)'s state is defined as \(s_{n}=\{g_{n},c_{n}\}\). For each \(m\in\mathcal{M}\), let \(CO_{m}\) denote the set of UAVs which select coalition \(m\) for data transmission, i.e, \(CO_{m}=\{n\in\mathcal{N}:c_{n}=m\}\). In addition, the central UAV's position is denoted as \(g_{0}=\{x^{*},y^{*},h^{*},h^{*}>h\}\). For each \(i\in I\), suppose that \(\sigma(i)\) is the importance (traffic, etc.) of mission cell \(i\), and is denoted by the form of a normalized density function. For simplicity, we set \(U_{\xi}\) as the reward for UAV set \(\xi\) completing the coverage of mission area \(I\) successfully, which is given as follows [1]:  
\[U_{\xi}=\int\limits_{I}h\big{(}\min\limits_{n\in\xi}\|g_{n}-g_{i}^{*}\|\big{)} \sigma(i)di, \tag{1}\]where  
\[h(\|g_{n}-g_{i}^{*})\|)= \begin{cases}1,&\|g_{n}-g_{i}^{*})\|\leq R_{n},\\ 0,&\quad\text{otherwise}.\end{cases}  \tag{2}\]  
Equation (2) indicates that, as long as area \(i\) is within the detection range of UAV \(n\) in the network, it will be considered successfully covered by UAV \(n\) with all data traffic collected. Hence, \(U_{\xi}\) represents the coverage performance (says reward) of mission area \(I\) under UAV set \(\xi\). In particular, the overall coverage reward of UAV network is \(U_{\mathcal{N}}\). From the above description, data traffic collected by distributed UAVs will be transmitted through the UAV-to-UAV link to the central control UAV for processing. In the UAV-assisted sensor network, most of the power energy consumed by wireless sensors is derived extensively from a transmission operation that consists of sending and receiving.