## 3 Routing Metrics Design  
### Energy Consumption of Network Nodes  
Assuming that the initial energy of all UAV nodes in the unmanned cluster network is \(E_{start}\), the lifetime of network nodes is only related to their energy consumption without considering the damage caused by enemy attacks. The faster the energy consumption of a network node, the shorter its lifetime. Therefore, if the remaining energy of a node in the network is 0, it indicates that this node has exhausted its energy and will be separated from the network, unable to participate in subsequent data forwarding, and the network link connected to this node will also be broken. The remaining energy \(E_{left}\) of network node is calculated as follows:  
\[E_{left}=E_{start}-P_{idle}\times t-\sum_{N_{1}}E_{send}-\sum_{N_{2}}E_{recv} \tag{1}\]  
where \(P_{idle}\) represents the power consumption of the node in the idle state and \(t\) indicates the current survival time of the node. \(E_{send}\) and \(E_{recv}\) are the energy consumption for nodes when sending and receiving messages, respectively. \(N_{1}\) and \(N_{2}\) denote the number of messages sent and received by the nodes within the time period \(t\). When calculating the energy loss of unmanned cluster network nodes for sending and receiving data packets, the energy loss model of node communication adopted in this paper is shown in Figure 2.  
The energy loss of the source node when sending a k-bit data packet to the destination node at a distance of d is as follows:  
\[E_{send}(k,d)= \begin{cases}k\times E_{elec}+k\times\varepsilon_{fs}\times d^{2},d<d_{0}\\ k\times E_{elec}+k\times\varepsilon_{amp}\times d^{4},d\geq d_{0}\end{cases}  \tag{2}\]  
where \(E_{elec}\) represents the energy consumed by the node to send unit bit data (unit is J), \(\varepsilon_{fs}\) denotes the energy loss coefficient under the free space model, and \(\varepsilon_{amp}\) is the energy loss coefficient under the multipath attenuation model, with the distance threshold \(d_{0}=\sqrt{\varepsilon_{fs}/\varepsilon_{amp}}\). The energy loss of the destination node when receiving a \(k\)-bit data packet is:  
\[E_{recv}(k)=k\times E_{elec} \tag{3}\]  
where \(E_{elec}\) represents the energy consumed by nodes to receive unit bit data (unit is J). Then, the energy loss rate \(C_{i}\) of any node i in the network is as follows:  
\[ \begin{array}{ll}C_{i}&=1-\eta_{i}\\ &=\left(1-\frac{E_{i\_left}}{E_{i\_start}}\right)\times 100\%\\ &=\frac{E_{i\_start}-\left(E_{i\_start}-P_{idle}\times t_{i}-\sum\limits_{N_{ 1}}E_{i\_send}-\sum\limits_{N_{2}}E_{i\_recv}\right)}{\frac{E_{i\_start}}{E_ {i\_start}}}\times 100\%\\ &=\frac{P_{idle}\times t_{i}+\sum\limits_{N_{1}}E_{i\_send}+\sum\limits_{N_{ 2}}E_{i\_recv}}{E_{i\_start}}\times 100\%\end{array}  \tag{4}\]  
where \(\eta_{i}\) denotes the energy residual rate of node \(i\), \(E_{i\_start}\) represents the initial energy of node \(i\), \(E_{i\_left}\) is the remaining energy of node \(i\) at this moment. Figure 2: Network node communication energy loss model. Thus, it can be seen that the more times a node participates in message forwarding in the network, the more energy it consumes, and the greater the energy loss rate becomes. However, when measuring the lifetime of network nodes, it is not accurate to only rely on the energy loss rate of nodes. If a node in the network exhibits a high energy loss rate but is situated at the network's periphery, resulting in fewer subsequent message forwarding opportunities, its overall lifetime will become longer. Therefore, this paper introduces the concept of node degree in order to accurately judge the lifetime of network nodes. When the degree of a node in the network exceeds the average degree of the network nodes, it indicates that this node has more one-hop neighbors and will consequently undertake more message forwarding tasks, leading to an increasing trend in energy depletion. Conversely, if a node's degree is below the average, the energy depletion trend will decrease.