## 3 Routing Metrics Design
### Relative Mobility of Network Nodes  
In the unmanned cluster network, each UAV node is always moving at a high speed, and the relative position between the nodes is changing rapidly, which leads to the frequent occurrence of network link breakage. Therefore, the relative mobility of nodes at both ends of the link should be fully considered in the establishment of routing in the unmanned cluster network, and the motion state of the two nodes should be as close as possible to ensure the reliability and stability of information transmission to the greatest extent.  
Each node in the unmanned cluster network is equipped with multi-source sensors, which allow it to obtain its own position and speed information in real time during the movement process. Therefore, the relative moving speed \(v_{i,j}\) between any two nodes \(i\) and \(j\) in the network can be expressed as:  
\[v_{i,j}=\sqrt{\left(v_{i,x}-v_{j,x}\right)^{2}+\left(v_{i,y}-v_{j,y}\right)^{2 }+\left(v_{i,z}-v_{j,z}\right)^{2}} \tag{6}\]  
where \(v_{i,x}\), \(v_{i,y}\) and \(v_{i,z}\) are the velocity components of node \(i\) in the \(x\), \(y\) and \(z\) axes, respectively; \(v_{i,x}\), \(v_{i,y}\) and \(v_{i,z}\) are the velocity components of node \(j\) in the \(x\), \(y\) and \(z\) axes, respectively. Each node is unified in the same reference coordinate system when calculating the position and speed information, and the speed component is positive when flying along the axis direction, otherwise it is negative.  
To more effectively measure the relative motion difference between nodes, this paper introduces the concept of relative mobility, expressed as follows:  
\[r_{i,j}=\frac{v_{i,j}}{|v_{i}|}=\frac{\sqrt{\left(v_{i,x}-v_{j,x}\right)^{2}+ \left(v_{i,y}-v_{j,y}\right)^{2}+\left(v_{i,z}-v_{j,z}\right)^{2}}}{\sqrt{\left( v_{i,x}\right)^{2}+\left(v_{i,y}\right)^{2}+\left(v_{i,z}\right)^{2}}} \tag{7}\]  
where \(r_{i,j}\) represents the relative mobility between nodes \(i\) and \(j\), \(v_{i,j}\) denotes the relative moving speed between nodes \(i\) and \(j\), and \(|v_{i}|\) indicates the absolute speed of node \(i\).  
In order to simplify the subsequent model calculation and network simulation, this paper focuses on the topological changes in the unmanned cluster network in a two-dimensional plane. Therefore, when calculating the relative mobility between nodes, the velocity component of nodes in the \(z\)-axis direction will not be considered, and the relative mobility \(r_{i,j}\) can be expressed in the following form:  
\[r_{i,j}=\frac{v_{i,j}}{|v_{i}|}=\frac{\sqrt{\left(v_{i,x}-v_{j,x}\right)^{2}+ \left(v_{i,y}-v_{j,y}\right)^{2}}}{\sqrt{\left(v_{i,x}\right)^{2}+\left(v_{i,y }\right)^{2}}} \tag{8}\]  
If the relative mobility \(r_{i,j}\) between nodes \(i\) and \(j\) is greater, it indicates that the current motion direction and motion state of the two nodes are too different, and the network link between two nodes is more unstable, so it is necessary to avoid this link for data transmission as far as possible. Conversely, a smaller relative mobility signifies that the motion direction and state of the nodes are similar, leading to a more stable link, which should be prioritized for communication.