# Terminal Distributed Cooperative Guidance Law for Multiple UAVs Based on Consistency Theory
## 4 The Upper-Level Distributed Coordination Strategy Based on Consistency  
When the upper layer of the two-layer guidance architecture adopts the centralized coordination strategy, the coordination variable only exists in one member of the formation, which is easier to realize. However, this strategy requires the information of the global system, and when the centralized cooperative member is attacked and fails, the cooperative control of the whole formation will fail, which reduces the robustness and reliability of the system. Therefore, a distributed cooperative guidance law based on consistency theory is designed in this paper. Let us assume that \(n\) UAVs launched simultaneously are required to carry out a saturation attack on a fixed target at the same time. The formation structure composed of multiple UAVs is regarded as the network communication topology structure, and each UAV is regarded as the network communication node. The acceleration command of the _ith_ UAV is expressed as:  
\[a_{M,i}=a_{M,1,i}+a_{M,2,i}(i=1,...,n) \tag{37}\]  
where, \(a_{M,1,i}\) is the local control term of the _ith_ UAV for zero miss distance, and \(a_{M,2,i}\) is the cooperative control item for realizing cooperative attack. The local control item selected in this paper is:  
\[a_{M,1,i}=a_{M,i}^{qq}=-\frac{V_{M,i}}{K_{2,i}+K_{3,i}}\bigg{(}(1+K_{1,i})+(K_ {2,i}+K_{3,i})\frac{V_{M,i}\sin\sigma_{M,i}}{r_{i}}\bigg{)} \tag{38}\]  
Figure 2: Relative motion relationship based on predicted collision point. The collaborative control item can be designed as:  
\[a_{M\_2,i}=f\big{(}s_{i1}(t)t_{go,1},...,s_{iq}(t)t_{go,4},...,s_{in}(t)t_{go,n} \big{)} \tag{39}\]  
where, \(s_{ij}(t)\) is the function of time, and \(f\) is the network communication connection. At time \(t\), when the \(jth\) UAV can receive the information transmitted by the \(ith\) UAV, \(s_{ij}(t)=1\), otherwise, \(s_{ij}(t)=0\), and \(s_{ii}(t)=1\). Then the instantaneous communication matrix describing the information exchange between UAVs in formation can be defined as:  
\[S(t)=\left[ \begin{array}{cccc}s_{11}(t)&s_{12}(t)&...&s_{1n}(t)\\ s_{21}(t)&s_{22}(t)&...&s_{2n}(t)\\...&...&...&...\\ s_{n1}(t)&s_{n2}(t)&...&s_{nn}(t)\end{array} \right] \tag{40}\]  
The following formula can be obtained by deriving the time-to-go:  
\[ \begin{array}{ll}\dot{t}_{go,i}&=K_{1,i}+(K_{2,i}+K_{3,i})\dot{\sigma}_{M,i }\\ &=K_{1,i}+(K_{2,i}+K_{3,i})\Big{(}\frac{a_{M,i}}{V_{M,i}}+\frac{V_{M,i}\sin \sigma_{M,i}}{r_{i}}\Big{)}\\ &=K_{1,i}+(K_{2,i}+K_{3,i})\frac{V_{M,i}\sin\sigma_{M,i}}{r_{i}}+(K_{2,i}+K_{3,i})\frac{a_{M,1,i}}{V_{M,i}}+(K_{2,i}+K_{3,i})\frac{a_{M,2,i}}{V_{M,i}}\\ &=f_{1,i}(r_{i},V_{M,i},\sigma_{M,i})+f_{2,i}(r_{i},V_{M,i},\sigma_{M,i})a_{M,2,i}\end{array}  \tag{41}\]  
where,\(f_{1,i}(r_{i},V_{M,i},\sigma_{M,i})=K_{1,i}+(K_{2,i}+K_{3,i})\frac{V_{M,i}\sin \sigma_{M,i}}{r_{i}}+(K_{2,i}+K_{3,i})\frac{a_{M,1,i}}{V_{M,i}},f_{2,i}(r_{i}, V_{M,i},\sigma_{M,i})\)\(=(K_{2,i}+K_{3,i})/V_{M,i}\). When \(a_{M\_2,i}=0\), it means that there is no need to adjust the impact time of the UAV, so the impact time of the UAV satisfies \(\dot{t}_{f,j}=0\). From \(t_{go,i}=t_{f,j}-t_{i}\), it can be known that \(\dot{t}_{go,i}=-1\). Considering that \(f_{1,i}(r_{i},V_{M,i},\sigma_{M,i})\) does not explicitly contain \(a_{M\_2,i}\), then \(f_{1,i}(r_{i},V_{M,i},\sigma_{M,i})=-1\).