## 3 System Models
### Sensing Coverage Model
The specific calculation is shown in (3)-(6), where \(a^{i}_{v}\) represents the \(s_{i}\) average AoCS._  
\[a^{j}_{v}(m)=\left\{\sum\limits_{k_{2}=1}^{l_{Q_{i}}}a^{i,Q_{i}(k_{2})}_{c}(m )-\sum\limits_{k_{1}=1}^{l_{q_{i}}}a^{i,Q_{i}(k_{1})}_{c}(m)\right\}/2-\left\{ \sum\limits_{k_{1}=1}^{l_{q_{i}}}a^{i,Q_{i}(k_{1})}_{c}(m)\right\}/3 \tag{3}\]  
\[a_{TC}(m)=\sum\limits_{i=1}^{N}a^{i}_{v}(m). \tag{4}\]  
\[a^{i}_{I}(m)=a_{m}-\left\{\sum\limits_{k_{2}=1}^{l_{Q_{i}}}a^{i,Q_{i}(k_{2})}_ {c}(m)-\sum\limits_{k_{1}=1}^{l_{q_{i}}}a^{i,Q_{i}(k_{1})}_{c}(m)\right\}. \tag{5}\]  
\[a_{TSA}(m)=a_{TC}(m)+a_{TI}(m)=\sum\limits_{i=1}^{N}\left\{a^{i}_{v}(m)+a_{m} -\left\{\sum\limits_{k_{2}=1}^{l_{Q_{i}}}a^{i,Q_{i}(k_{2})}_{c}(m)-\sum\limits_ {k_{1}=1}^{l_{q_{i}}}a^{i,Q_{i}(k_{1})}_{c}(m)\right\}\right\} \tag{6}\]```
1:INPUT:\(E_{r}(m)\), \(D(m)\), \(R_{m}\)
2:Outputs:\(A_{c}(m)\)
3:For \(i=1:(N-l_{s}(m))\)
4: Find \(Q_{i}\), \(q_{i}\), \(l_{Q_{i}}\) and \(l_{q_{i}}\)
5: If \(Q_{i}=\varnothing\)
6:\(a_{c}^{i}(m)=0\)
7: Else
8: For \(j=1:l_{Q_{i}}\)
9: Calculate the \(\angle S_{ji}\) of \(s_{j}\)
10:\(a_{\triangle ij}=R_{m}{}^{2}sin(\angle S_{ji})\cos(\angle S_{ji})\);
11:\(a_{c}^{ij}=\pi R_{m}{}^{2}((\angle S_{ji})/360^{\circ})-a_{\triangle ij}\)
12: If \(s_{j}\) is not in \(q_{i}\)
13:\(a_{c}^{i,j,k}=0\);
14: Else
15: Find another three-intersecting node \(s_{k}\)
16: If double-count
17:\(a_{c}^{i,j,k}=0\)
18: Else
19: Center angle \(\angle S_{j,k}\) of \(a_{c}^{i,j,k}\) in \(s_{j}\) can also be calculated
20: So as \(\angle S_{i,j,k}\) and \(\angle S_{k,ij,j}\); \(h_{\triangle ijk}^{i}\), \(h_{\triangle ijk}^{j}\) and \(h_{\triangle ijk}^{k}\) can also be obtained
21:\(ss=(h_{\triangle ijk}^{i}+h_{\triangle ijk}^{j}+h_{\triangle ijk}^{k})/2\)
22:\(a_{\triangle ijk}=\sqrt{ss(s-h_{\triangle ijk}^{i})(ss-h_{\triangle ijk}^{ j})(ss-h_{\triangle ijk}^{k})}\)
23: Take \(h_{\triangle ijk}^{i}\) as an example
24:\(h_{\triangle ijk}^{i}=\sqrt{(2R_{m}{}^{2}-\cos\angle S_{ijk})/2R_{m}{}^{2}}\)
25: The three-intersection triangle and sector area of \(s_{i}\)
26:\(a_{\triangle ijk}^{i}=h_{\triangle ijk}^{i}(\sin(\angle S_{ijk}/2)R_{m})/2\); \(a_{\dash i}^{-i}=\pi(R_{m})^{2}(\angle S_{ijk})/360^{\circ}\)
27:\(a_{\triangle ijk}^{j}\), \(a_{\triangle ijk}^{k}\), \(a_{\triangle ijk}^{-j}\) and \(a_{\dash k}\) can also be solved
28:\(a_{c}^{i,j,k}=a_{\triangle ijk}+a_{\dash i}+a_{\dash j}+a_{\dash k}\)\(+a_{\dash k}\)\(-a_{\triangle ijk}^{k}-a_{\triangle ijk}^{i}-a_{\triangle ijk}^{j}\)
29: End
30: End
31: End
32: End
33:\(a_{c}^{i}=\sum\limits_{j=1}^{l_{Q_{i}}}(a_{c}^{ij}-a_{c}^{i,j,k})\)
34: End
```

**Algorithm 1** Real-time AoCS Calculation. ## 4 Problem of Mobile Charging Sequence Scheduling for Network QSC

In this section, we describe the MSSQ problem and prove that MSSQ is NP-complete. ### Problem Formulation

With the increasing of the number of nodes, more nodes may stop working if they run out of energy, because the charging capacity of MC cannot meet the network's total energy consumption. At this time, the network topology changes, and the coverage vulnerability makes the sensing information incomplete, thus reducing the network QSC. How to guarantee the maximum network QSC in unit charging cycle under the condition of the limited charging capacity of MC is the goal of the MSSQ problem. We redefine a new performance index for network QSC as sensing coverage and node survival rate (\(SCNS\)), which is explicitly expressed as \(SCNS(\Phi(m))=\delta_{1}\frac{\pi r_{\mathrm{TSQ}}(m)}{a_{m}}+\delta_{2}\frac {N-l_{s}(m)}{N}\), where \(l_{s}\) is the number of nodes in the network's total energy consumption. The network QSC is a network QSC, which is a network QSC, which is a network QSC, which is a network QSC. algorithm is always limited, particles cannot reach any point in the whole feasible space during the search process. Therefore, the PSO algorithm cannot converge to the optimal global solution, which is the defect of the PSO algorithm.