## 3 System Models
### Sensing Coverage Model
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline IQPSO & 55.30 & 58.08 & 65.64 & 63.22 & 62.58 & 58.52 & 58.93 & 62.53 & 61.15 & 63.68 \\ QPSO & 54.35 & 57.22 & 63.13 & 62.72 & 61.88 & 58.42 & 58.89 & 61.86 & 59.26 & 63.01 \\ \hline  & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** & **20** \\ \hline IQPSO & 59.02 & 60.37 & 61.48 & 55.79 & 61.98 & 59.82 & 59.29 & 58.55 & 59.99 & 59.05 \\ QPSO & 58.61 & 59.28 & 60.88 & 55.70 & 60.11 & 57.02 & 58.90 & 57.89 & 58.34 & 56.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of \(TSCNS\). Figure 2: Iterative process of the IQPSO. (**a**) Performance index. (**b**) Error. assumed that 80 nodes are randomly and uniformly distributed in a fixed 100 m \(\times\) 100 m 2D monitoring plane, and the initial residual energy of each node \(e_{i}\) is randomly generated between 30%\(e_{m}\)-60%\(e_{m}\). The energy consumption of each node, \(v_{cs}\), is randomly generated between (0.2-1.8) J/s. In addition, the MC moving speed is 5 m/s, the charging power is 40 J/s, and the energy consumption rate of the moving unit distance is 1 J/m. We have conducted a 50-h simulation test on four NVIDIA GeForce GTX 2080 servers for the verification of the proposed algorithm and different comparison simulations. ### Baseline Algorithms

In this part, the proposed algorithm's performance will be compared with two typical heuristic algorithms: the QPSO and Greedy algorithms [34]. The survival rate of the network nodes and the selection of nodes with larger AoIS will affect network QSC; therefore, regarding the Greedy algorithm, we designed Greedy-E and Greedy-A algorithms. (1) The QPSO algorithm is an iterative optimization algorithm. The particle represents a possible charging sequence. Particles have quantum behavior, and their action is affected by potential quantum gravity. The QPSO algorithm updates the charging sequence by tracking the individual and global optimal performance indicators found by itself and the population. (2) The MC executes a greedy charging strategy in the Greedy algorithm according to a specific network index. In the Greedy-E algorithm, MC always charges nodes according to the order of the remaining energy of the node. (3) Different from the Greedy-E, the MC of the Greedy-A algorithm sorts the AoISs of the nodes to be charged in real-time from large to small and continuously selects the node with the largest real-time AoIS to charge. ### Comparison of Network Scales

On the premise that the MC charging power remains unchanged, increasing the number of nodes will directly affect the charging decision. In this part, we will analyze the changes in the network QSC, the average coverage rate, and the number of off-working nodes for \(N=\{30,50,70,90,110,130\}\) within the fixed monitoring range (as shown in Figure 3). As shown in Figure 4a, the network QSC gradually enhances with the increase in \(N\). When \(N\leq 50\), the suboptimal mobile charging sequences obtained by the four algorithms are almost the same. The MC charging power approximately meets the overall network demand. At \(N=30\), both the IQPSO and QPSO algorithms can achieve full network coverage in the charging process (Figure 4b). The WRSN works continuously, so the \(TSCNS\) of IQPSO and QPSO can reach 30. As \(N\) continues to increase, the charging power of the MC does not meet the overall consumption of the network, increasing the number of

Figure 3: Different network scales. off-working nodes, as shown in Figure 4c. At \(N=70\), the number of off-working nodes of the IQPSO and QPSO algorithms are highly similar, but it has obvious advantages in optimizing the network QSC and average coverage rate. \(\delta_{1}>\delta_{2}\), thus the MC pays more attention to the network sensing coverage than the number of off-working nodes and the IQPSO algorithm will charge the nodes with a larger AoIS and ignore the cost of the large number of off-working nodes.