# Swarm Intelligence Techniques for Mobile Wireless Charging
## 5 MCs Coordination and Charging Traversal Strategies
### Partial vs. Full Charging  
One straightforward strategy about the MC's visit to a sensor-node would be to fully charge the node. By so doing, the MC would have maximized the time interval of revisiting the sensor-node before its energy is depleted. However, the operations of the network are such that energy is dissipated at the sensor-nodes for data transmissions and at the MC for charging activities, thus making it difficult for the MC to deliver energy to more and more sensor-nodes, since the MC will have increasingly less energy to distribute.  
Another strategy would be for the MC to judiciously distribute its available energy to as many sensor-nodes as possible to prolong the network lifetime. With this rationale,  
Figure 5: Number of alive nodes over time for different MC initial energy percentages.  
the amount of energy that the MC can deliver to a node \(j\) is proportional to the residual charging energy of the MC. Simply put, the MC charges a node until its energy becomes  
\[\mathfrak{P}\approx\frac{\hat{E}_{MC}^{\text{curr}}}{\hat{E}_{MC}^{\text{init}}} \cdot\hat{E}_{\text{sensor}}^{\text{max}} \tag{8}\]  
To determine the best charging strategy of the MC and the energy that it transmits to the sensor-nodes, we adapt the MC charging model and strategy in [22; 46], where the full charging strategy is compared against our adaptive partial charging strategy. The model in [46] used [PERSON] free space propagation model to compute the charging efficiency of the nodes according to Equation (9):  
\[P_{rp_{u}}=\left\{\begin{array}{l}\frac{G_{t}G_{r}\mathfrak{n}\ P_{t}}{P_{t}} \left(\frac{\lambda}{4\pi(d_{p_{u}}+\mathfrak{H})}\right)^{2},\ d_{p_{u}}\leq \text{R}_{\text{mc}}\\ 0,\ d_{p_{u}}>\text{R}_{\text{mc}}\end{array}\right. \tag{9}\]  
where \(p_{u}\) are the \(u\)th charging points of the MCs, \(G_{t}=8\)dBi (transmit gain), \(G_{r}=2\)dBi (receive gain), \(\lambda\) is the wavelength, \(P_{t}\) is the polarization loss, \(\mathfrak{n}\) is the rectifier efficiency, \(\mathfrak{H}\) is an adjustable parameter that adjusts Friis' free space equation for short distance transmissions, \(P_{t}\) is the transmit power, \(d_{p_{u}}\) is the distance between node \(j\) and the MC, and \(\text{R}_{\text{mc}}\) is the charging radius of the MC. If \(d_{p_{u}}\leq\text{R}_{\text{mc}}\), Equation (9) is transformed [46] as:  
\[P_{r}=\frac{P_{t}\mathfrak{V}}{\left(d_{p_{u}}+\mathfrak{H}\right)^{2}} \tag{10}\]  
where \(\mathfrak{V}=4.32\times 10^{-4},\mathfrak{H}=0.2316\).  
The energy of the sensor-node, after being charged by the MC, is given in Equation (11) [47]:  
\[E_{sensor}=\min\left\{E_{j}+\sum_{p_{u}}\bigl{(}P_{rp_{u}}\times\mathfrak{t} _{p}\bigr{)},\ \hat{E}_{sensor}^{max}\right\} \tag{11}\]  
where \(E_{j}\) is the residual energy of the sensor-node \(j\) before charging, \(\mathfrak{t}_{p}\) is the charging time of the MC, \(P_{rp_{u}}\times\mathfrak{t}_{p}\) represents the energy received by node \(j\) from the MC, and \(\hat{E}_{sensor}^{max}\) is the maximum storage energy threshold of the sensors.  
Here, we randomly select 40% of \(\hat{E}_{total}\) as the initial energy of the MC. The results are shown in Figure 6. The basic result obtained shows that our partial charging strategy is efficient compared to a full charging strategy. Our partial charging scheme outperforms its full charging counterpart after a given number of generated events. The outcome of this investigation reveals the fact that the MC expends more energy on sensor recharging when applying the full charging method. Hence, much of the MC's energy is consumed quicker, leading to a rise in the node death rate.