# Swarm Intelligence Techniques for Mobile Wireless Charging
## 5 MCs Coordination and Charging Traversal Strategies
### The Charging Traversal Strategy  
Here, the MC traverses the network area it is assigned to and charges the sensors in that region. Studies on charging traversal strategies are currently limited to a single mobile charger (MC). In our approach, we have extended this to multiple MCs and have also given special attention to the amount of _knowledge_ possessed by the MCs, in terms of its region. Hence, to suitably design the MC's charging traversal strategy, we distinguish the MC's amount of knowledge under the following three major characteristics: no network knowledge (NNK), local network knowledge (LNK), and global network knowledge (GNK). In the case of NNK, the MC is assumed to be 'blind' and, thus, is limited in using sophisticated charging methods. The trajectory of the MC is also restricted to several naive options, presented in [22]. Our approach uses the 'blind' scanning of the network area, where the MC begins its tour from the sink and traverses an exhaustive route until it reaches the boundaries of the network region. The advantage of this movement is that the MC tours the entire network to charge almost all the nodes until its energy is completely depleted. However, owing to lack of knowledge, this movement is not adaptive. Figure 6: Number of alive nodes for full and partial charging with 40% of total energy. Figure 7: MC distributed coordination. (**a**) Before the coordination, (**b**) during the coordination, (**c**) after the coordination. In terms of LNK, the MC operates with a local network assumption. The slice relating to charger \(k\) is divided into \(l\) sectors \(S_{kl}\) of the same width, as shown in Figure 3b. The sectors in charger \(k\) are prioritized based on the high number of sensors with a low residual energy status. We adapt the theoretical model in [10] for the charging process. Let \(E_{kl}^{min}\) represent the lowest residual energy level of a sensor-node in the sector \(S_{kl}\). Let \(E_{kl}^{min+}\) represent an energy level close to \(E_{kl}^{min}\), then \(E_{kl}^{min+}=E_{kl}^{min}+\Delta\cdot\frac{E_{kmax}^{max}}{E_{kl}^{min}},\ \ \Delta\in(0,\ 1)\). Let \(n(S_{kl})\) denote the number of sensors in Sector \(S_{kl}\) with residual energy between \(E_{kl}^{min}\) and \(E_{\min+}^{kl}\), then \(n(S_{kl})=\sum\limits_{e=E_{kl}^{min+}}^{E_{kl}^{min+}}n(e)\) where \(n(e)\) is the number sensors with the energy level \(e\). The MC \(k\) charges the sector \(S_{kl}\) and maximizes the process in the form of \(\prod\limits_{S_{kl}}\max\left\{n(e)\ \cdot\ E_{sensor}^{max}-E_{kl}^{min}\right\}\). The motive behind this charging process is to group many sensor-nodes according to slices (sectors) and to select a particular group based on their energy requirements. The group that requires more energy than the others is first selected for charging. The GNK charging strategy considered in our model is impacted by two important metrics, energy and distance. These two factors have equal weight, and one is not more dominant than the other. The MC calculates the product of these two metrics for every node in their cluster and chooses to charge the node with the minimized product. For each phase, the MC moves to a sensor in the cluster in a way that reduces the product of each sensor's energy and the distance from the MC. Specifically, the MC charges the node \(\mathrm{j}^{\prime}=\arg_{\mathrm{j}\in\mathrm{C_{k}}}\min\left\{\left(1+ \frac{d_{jk}}{2R}\right)\cdot\left(1+\frac{E_{j}}{E_{sensor}^{min}}\right)\right\}\) where \(E_{j}\) is the residual energy of the sensor \(j\). In other words, the charging strategy is prioritized among nodes with a low residual energy and a minimum distance from the MC. The analytical studies conducted in this section enable us to investigate the traveling distance of the MCs operating under the three scenarios that have already been discussed. Essentially, the traveling distance of the MCs is an indirect reflection of the coordination process and the charging strategy. The traveling distance also has an impact on the relevant movement cost.