# Extending Wireless Reschargeable Sensor Network Life without Full Knowledge
## 1 Introduction
The problem is as follows: given a set of sensor nodes on a line graph as demonstrated in Figure 1, with each node at an unknown power level, and a UAV as an MCR with limited power, increase the life of the WRSN as close to optimal as possible. The network dies once \(k\) nodes reach zero residual power. There is no knowledge of the exact power level of any node prior to the UAV visiting the node, making it only possible to identify the nodes that need to be charged after they are visited. On the other hand, we assume the nodes have a known discharge rate and a known power level at a previous time instance. The network size is such that if the UAV visits the whole network, it will only be able to charge a single node. The UAV can charge one node at a time, but may still charge several nodes in a single round-trip. It needs to identify the furthest  
Figure 1: An unmanned aerial vehicle (UAV) charging a wireless rechargeable sensor network (WRSN) based on the stopping point: (**a**) optimal stopping point, (**b**) early stopping, (**c**) late stopping. Blue indicates power level of sensor node, orange added power by wireless charging. beneficiary point of exploration that helps in determining the best set of nodes to charge. Charging this set extends the network life close to what an optimal algorithm with full knowledge can achieve. One of the key challenges associated with charging WRSN is determining which node to charge if not all nodes can be charged. Figure 1 shows a WRSN with a UAV used as the MCR and the challenges associated with charge selection. This figure shows three stopping points for the charging algorithm, the best stopping point Figure 1a, an early stopping point Figure 1b, and a late stopping point Figure 1c. A full knowledge algorithm can determine the optimal stopping point for a UAV; in Figure 1, it is sensor node \(n_{o}\). Reaching this point enables the UAV to charge the set of nodes that will extend the network life to the most, while still enabling the UAV to return back to \(B_{S}\). As can be seen in Figure 1a, the UAV was able to bring the two visible nodes to greater than 50% of their power capacity. While stopping short at node \(n_{i}\), as shown in Figure 1b, will enable charging node \(n_{i}\) to a higher level, and prevent the UAV from charge node \(n_{o}\), this, in turn, results in an early death of the WRSN. On the other hand, reaching node \(n_{j}\), Figure 1c, will consume more power, causing the UAV to not have enough power left to charge \(n_{i}\) or charge the nodes to less levels, leading to a lower network life extension. Without prior knowledge of the sensor nodes' power levels, determining this stopping point becomes challenging. The need to identify the low power nodes and the stopping point is crucial for optimal charging of a WRSN. This necessitates the need to identify the lowest power nodes in the network fast, and at a low cost. Once a charging algorithm can predict, with some certainty, that it has identified the nodes with lowest power levels, it may terminate further exploration. We use a probabilistic approach to address the charging of large scale WRSN. Our algorithm utilizes probability to make stopping decisions. We also use a charging algorithm that charges a subset of nodes only considering power levels observed during flight. Determining the power level of nodes in a WRSN is very important to optimally charge the network. Charging and exploring a WRSN based on the actual collected power information, at the time of exploration, enables the conservation of power and scalability of efficient WRSN charging. The main contributions of this paper are:  
* Presenting ANLPP, a novel algorithm that increases the life of a WRSN with no knowledge of sensor nodes' power levels and without the need to fully explore the network. Simulation results showing that ANLPP performs on average at 90% of what an optimal full knowledge algorithm could achieve.