# Extending Wireless Reschargeable Sensor Network Life without Full Knowledge
## 1 Introduction  
With the increase in popularity of Wireless Sensor Networks (WSN), the need for sustainable networks becomes more and more prominent. Low cost sensors may make it appealing to replace sensor nodes when their power level is depleted. Simply replacing sensor nodes is not only costly but also harmful to the environment [1]. In addition, finding the sensor nodes that need replacement or charging is challenging [2]. There are many approaches to increasing the life of a WSN ranging from improving communication protocols [3], smarter energy management [4], energy harvesting [5], reclamation and replacement [6], to periodic recharging [7]. In this work, we focus on using an Unmanned Aerial Vehicle (UAV) [8], to charge a WRSN. This has benefits such as the ability to reach locations that are harder to access, but also adds other challenges such as higher energy use while in flight. Among works that recharge a WRSN with a Mobile Charging Robot (MCR) [7], many aim to address the optimal path planning problem [9] and the charge selection problem simultaneously [10; 11]. This renders the charging problem hard, nondeterministic polynomial complete (NPC) [12], causing the solution to be infeasible for large-scale WRSN. Even when utilizing several MCR units, the problem is still shown to be nondeterministic polynomial hard (NP-Hard) [13]. Our work decouples the charging problem from path planning, resulting in a computationally tractable solution. Our charging solution also requires no a priori knowledge of the current nodes' power levels, enabling it to scale with large WRSN. Reducing data collection in WRSN not only reducesthe transmission power consumption at each sensor node, but also the overall computational cost across the network. Reducing the data flow requirements on a WRSN enables it to scale better. Large-scale WSNs are defined as either networks covering large areas or networks of high density [14]. While high density with small areas can still be dealt with by charging multiple nodes at the same time [9], collecting power information means more overall node power is wasted delegating power information. As for large area WSNs, they may reach a size that is impossible for an MCR to fully cover. While advancement in Lithium-Ion batteries [15] may enable an MCR to overcome parts of this limitation, the need for the network to provide power information becomes more expensive with larger areas. Another solution is to reduce the cost of information collection by simultaneously collecting information while charging [16], and providing an optimal policy for power allocation. Eliminating the need for power information delivery reduces the load on the WRSN. We propose ANLPP (All Network Least Possible Probability), an algorithm that does not require a priori knowledge of WRSN power levels. To the best of our knowledge, this is the first non-exhaustive attempt to charge a WRSN with no a priori knowledge of the sensor nodes' power levels. We consider without the loss of generality a line graph network topology shown in Figure 1, similar to [10]. Assuming path planning is already provided then any network topology can be reduced to a line topology, in the sense of its path plan. The line topology is also appropriate since we use a UAV as the MCR [17], which is able to quickly traverse the area. This layout is also very practical and used to cover, operate, or maintain line based systems such as power lines [18], oil lines, bridges [19], rail-roads [20], and border protection. Line layout is also applied when the robots are constrained to a single path of movement in a rough terrain, or when they are moving along a rail [21]. We consider the definition of WRSN life as the time a percentage of the network dies [22; 23]. The general problem that we consider in this paper is the stopping point in an exploration path, and the amount of power to charge each node.