# Optimizing Charging Pad Deployment by Applying a Quad-Tree Scheme
## 1 Introduction  
_Wireless sensor networks_ (WSNs) are a kind of wireless network, facilitated by an architecture that allows _sensor nodes_ (SNs) to be deployed, with data transmission typically passing through some other intermediate nodes. Deploying WSNs in inaccessible areas enables automatic data collection, making them valuable for monitoring physical resources such as in military applications, medical care, and safety monitoring [1]. Sensor nodes are often deployed outdoors or in hazardous environments, and their battery life is finite. As a result, power loss can lead to node failure and various serious issues, impacting data transmission and potentially causing network paralysis. Additionally, replacing faulty sensor nodes in challenging conditions poses significant challenges due to accessibility constraints and environmental harshness. The difficulty and expense of battery replacement in such environments have made energy management a critical concern for WSNs. The recentadvancement in _wireless power transmission_ (WPT) has led to the development of _wireless rechargeable sensor networks_ (WRSNs), since this technology provides a mean to replenish sensor nodes wirelessly, offering a solution to the energy challenges faced by WSNs. Most of the recent previous work has focused on charging sensor nodes using _wireless charging vehicles_ (WCVs) equipped with high-capacity batteries and WPT devices. In these schemes, a vehicle can move close to a sensor node and wirelessly charge it without physical contact. These studies have involved utilizing multi-functional vehicles [2], simultaneous charging of multiple sensor nodes [3], designing mobile charging protocols [4], or planning optimal collaborative charging schedules of multiple vehicles to enhance sensor network performance [5]. While these schemes can mitigate the energy problem to some extent, they overlook two primary challenges when applying WCVs for wireless charging: off-road navigation and vehicle speed limitations [6]. In order to improve the mentioned shortcomings, recent studies [6; 7; 8; 9; 10] have explored the use of _unmanned aerial vehicles_ (UAVs) for charging sensors in WRSNs. UAVs have now found extensive applications in the commercial sector, including surveillance, remote sensing, aerial photography, search and rescue, and on-demand emergency communication. Here a UAV equipped with WPT devices is called a _wireless charging drone_ (WCD, or drone in short) [6]. In [8], [PERSON] et al. aimed to enhance the total energy of drones while charging energy-limited devices. [PERSON] et al. [9] proposed a method to charge WRSN sensor nodes using drones, considering energy consumption from flight distance and striving to improve charging efficiency. [PERSON] et al. [10] investigated drones equipped with large-capacity batteries to deliver energy to sensor nodes. One advantage of drones is their ability to access and charge more difficult-to-reach sensor nodes. In addition, the flying speed of drones is faster than the speed of vehicles. However, since the battery capacity of drones is limited, the flight distance of the drone is limited when compared to vehicles. To reduce the need for frequent return trips to the base station for drones, the development of wireless charging pads (pads) for automatic drone landing, combined with high-power and efficient wireless power transmission systems, enables drones to be automatically charged within a short timeframe [6; 11; 12]. To overcome the off-road navigation and travel speed limitations of vehicles, [PERSON] et al. [6] first proposed a new WRSN model equipped with one drone coupled with several pads deployed to charge the drone when it cannot reach the subsequent stop. Their wireless charging pad deployment aims to apply the minimum number of pads so that at least one feasible routing path from the base station can be established for the drone to reach every SN in a given WRSN. The wireless charging pad deployment originally allowed pads to be deployed to any point in the defined area.