# Retractable Wireless Charging Windings for Inspection Robots
## 1 Introduction  
The adoption of mobile robotic systems continues to accelerate as application demands increasingly extend beyond the limitations of fixed workspaces, driving the need for greater deployment flexibility [1]. This trend is evident across various domains, with the emergence of ground-based, aerial, and underwater robotic platforms. Several application areas include inspection tasks in oil and gas refineries [2], radiation monitoring and mapping [3, 4], underwater surveying [5, 6], and operations in nuclear decommissioning environments [6, 7]. One of the primary limitations to the sustained operation of mobile robots is the capacity of the onboard batteries, particularly in environments such as subterranean or reinforced concrete infrastructure, where access for maintenance is restricted [1]. Traditionally, robots must either return periodically to a charging station or undergo manual battery replacement on-site [1]. While these methods mitigate the battery constraint, they introduce significant operational downtime. An alternative approach is the use of tethered power and communication lines. However, this introduces further challenges, including entanglement, limited maneuverability around obstacles and added payload burden due to the tether itself thus reducing the system's agility and operational scope [8]. Alternatively, wireless power transfer (WPT) offers a feasible solution by enabling untethered energy delivery and potentially supporting continuous operation without physical connection or excessive intervention. In terms of power levels and operating ranges, WPT technologies are most commonly applied to two distinct categories. High-power applications, such as electric vehicles, typically operate at kilowatt (kW) levels and rely on close-proximity coupling, with transfer distances generally under 0.3 m. On the opposite end, low-power systems are widely used for applications such as consumer electronics and medical implants, which operate at milliwatt to watt levels and over centimetre-scale distances [9]. WPT is also employed in wireless sensor networks (WSNs), where ultra-low-power transmission can occur over distances extending to the kilometre scale [10]. The source of power for these mobile robots is usually lithium batteries which can generally last for 30 min up to 8 h at most depending on the usage [11]. Mobile robots are typically equipped with a set of payloads such as sensors, cameras, positioning systems and other necessary equipment designed for the assignment completion [12]. Therefore, increasing the number of onboard batteries in mobile robots often presents challenges related to space constraints and weight limitations. Table 1 shows the summary of parameters on the robot's power and battery requirements where \(P\) is the power consumption, \(T\) is the operational time with the battery energy (\(E_{b}\)), \(t\) is the robot's charging time and \(W\) represents the maximum payload of each robot. Husky and ANYmal are ground-based robots (UGV), Hydrus-300 and BlueROV represent autonomous underwater vehicles (AUVs), and Phantom 4 and Matrice 300 are examples of unmanned aerial vehicles (UAVs). The average power requirement for these mobile platforms is 100 W to 200 W, with an average operational time of 2.5 h based on battery capacity. Among the various WPT techniques, inductive power transfer (IPT) remains a popular choice due to its relatively high efficiency over short to mid-range distances and its suitability for high-power applications [17; 18]. In addition to IPT, capacitive-coupled wireless power transfer (CC) has also gained traction in recent years, particularly for short-range, high-power applications. Capacitive systems use electric field coupling between conductive plates to transfer energy, and are often favored for their compact form factor, reduced magnetic interference, and potential for high power densities [19].