## 1 Introduction  
Radio frequency (RF)-based wireless power transfer (WPT) is crucial to developing self-sustaining Internet of Everything (IoE) networks in the 6G era, providing continuous power to devices such as wearable, robotic, and extended reality devices without the need for frequent battery replacement or a wired connection [1; 2; 3; 4]. It adapts to various conditions, enhancing transmission capacity and service quality. Additionally, unmanned aerial vehicles (UAVs) have recently gained great attention for their flexibility, mobility, and cost-effectiveness in various fields, including communication, disaster management, and military operations [5; 6; 7; 8; 9; 10; 11]. In this context, UAV-enabled WPT is widely considered a promising technology for efficiently providing power to ground devices, overcoming the limitations of traditional fixed-location power transmitters [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. By leveraging favorable 3D line-of-sight (LoS) channels, UAVs can serve as aerial power transmitters, reducing transmission distance, avoiding obstacles, and effectively accessing remote areas in challenging environments such as maritime networks and smart cities. Therefore, solutions based on UAV-enabled WPT can address urgent power demands or bottlenecks, thereby extending the lifespan of energy-constrained devices. In practical scenarios, moving the UAV closer to one device may increase the distance from other devices, thereby reducing the overall energy transfer efficiency. Therefore, there has been extensive research on sophisticated UAV trajectory designs capable of enhancing energy transfer efficiency for multiple ground devices [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]; for example, studies have focused on one-dimensional (1D) and two-dimensional (2D) trajectories at a fixed altitude for multiple ground devices in single-UAV-enabled WPT systems [12; 13], as well as more practical UAV systems [14], and three-dimensional (3D) trajectories within a certain UAV altitude range [15]. In addition, a directional antenna array for single-UAV-enabled WPT systems was introduced to improve the power transfer efficiency based on the joint design of the trajectory and antenna array orientation [16; 17]. UAV altitude and energy beamforming were also jointly designed to maximize power transfer efficiency by directing the energy beams toward the devices at the same time [18]. WPT systems, including multiple UAVs, with particular attention paid to the latter's trajectories, have been studied in various environments in order to enhance WPT coverage while improving power transfer efficiency [19; 20; 21; 22]. Radar sensing has received significant attention as a key technology for future 6G networks since it allows for the provision of high-accuracy sensing services for various applications [23; 24; 25; 26]. Notably, conventional radar sensing and WPT, although promising, have typically been studied and implemented as separate systems. Recently, a new paradigm called integrated sensing and wireless power transfer (ISWPT), which combines radar sensing and WPT operations on a unified hardware platform sharing the same spectrum resources, has been proposed [25], inspired by integrated sensing and communication (ISAC) systems, where radar sensing and communication operations are integrated into one hardware platform. ISWPT systems provide potential advantages in terms of reduced size, cost, and power consumption of the hardware platform, as well as more efficient use of spectrum resources [25; 26]. In their initial work, the authors of [25] characterized the fundamental trade-off between radar sensing and WPT operations by optimizing transmit beamforming. Additionally, the authors of [25] studied a transmit beamforming design for near-field ISWPT systems, in which the devices to be charged are located in the near-field region.