## 2 Related Work  
Traditional wireless sensor networks (WSNs) are mainly powered by batteries. However, the increasing demand for WSNs has resulted in higher energy consumption of sensor nodes. Their limited battery capacity hinders the development of WSNs. Due to infeasibility and danger of replacing sensors' batteries in many applications [17; 26], previous studies have aimed to maximize network lifetime through energy conservation [27]. Additionally, extending the lifetime of the network can be achieved through mobile data collection methods that balance energy consumption [28; 29; 30]. Energy consumption and mobile data collection can only prolong the lifetime of network to a limited degree. Therefore, harvesting energy from environmental sources, such as solar power [31; 32], to recharge sensor batteries is a promising scheme. However, due to their dynamic nature, energy harvesting is too unpredictable to provide stable energy for sensors. Wireless power transfer technology (WPT) has recently emerged as a reliable and convenient method for replenishing energy for sensors, resulting in the development of WRSNs, which have attracted significant research attention. Various studies have focused on supplementing nodes via mobile chargers, such as wireless charging vehicles (i.e., vehicle carrying wireless device). In monitoring tasks where environmental parameters remain relatively constant, the energy consumption of nodes can be estimated using historical data, making periodic schemes a popular choice. [PERSON] et al. [4] proposed a hybrid particle swarm optimization genetic algorithm for periodic charging planning in vehicle with limited energy, ensuring optimal energy utilization and the avoidance of node failures. [PERSON] et al. [5] designed optimal trajectories for a given number of vehicles based on the routing loads of nodes to maximize the overall network's lifetime. [PERSON] et al. [6] developed a scheduling algorithm to mitigate data loss by considering node energy and connectivity criticality. [PERSON] et al. [7] formulated an NP-hard energy consumption minimization problem for charging IoT devices and proposed an efficient algorithm named best charging efficiency (BCE) to solve it. [PERSON] et al. [8] jointly considered charging tour planning and mobile charger depot positioning for largescale WSNs, solving the problem through three stages: charging tour planning, candidate depot identification and reduction, and depot deployment and charging tour assignment. In certain applications, dramatic environment parameters make predicting nodes' charging demand difficult, necessitating path scheduling schemes based on on-demand charging. For instance, [PERSON] et al. [9] developed a temporal-spatial charging scheduling algorithm aimed at minimizing dead nodes while maximizing energy efficiency to prolong network lifetime, along with a primary and passer-by scheduling algorithm outlined in [16]. [PERSON] et al. [10] investigated how to schedule vehicles and allocate charging time for each requesting node simultaneously. [PERSON] et al. [11] proposed a fuzzy logic-based scheduling scheme that blends residual energy, distance to vehicle, and critical node density to plan scheduling. [PERSON] et al. [12] developed their charging strategy from the clustering method, selecting nodes to be charged, charging path, and charging schedule in four aspects. [PERSON] et al. [13] applied a genetic approach based on sensor deadlines and distance to vehicle to schedule multiple vehicles efficiently. [PERSON] et al. [14] utilized a novel vehicle equipped with multiple battery cells, allowing for unloading battery cells on site with the sensor to save on waiting time during charging. Lastly, [PERSON] et al. [15] proposed an efficient method based on a gravitational search algorithm by presenting a novel agent representation scheme and an efficient fitness function combining spatial and temporal constraints.