## 1 Introduction  
Natural disasters, such as earthquake, flood, and typhoon, often cause huge and unpredictable losses to human lives and properties [1, 2, 3]. Most of these disasters will result in unavailability of, or severe damage to, traditional terrestrial wireless infrastructures, as well as disruption to regional communication, which brings challenges to post-disaster response and relief [4, 5, 6]. By virtue of the advantages of dynamic mobility, flexibility, and on-demand deployment, unmanned aerial vehicles (UAVs) have been deemed as a promising technique in post-disaster area communication recovery [7, 8, 9]. In particular, the existence of line-of-sight (LoS) links between UAV and ground users has aroused a fast-growing interest in utilizing UAVs as aerial wireless platforms [10, 11, 12, 13], while the limited power supply in disaster areas restricts the users' survival time and equipment performance, which also puts forward higher requirements for UAV-aided post-disaster services. To tackle the above mentioned challenge, the combination of mobile edge computing (MEC) and wireless power transfer (WPT) seems to be an effective approach [14, 15, 16]. On one hand, by offloading computation tasks to UAVs, users can significantly improve their data processing capabilities [17, 18, 19, 20]. On the other hand, with the aid of WPT technology, users can harvest radio-frequency (RF) signals from UAVs to prolong their survival time [21, 22, 23]. Unfortunately, the severe propagation loss of the wireless signals over long distances will degrade the performance of wireless information transfer (WIT) and WPT [24; 25; 26]. To improve the efficiency of WIT and WPT, UAVs should know the exact location of users in advance. However, in post-disaster areas, the exact location of users is difficult to obtain. The incomplete location information profoundly affects the trajectory planning of UAV and reduces the energy acquisition efficiency of users and the service quality of UAV [27; 28; 29; 30]. Therefore, the robust design of trajectory and resource allocation of UAVs in post-disaster areas is of paramount importance. Motivated by the requirements of a UAV-enabled wireless platform in a post-disaster area, we consider a robust UAV-enabled wireless-powered MEC system in this paper. In this system, a UAV equipped with MEC device and RF transmitter flies to the post-disaster area to provide computing and charging services for ground users. In this paper, we assume that terrestrial communications were destroyed in the disaster. Affected by this, the UAV only knows the rough areas where the users are, but the exact locations of the users are unknown. In order to ensure that users have enough power to maintain until the arrival of ground rescue, our target is to maximize the energy acquisition of each user while meeting the computation needs of users. The considered problem is a non-convex semi-infinite optimization problem, which is intractable and hard to solve. In order to solve this intractability, we transform the original problem into a solvable form by ignoring the uncertainty of location first. Considering the coupling between computation offloading optimization and trajectory planning, an iterative optimization method is proposed by using Lagrange dual method and successive convex approximation (SCA) technology, respectively. Then, a cutting-set method is proposed to continuously decrease the impact of worst-case location of users on optimization. Due to the worst-case location of users changing with the optimization of UAV trajectory, the cutting-set method is achieved by alternating optimization, i.e., optimizing the UAV trajectory for given subsets of worst-case users' locations in the optimization step, and updating the subsets of worst-case users' locations according to UAV trajectory in the pessimization step. To summarize, the difference between our work and those in [13; 18] is mainly twofold.