## 1 Introduction  
In recent years, Wireless Sensor Networks have tended to be deployed in a wide area such as forests [1], cities [2], and underwater [3]. With the development of unmanned vehicles, sensors now can be mounted on them to extend their exploring scope. Normally, these vehicles are far from each other and require data collectors to hand in their data. For example, Autonomous Underwater Vehicles (AUVs) have been deployed in the deep sea [4; 5] to do data collection and event detection. They will appear frequently for data reporting to avoid underwater acoustic transmission, which suffers from very significant signal attenuation [6]. When they are underwater, their exploration work is often with a fixed schedule since the trajectory and working spots are predetermined. After these AUVs surface, a moving mobile sink will come to collect the data via wireless communications. UGVs are also favorable for sensor network applications [7]. The mobile sink cruises in the area and visits each unmanned vehicle in a timely manner and uploads collected data via a satellite communication. In these scenarios, a unique problem is how to maximize the data collected via the trajectory planning of the mobile sink. To deploy a stationary data collector at the spot of of each UGV appearance is costly and not feasible in some cases, e.g., ocean bottom surveillance scenarios, since it is impossible to anchor the collector in the deep sea without it drifting away. Therefore, using a mobile sink is feasible and economical. The key challenge is that the mobile sink must arrive at the spot at a certain time to meet the UGV according to its work cycle. Arriving before the UGV appears or after it goes back will cause the data collecting procedure to fail. Therefore, the constraints are not only the shorter path but also the timing opportunities. In traditional scenarios, the problem can be fully or partly converted to the Traveling Salesman Problem since the node is always available. However, in our case, the data generators will only allow a short meeting time during a periodical cycle so that the visiting sequence and distance between two nodes will have a great impact on the global performance. There is previous work studying the trajectory planning of mobile nodes in fragmented wireless sensor networks [8; 9; 10; 11]. In our paper, we consider a common scenario in which UGVs are working in the obstacle area to collect data. They will appear at some locations and hand data to the mobile sink cycle by cycle. UGVs contact the mobile sink in a wireless communication and the latter one uploads the data to the satellite. Figure 1 shows the proposed scenario. The target area is divided into several sub-parts since it is impossible for a single UGV to explore the entire area. Therefore, each UGV will work in its own sub-part independently where the acreage, the environment, and the tasks may be quite different. In other words, each cycle of the UGVs is different. Even for the same UGV, the cycle time is not identical due to unexpected events and condition of the path. Since this will introduce extra delay during the process of reappearing or resurfacing [3], a UGV will appear only for a short time in each cycle. Without loss of generality, in this paper, we assume that each UGV will only appear for one time during a cycle as shown in Figure 1. Furthermore, the UGV will not stay long at the appearing spot. In other words, the size of the time window is negligible compared with the distance between appearance spots. In this paper, we consider the trajectory planning of the mobile sink aiming at maximizing the collected data during a given time period, which, in turn, minimizes the average data reporting delay. After that, if there exists more than one path that passes the same amount of UGVs, we will further identify the shortest path among them.