# AUV Trajectory Planning for Optimized Sensor Data Collection in Internet of Underwater Things
## 1 Introduction  
The growing demand for natural resources and the rising interest in space exploration have intensified global attention on underwater research [1, 2, 3, 4]. In response, the Internet of Underwater Things (IoUT) has emerged as a transformative paradigm, enabling the exploration of previously inaccessible and unexplored underwater environments. Representing a major advancement in marine technology, IoUT facilitates intelligent, interconnected sensing and communication across underwater networks, thereby expanding the possibilities for research, monitoring, and resource management in underwater domains [1, 5]. The Underwater Acoustic Sensor Network (UASN) is a fundamental component of the IoUT framework. It consists of strategically deployed sensor nodes that provide the essential infrastructure for underwater sensing and communication [5, 6, 7, 8]. These nodes gather environmental data from the underwater environment and transmit it to surfaceunits or mobile data collectors [1; 7; 9]. UASNs are critical for various applications, including environmental monitoring, marine resource exploration, underwater infrastructure inspection, and national defense operations [10; 11; 12]. UASNs primarily use acoustic signals for underwater communication, as radio and optical waves attenuate rapidly in water, severely limiting their effective range [11; 13; 14]. In contrast, acoustic signals can support long-range communication over several kilometers, making them a practical and widely adopted choice for underwater wireless networks [9; 14]. Despite these advantages, acoustic communication faces several challenges that limit its efficiency under certain conditions. Most notably, it offers limited bandwidth and the slow propagation speed of sound in water introduces considerable transmission delays [1; 6; 8; 9]. These constraints hinder the timely and efficient transfer of large volumes of data over long distances [6]. Moreover, underwater acoustic communication requires significantly higher transmission power than radio-based systems, while recharging the batteries of submerged sensors remains a difficult and energy-intensive task [8]. Autonomous Underwater Vehicles (AUVs) have become crucial for enhancing the efficiency and flexibility of underwater sensor networks [6; 15]. Unlike stationary sensor nodes, AUVs can follow either predefined or adaptive trajectories, enabling them to approach sensor nodes directly and collect data for subsequent offloading to a relay node [5; 6; 7; 15; 16]. This feature reduces the energy consumption of sensor nodes by eliminating the need for energy-intensive, long-range multi-hop transmissions, thereby extending the overall lifespan of the UASN [7; 10; 15; 16]. Additionally, an Unmanned Surface Vehicle (USV) can serve as a relay node within a UASN. When operating collaboratively, USVs and AUVs can significantly enhance UASN performance in various ways [17; 18; 19; 20]. In such a configuration, the AUV is responsible for collecting data from sensor nodes and surfacing to transfer the information to the USV at a pre-determined location. The USV subsequently relays the data to onshore operators for further analysis [17]. This integration enhances the mobility and flexibility of UASNs, effectively addressing the inherent limitations of static sensor deployments. In underwater sensing applications, the significance of collected data varies. Frequently monitored data, such as normal temperature or pressure, are generally non-urgent and have less importance [1; 7; 11]. Conversely, data exhibiting anomalous values are highly time-sensitive and may indicate impending disasters or emergencies, such as toxic chemical spills or natural calamities, requiring prompt intervention [1; 6; 7; 11]. As the former data type is consistently observed, the latter is not commonly encountered but requires rapid uploading due to its critical significance and the urgent need to mitigate potential threats [1; 6; 7; 11].