# AUV Trajectory Planning for Optimized Sensor Data Collection in Internet of Underwater Things
## 1 Introduction
### Related Work  
Efficient data collection strategies for UASNs in IoUT applications have attracted increasing attention due to the challenges of the harsh underwater environment, including limited bandwidth, high latency, and energy constraints [25; 26]. A range of recent studies has explored the use of Unmanned Aerial Vehicles (UAVs) to address these challenges. In [27], the authors propose a hybrid collaborative data collection (HCDC) scheme using hierarchical deep reinforcement learning, which significantly reduces UAV flight time and data acquisition delays. Authors in [28] develop an energy-efficient UAV scheduling strategy based on a knowledge transfer-enhanced particle swarm optimization algorithm, achieving improved energy balance and extended network lifetime. Similarly, ref. [29] introduces a bilevel optimization approach that jointly optimizes UAV deployment and trajectory planning to minimize energy expenditure during data retrieval. However, these UAV-based solutions are inherently limited to surface-level operations, constraining their ability to directly access deeply located underwater sensors. To overcome this limitation, several studies have explored the use of AUVs as mobile data collectors. AUVs can operate closer to underwater nodes, thereby enhancing data transmission reliability, reducing communication delays, and conserving energy [30; 31; 32; 33]. A notable advancement in AUV-based data collection is the incorporation of the VoI framework, which quantifies both the importance and timeliness of data to guide trajectory planning [34; 35]. The definition and modeling of VoI vary significantly across the literature. A common approach assigns VoI based on data importance and urgency, where initial values are inferred from historical data distributions. Under this framework, rare or highly irregular events, such as tsunamis, are assigned high initial VoI scores that diminish rapidly to reflect their urgency [1]. Similarly, some studies adopt probabilistic frameworks that relate VoI to the likelihood of event occurrence. For example, ref. [7] models the collected data using a Poisson distribution, where infrequent occurrences in historical records imply greater rarity and, hence, greater importance. Another related method applies anomaly detection, where VoI is elevated for data that deviates significantly from known patterns, emphasizing information novelty in heterogeneous underwater wireless sensor networks (H-UWSNs) [10]. In contrast, a different class of VoI models focuses exclusively on time-based decay, disregarding event rarity. These approaches embed VoI decay directly into the decision-making process for AUVs. In [9], VoI is treated as a non-increasing function that decays exponentially over time, with the decay rate reflecting the urgency of the observed event. This formulation allows AUVs to prioritize visits to sensor nodes producing high-urgency data. Similarly, ref. [6] introduces a unified metric that combines time decay and data importance to guide sink node selection and AUV trajectory optimization. More recent approaches, such as [11], incorporate a normalized VoI metric into the reward function of a multi-agent reinforcement learning (MARL) framework, enabling agents to learn routing policies that dynamically favor more valuable data. Likewise, ref. [16] proposes a composite VoI model that integrates signal relevance, age-based exponential decay, and expected utility. This model is embedded within a deep reinforcement learning framework to coordinate the collaborative paths of multiple AUVs. Collectively, these approaches highlight the dynamic and multi-dimensional role of VoI in optimizing underwater sensing missions. VoI-driven trajectory planning has proven to be an effective strategy for enhancing data collection efficiency. In [8], the authors propose a dynamic path planning method that steers AUVs to maximize accumulated VoI, prioritizing the collection of both timely and significant data.