# AUV Trajectory Planning for Optimized Sensor Data Collection in Internet of Underwater Things
## 3 Results and Discussion  
This section evaluates the performance of the proposed method through MATLAB simulations. The results demonstrate its effectiveness in selecting optimal USV start and end positions and in generating an AUV trajectory that enables efficient data collection in UASNs for IoUT applications, while maximizing the total residual Vol. The AUV preserves approximately 64-70% of the total residual Vol upon returning to the USV. Benchmarking is essential to demonstrate the performance of the proposed method. However, direct comparison with some related approaches is limited due to substantial differences in platforms, assumptions, and system configurations. For instance, many studies rely on UAVs [27; 28; 29], do not explicitly model time-decaying Vol or distinguish between emergency and non-emergency data [27; 31], depend on multi-hop routing [1; 16], or involve multi-AUV coordination [16; 31]. To provide meaningful insight, the baseline methods selected in this section are intended to highlight specific aspects of the proposed approach. We aim to demonstrate its effectiveness by showing how incorporating kinematic constraints and waypoint flexibility can positively impact residual Vol, and by revealing the limitations of optimizing solely for travel efficiency while ignoring the temporal sensitivity of information value. In this section, we benchmark the method against three baseline strategies. First, a straight-line path strategy connects waypoints using direct Euclidean paths without considering the AUV's maneuvering limitations, as presented in [39]. While this approach produces shorter paths, it overlooks the vehicle's kinematic feasibility. In contrast, our method generates practical trajectories using arc-plus-straight-line motion, reducing overall travel time and improving Vol preservation by respecting the AUV's motion constraints. Second, we compare against a strategy in which each CH is represented by a single fixed point located above it on the \(z_{d}\)-plane. This approach aligns with prior studies that consider only the node locations and optimize the visiting sequence accordingly, as shown in [42; 43]. In contrast, our approach selects from multiple candidate points along the horizontal circle \(C_{i}\) of each CH, offering greater routing flexibility and reducing travel requirements while maintaining efficient data collection performance. Finally, we benchmark against a conventional Traveling Salesman Problem (TSP)-based approach, which has been widely adopted in prior studies such as [39; 44] for planning AUV trajectories for data collection. This method first solves the Euclidean TSP over all candidate waypoints and then applies the proposed Dubins-like trajectory planning. Whilethis method minimizes total travel distance, it remains unaware of VoI dynamics. In contrast, our approach integrates VoI decay, kinematic feasibility, and strategic waypoint selection, resulting in improved mission performance. The system parameters are set as follows: \(u_{\text{max}}=2\) m/s, \(\omega_{\text{max}}=2\) m/s, \(r_{\text{max}}=2\) rad/s, \(z_{d}=-15\) m, \(R_{i}=16\) m, and \(\tau=1\) s. The AUV is deployed from a USV that moves from \(S_{s}\) to \(S_{f}\) along the sea surface (\(z=0\)). The simulation environment is a 3D underwater region defined by \(x\in[0,\ 50]\), \(y\in[0,\ 50]\), and \(z<0\), with depth variations generated using a grid combining smoothed noise and sinusoidal patterns, centered around a mean depth of \(-25\) m. The network consists of 100 sensor nodes divided into five clusters (\(M=5\)), each represented by a designated CH. The importance degree \(\mathcal{I}_{i}\) for each CH is assumed to be pre-determined based on input from neighboring sensor nodes and broadcasted to the AUV prior to mission start. The simulation is conducted based on the UASN model illustrated in Figure 4. Figure 4 displays the target underwater environment, including the sensor nodes and the uneven seafloor.