## 2 Materials and Methods  
Global path-planning methods for AUVs can generally be classified into two categories: those that incorporate a dynamic model of the vehicle and those based solely on kinematic constraints. In this section, the nonlinear AUV model utilized in this study is presented, along with the RL methods that directly leverage this model. Additionally, a brief overview of the classical path-planning algorithms used is provided, followed by a discussion on how  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Title (Year)** & **Map Type** & **RL Algorithm** & **Motion Model** & **Environment** & **Platform** & **Key Contribution** \\ \hline _AUV Obstacle Avoidance via Deep RL_ ([PERSON] et al., 2021) [48] & Active sonar (mapless) & Double DQN (LSTM) & 3-DOF dyn. & Simulation & AUV & End-to-end obstacle avoidance using sonar inputs. Demonstrates collision-free navigation in unknown areas underwater. \\ \hline _Path Planning under Ocean Currents with DDQN_ ([PERSON] et al., 2023) [49] & 2D grid & Double DQN (CNN) & Dynamic (w/ current) & Simulation & AUV & Incorporates current disturbances into the CNN-based planner. Outperforms A* and RRT in strong current fields. \\ \hline _SAC-Based Game Trainures_ ([PERSON] et al., 2022) [50] & Random obstacles & SAC (game-theoretic) & Dynamic & Simulation & AUV & Adversarial approach with policy adaptation to the environment (obstacles). Improves robustness under high uncertainty. \\ \hline _Adaptive Deep RL for 3D Navigation_ ([PERSON] et al., 2024) [51] & Vision-based, mapless & PPO & 6-DOF dyn. & Simulation & AUV & End-to-end 3D navigation using visual inputs. Stably achieves goals in complex underwater spaces. \\ \hline _Noisy Dueling Double DQN for AUV_ ([PERSON] et al., 2024) [52] & 2D grid + current data & ND3 QN (drift) & Simulation & AUV & Uses dueling Q-nets with parametric noise for better exploration and stable training. Handles variable currents. \\ \hline _Improved PPO for USU Obstacle Avoidance_ ([PERSON] et al., 2023) [53] & Radar-based local map & PPO (CNN) & Dynamic & Simulation & USV & Modified PPO with priority replay and a CNN architecture for the radar input. Converges faster and avoids collisions effectively. \\ \hline _Offline RL for USU Trajectory Tracking_ ([PERSON] et al., 2024) [54] & N/A (route known) & SAC (en-smello) & Dynamic & Sim + real (full-scale) & USV (full-scale) & Offline-trained controller validated in simulations and sea trials. Robust to waves and currents. \\ \hline _DDPG-Based Global Path Planning to USUVs_ ([PERSON] et al., 2023) [55] & 2D grid (static obs.) & DDPG & Kinematic & Simulation & USV & A global planner surpassing A* and heuristics in its path length, safety, and computation time. \\ \hline _Safe Lyapunov-DDPG for Target Interception_ ([PERSON] et al., 2022) [56] & No map (moving target) & SLDDPG & Dynamic & Simulation & USV & Integrates Lyapunov constraints for safe interception. Ensures bounded errors and avoids collisions. \\ \hline _Multi-AUV Cooperative Hunting with MAPPO_ ([PERSON] et al., 2025) [57] & No explicit map & MAPPO & Dynamic & Simulation & Multi-AUV & Knowledge-guided policy from potential fields. Coordinates multiple AVs for target pursuit under currents. \\ \hline _Our (2025)_ & Simplified ENC (binary) & SAC, TQC & TQC & 6-DOF dynamic (full motion model) & Simulation (real port AUV map) & Proposes a curriculum-trained deep RL approach on a real-world ENC map, integrating a full 6-DOF AUV motion model. Demonstrates smooth, high-speed collision-free trajectories. Outperforms classical methods (A*, PSO, GA) in its success rate and mission time across multiple scenarios. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparative overview of RL-based path planning methods for underwater and surface vehicles (2015–2025).  
the generated paths are smoothed and converted into feasible trajectories while considering the motion constraints of the AUV.