## 1 Introduction  
In recent years, the global underwater robotics market has been experiencing rapid growth (Figure 1). Underwater robots have a wide range of applications and significant market demand in fields such as deep-sea exploration, aquaculture, and marine engineering [1]. Currently, a variety of robots have been developed that can operate at different depths and perform multiple tasks, including oil extraction, seabed mineral surveys, salvage operations, pipeline laying and inspection, cable installation and inspection, offshore aquaculture, dam inspections in rivers and reservoirs, and military applications [2]. Underwater robots are increasingly vital in military and civilian sectors, among which autonomous navigation and path planning are considered core technologies. A significant body of research has focused on the path planning and simulation of underwater robots, with particular emphasis on enhancing performance in complex marine environments. A deep-sea condition-based simulation system has been developed to replicate underwater scenarios, highlighting the importance of intelligent path planning for improving operational efficiency [3]. However, such systems often assume simplified current fields and do not integrate high-fidelity control or close-range hydrodynamic effects, which limits their predictive capability in dynamic environments. A six-degrees-of-freedom underwater robot model has been proposed to track moving targets, offering high precision and incorporating ocean current effects; however, it is limited to tracking along fixed linear paths and does not account for wake flow during close-range maneuvers, reducing its applicability in dynamic settings [4], which are especially critical during docking, inspection, or other operations that require precise proximity control. The genetic algorithm-based simulation framework considers automatic obstacle avoidance and two-dimensional ocean current influence, yet it remains constrained to planar analysis, omitting the impact of three-dimensional current disturbances and wake effects on trajectory accuracy [5], limiting its applicability in complex ocean environments where vertical current gradients and vortex shedding significantly affect vehicle stability. Another model integrates path planning in ocean environments but lacks support for three-dimensional current simulations, thus failing to provide robust trajectory optimization for real-world deployment [6]. While effective in route optimization, this model abstracts away from physical hydrodynamics and fails to simulate near-field flow interactions needed for real-time control. Force and motion data of a tethered ROV operating under combined wave and current conditions have been presented to provide a reliable benchmark for validating numerical simulation methods [7]. The fixed structure cannot support trajectory tracking or adaptive control in unstructured flow fields. However, the fixed configuration of the ROV in this setup limits its applicability to scenarios requiring real-time control and unrestricted movement. A computational fluid dynamics (CFD)-based modeling approach has also been employed to analyze hydrodynamic forces on ROVs under varying current speeds and flow directions [8], suggesting that similar hybrid techniques could be adapted to underwater domains, especially for real-time trajectory tuning in turbulent fields. Nevertheless, this method lacks integration with trajectory tracking and closed-loop control mechanisms. In a related domain, an aerodynamic optimization method has been proposed for reducing drag on vehicle surfaces using CFD in combination with machine learning and genetic algorithms [9]. Although applied in an atmospheric environment, this approach highlights the potential of simulation-driven optimization strategies for improving underwater trajectory planning in complex flow fields.