## 6 Discussion and Future Work  
This study investigated the motion behavior of an ROV under the influence of ocean currents and wake disturbances. The primary contribution lay in improving the accuracy of the hydrodynamic damping matrix \(\mathbf{D}\), which is often oversimplified in traditional models. Refining this matrix based on empirical data and theoretical corrections, we aimed to enhance the ROV's responsiveness to lateral and angular hydrodynamic forces. However, several simplifications in the overall system remain, mainly inherited from the baseline control framework and the need to constrain computational complexity. These include the following:  
1. The control structure is based on a traditional PID controller, which, although widely used in marine systems, does not adapt to environmental variations or uncertainties. 2. The environmental model assumes quasi-steady ocean currents and simplified wake interference, which may not fully capture real-world turbulence or chaotic fluctuations. 3. The simulation does not incorporate external feedback loops, real-time sensor data, or actuator dynamics. 4. The study is limited to a single-ROV scenario and does not account for distributed cooperation or inter-ROV interference. While these simplifications are standard in preliminary marine vehicle modeling, we performed a comparative simulation to evaluate their quantitative impact. Specifically, we examined the difference in trajectory when wake flow effects were excluded from the damping matrix \(\mathbf{D}\). The results indicate that neglecting wake interference can result in trajectory deviations of up to 3.9% in lateral motion under certain ocean current configurations. Therefore, the assumption of steady-state flow and uniform damping, as used in traditional models, may underestimate hydrodynamic disturbances in real-world conditions. This further justifies the inclusion of an empirically corrected damping matrix in our study. Based on similar findings in related hydrodynamic simulation studies, other assumptions, such as fluid incompressibility and rigid body modeling, are expected to introduce smaller errors (typically below 1.5%) in low-speed operations. Moreover, the current damping model assumes a diagonal damping matrix with simplified quadratic nonlinear terms, neglecting cross-coupling between different degrees  
Figure 13: The simulation result of the proposed model. of freedom and potential higher-order nonlinear damping effects. While this assumption balances model complexity and computational efficiency, it limits the ability to capture complex hydrodynamic interactions that may significantly influence ROV dynamics in turbulent or rapidly changing flow conditions. Future research will focus on incorporating these effects to enhance model fidelity and simulation accuracy. While unnecessary for focusing on the damping model's impact, these constraints could reduce the model's fidelity when applied to field deployments or more complex operational conditions. As noted by the reviewers, unexpected environmental fluctuations, model uncertainties, and control delays may affect both performance and stability, especially in unstructured or chaotic marine environments. In future works, we plan to address these limitations in several directions. First, we will consider time-varying and turbulent flow fields to better model realistic ocean disturbances. Second, advanced control strategies, such as model-predictive control (MPC) or data-driven adaptive methods, may be incorporated to improve system robustness. Third, extending the framework to include multi-ROV interactions and cooperative decision-making will allow for more complex mission scenarios. Additionally, improving the visual simulation platform and analyzing computational efficiency will be necessary for real-time deployment on embedded hardware.