## 2 Extension and Refinement of the Ocean Disturbance Simulation System Model
### Theoretical Basis  
The proposed method established a closed-loop framework within the MATLAB/Simulink environment to enable accurate motion control and dynamic simulation under ocean current disturbances. The system architecture comprised four interdependent modules--Kinetics, Kinematics, Controller, and Allocation--constituting an underwater vehicle's fully integrated motion control and simulation loop [10]. The functional descriptions of each module are as follows. 1. Kinetics Module  
The Kinetics module models the dynamic behavior of the underwater vehicle by solving the six-degrees-of-freedom (6-DOF) Newton-Euler equations of motion. It receives external force and moment inputs \(\mathbf{\tau}\) and ocean current disturbances \(v\) and computes the linear and angular accelerations of the vehicle. The dynamic model includes an inertia matrix \(\mathbf{M}\), a Coriolis and centripetal matrix \(\mathbf{C(v)}\), a hydrodynamic damping matrix \(\mathbf{D}\), and a restoring force vector \(\mathbf{G(n)}\), all contributing to a physically realistic simulation. The resulting accelerations are passed to the Kinematics module for further processing. 2. Kinematics Module  
This module estimates the real-time status of the robot, including position, velocity, and orientation (i.e., roll, pitch, and yaw angles). It integrates the accelerations provided by the Kinetics module to derive the vehicle's motion trajectory in the global frame. The module also accounts for initial pose conditions and continuously updates the robot's motion states throughout the simulation [11]. The resulting kinematic information is then forwarded to the Controller module to support closed-loop control [12]. 3. Controller Module  
The Thruster module acts as the actuator interface. It is responsible for transforming the individual thruster commands into a combined force/moment vector \(\mathbf{\tau}\) applied to the vehicle in six degrees of freedom. The module can compute the net force and moment exerted by all thrusters using the thruster configuration model, considering their positions, orientations, and operational characteristics [14]. The output \(\mathbf{\tau}\) is then used by the Kinetics module to update the robot's motion dynamics, thereby closing the simulation loop. In this paper, the dynamic model of the underwater vehicle is established based on the Newton-Euler equation. The dynamic model of the underwater robot is defined as follows:  
\(\mathbf{\tau}\) is the external input control force and moment;  
\(\mathbf{\
u}\in\mathbf{R^{6}}\) denotes the velocity vector of the underwater vehicle expressed in the body-fixed frame. It is composed of three linear velocity components (\(u\), \(v\), \(w\)) and three angular velocity components (\(p\), \(q\), \(r\)):  
\[v=[u,v,w,p,q,r]^{T}, \tag{1}\]  
\(\dot{v}\) denotes the time derivative of \(v\). The forms of each matrix are expanded as follows. Inertia matrix \(\mathbf{M}\)  
The inertia matrix \(\mathbf{M}=\mathbf{M}_{\mathbf{R}}+\mathbf{M}_{\mathbf{A}}\) consists of two parts:  
\(\mathbf{M}_{\mathbf{R}}\): inertia term composed of rigid body mass and rotational inertia;  
\(\mathbf{M}_{\mathbf{A}}\): the added mass matrix accounting for the fluid-induced inertial effects due to the hydrodynamic coupling between the vehicle and the surrounding water. The complete form is as follows. The body-fixed coordinate system is defined with its origin located at the vehicle's center of gravity (CoG). The x-axis points forward, the y-axis points to the starboard, and the \(z\)-axis points downward, following the standard right-hand convention. In the following matrix, \(m\) denotes the mass of the ROV. \(I_{x}\), \(I_{y}\), and \(I_{z}\) represent the moments of inertia about the roll, pitch, and yaw axes, respectively.