With advances in underwater exploration and intelligent ocean technologies, wheeled underwater mobile robots are increasingly used for seabed surveying, engineering, and environmental monitoring. However, complex terrains centered on seabed soft slopes—characterized by wheel slippage due to soil deformability and force imbalance arising from slope variations—pose challenges to the accuracy and robustness of trajectory tracking control systems. Model predictive control (MPC), known for predictive optimization and constraint handling, is commonly used in such tasks. Yet, its performance relies on manually tuned parameters and lacks adaptability to dynamic changes. This study introduces a hybrid grey wolf-particle swarm optimization (GPSO) algorithm, combining the exploratory ability of a grey wolf optimizer with the rapid convergence of particle swarm optimization. The GPSO algorithm adaptively tunes MPC parameters online to improve control. A kinematic model of a four-wheeled differential-drive robot is developed, and an MPC controller using error-state linearization is implemented. GPSO integrates hierarchical leadership and chaotic disturbance strategies to enhance global search and local convergence. Simulation experiments on circular and double-lane-change trajectories show that GPSO-MPC outperforms standard MPC and PSO-MPC in tracking accuracy, heading stability, and control smoothness. The results confirm the improved adaptability and robustness of the proposed method, supporting its effectiveness in dynamic underwater environments.

With the rapid development of deep-sea resource exploration and marine scientific research, wheeled remotely operated vehicles (ROVs) have become crucial for seabed operations. However, under complex seabed conditions, traditional ROV control systems suffer from insufficient trajectory tracking accuracy, poor disturbance rejection capability, and low dynamic torque distribution efficiency. These issues lead to poor motion stability and high energy consumption on sloped terrains and soft substrates, which limits the effectiveness of deep-sea engineering. To address this, we proposed a comprehensive motion control solution for deep-sea wheeled ROVs. To improve modeling accuracy, a coupled kinematic and dynamic model was developed, together with a body-to-terrain coordinate frame transformation. Based on rigid-body kinematics, three-degree-of-freedom kinematic equations incorporating the slip ratio and sideslip angle were derived. By integrating hydrodynamic effects, seabed reaction forces, the Janosi soil model, and the impact of subsidence depth, a dynamic model that reflects nonlinear wheel–seabed interactions was established. For optimizing disturbance rejection and trajectory tracking, a hierarchical control method was designed. At the kinematic level, an improved model predictive control framework with terminal constraints and quadratic programming was adopted. At the dynamic level, non-singular fast terminal sliding mode control combined with a fixed-time nonlinear observer enabled rapid disturbance estimation. Additionally, a dynamic torque distribution algorithm enhanced traction performance and trajectory tracking accuracy.