This paper explores the effectiveness of Model Predictive Control (MPC) for trajectory tracking in autonomous deep-sea tracked mining vehicles operating within polymetallic nodule mining environments, considering model uncertainties and external disturbances. Traditional applications of MPC in autonomous vehicle trajectory tracking, which typically rely on kinematic models under minimal external disturbance, often fail when faced with model inaccuracies and external disruptions. To address these challenges, we propose an MPC-based trajectory tracking algorithm that includes a speed correction controller for the drive wheel. This controller, developed through experimental data fitting, aims to mitigate issues such as vehicle body subsidence and track slippage. Tracking accuracy, particularly in curve navigation, is further enhanced through the use of Kalman Filtering (KF) and Adaptive Kalman Filtering (AKF) to counteract external disturbances. Moreover, we introduce an obstacle avoidance strategy utilizing a tri-circular arc trajectory with uniform curvature for path re-planning. This strategy effectively addresses dead zones and physical obstructions encountered during operation. The superiority of our approach compared to conventional Nonlinear MPC (NMPC) is demonstrated through extensive Simulink and Recurdyn co-simulations.