This paper studies the trajectory tracking control problem of an autonomous underwater vehicle (AUV). A robust model predictive control (MPC) framework based on the implementation of the receding horizon is implemented to address the challenges of unknown external disturbances and model uncertainties faced by the AUV in trajectory tracking control. Within this MPC framework, a formulation that simultaneously handles both practical actuator limitations and dynamic environmental constraints is introduced. Specifically, the controller enforces hard constraints on both the maximum driving force and also the maximum rate of change in the propeller driving force. This rate constraint is essential for ensuring the control signal respects the physical dynamics of the thrusters and prevents hardware damage. These hardware-level constraints are integrated with online updates of system state constraints which define the AUV’s working space, granting it autonomous obstacle avoidance capabilities. Finally, the performance of the controller is demonstrated by simulations and physical experiment results.