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The trajectory tracking problem for a fully-actuated real-scaled surface vessel is addressed in this paper by designing a backstepping controller with a multivariable integral action, considering the thruster allocation problem. The performance and robustness of this controller are evaluated in simulation, taking into account environmental disturbance forces and modeling mismatch, using a docking maneuver as a reference trajectory. Furthermore, a comparison between the backstepping controller and a nonlinear position PID-Control with flatness based-feedforward is also analyzed.