This article presents a redundant control strategy of fully-actuated underwater vehicles. The proposed strategy offers vehicles more control flexibility for addressing the position tracking problem under the attitudes and velocities constraints. In kinematics, position tracking is formulated as a convex optimization problem, where the velocity constraints are considered as a feasible region and the attitudes are bounded via a barrier function. Then, a conservative boundary is determined in the context of stability analysis of the dynamic controller with a disturbance observer and an auxiliary system so that kinematic variables lie in the constraints even with the velocity tracking error. Also, it is proven that the position tracking error can converge to a neighborhood about zero, which can be made arbitrarily small. The simulations and experimental results through multiple scenarios have illustrated the efficiency of the proposed strategy.