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Unmanned underwater vehicles perform inspection and maintenance tasks in complex and changing environments. Some of these tasks require synchronous navigation of multiple vehicles, which is challenging. This paper proposes a synchronous navigation scheme for two BlueROV2 underwater vehicles for a coordinated multi-vehicle task. In the proposed scheme, the vehicles perform the collaborative task of grasping, transporting, and releasing an object. In this scheme, no vehicle-to-vehicle communication is required. A model-free second-order sliding mode controller with finite-time convergence is used to accomplish this task. The controller’s convergence time is user-defined and does not depend on the physical or hydrodynamic parameters of the vehicle, unlike the other finite-time controllers found in the literature. Simulation experiments were conducted to verify the controller’s performance, including high ocean currents as external disturbances. Comparisons were made with two state-of-the-art controllers with finite-time convergence. The results showed that the proposed controller achieved the best results, as the user-defined convergence time was achieved for both vehicles and the collaborative task was completed, no ripples, deviations, or oscillations were observed, and no chattering occurred. The results proved the robustness of the controller in the presence of high ocean currents without the need to readjust the parameters.