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This paper presents a comparative study of docking algorithms intended for non-holonomic autonomous underwater vehicles, docking in funnel-shaped docking stations, operating under the influence of ocean currents. While descriptive surveys have been already reported in the literature, our goal is to compare the most relevant algorithms through realistic Monte Carlo simulations to provide an insight into their performance. To this aim, a new numerical performance indicator is proposed, which, based on the geometry of the manoeuvre, is able to characterize a successful or unsuccessful docking, providing a metric for comparison. The experimental study is carried out using hardware-in-the-loop simulation by means of the Stonefish simulator, including the dynamic/hydrodynamic model of the Sparus II AUV, models of all internal and external sensors, and the collision geometry representing the docking station.