In a previous study (see Jouffroy et al. (2011a) and Jouffroy et al. (2011b)), simple feedback algorithms referred to as Sector-of-Sight controllers were used to make Lagrangian profilers select ocean currents for transportation, and thereby achieve active horizontal displacement. In the present paper, we extend on earlier results by examining different aspects related to the convergence properties of our algorithms. Specifically, after considering the validity of the simple mathematical models that are used, we give an expression for an estimated time of arrival of the profiler on its waypoint, as well as a proof of convergence of our feedback controller in a coastal scenario where tidal currents are predominant. Simulation results illustrate the potential of the approach throughout the paper.