Defense Research and Development Canada (DRDC), in collaboration with the University of New Brunswick (UNB) and other partners, has proposed a program to develop an autonomous docking device capable of launching and recovering UUVs (Underwater Unmanned Vehicles) from a submerged submarine. The autonomous docking device being developed is called “hydrodynamically actuated manipulator” (HAM). The main objective of the HAM is to follow a real-time trajectory for launching and recovering UUVs. In this work, the first contribution is to provide a model for the HAM based on nonlinear ordinary differential equations. The second contribution is the stability assessment, and the estimation of convergence time of the closed-loop system based on a set of second order sliding mode controllers plus a PD term considering external uncertainties with linear and nonlinear growth. Numerical Simulations of a one-link pendulum and the HAM are considered as test beds in order to support the theoretical results.