With the growing interest in autonomous surface vessels in the recent years, besides the tasks of driving and positioning, more demanding maneuvers have to be considered, e.g., docking maneuvers. Difficult weather conditions increase the complexity of docking maneuvers because of their proximity to piers or other vessels. As an example, fast sideways winds induce a significant rotational moment on the ship and can prevent it from docking successfully. This contribution proposes a method to perform a simplified rope-assisted docking maneuvers for these cases which results in a differential algebraic (DAE) system description. The docking task is embedded in an optimal control problem (OCP), which is solved using a direct (simultaneous) method. Therein, two methods are proposed to integrate the DAE system numerically. To this end, a DAE solver tailored for the solution of index-1 DAE systems is compared to the proposed method which introduces a constraint force to the ODE that serves as an additional decision variable. Additionally, a mathematical description of the vessel’s environment such as static, and possibly dynamic, obstacles is included in the proposed OCP by means of a dual approach. The two integration techniques are compared using a simulated docking scenario.