Inequality Constrained Optimal Control for Rope-Assisted ASV Docking Maneuvers

Abstract

In difficult whether conditions the complexity of docking maneuvers of autonomous surface vessels (ASVs) increases. Docking maneuvers take place in proximity to piers and other vessels. The slow speed at which the maneuvers take place decreases the maneuverability of the vessel and environmental disturbances such as wind and waves increase in effect. In these scenarios ropes can be utilized to support the maneuver and compensate for the compromised actuation capabilities. The modeling of the modified mechanics plays a center role. It has been shown in previous work that this setup, connecting the vessel to the pier with a constant distance (e.g. with a rod) can be modeled using the concept of differential-algebraic equations (DAEs). With the adapted vessel dynamics a trajectory generation problem can be solved using optimal control theory. Here, a direct numerical method, in this case a full discretization of the optimal control problem (OCP), is used. The contribution in this paper allows for slackness in the rope. This is done by using a smooth penalty function, as well as solving a complementary problem. Both methods lead to feasible solutions. The penalty function shows are more smooth behavior but suffers from numerical robustness in comparison to the linear complementary solution.