Optimal Coordination of Autonomous Tugboats for Manoeuvring Ships

Tugboats are deployed to support underactuated vessels, such as container ships or unactuated offshore platforms during a manoeuvre. This requires precise manoeuvring and a high degree of coordination between the individual vessels involved to avoid collisions and to ensure the safety of crew members. Based on this, the interest in automating tugboats has increased. Therefore, this paper proposes a method for coordinating tugboats in a multi-vessel compound system, together with subsequent manoeuvre planning. To this end, direct contact and tow ropes are considered and defined as motion constraints. The mathematical models of the individual vessels are coupled by applying a Lagrangian approach from the theory of multi-body dynamics, resulting in the structure of a differential-algebraic equation (DAE). Through an index reduction, this DAE-system can be converted into a system consisting of ordinary differential equations (ODE) only, which enables a solution by means of standard numerical solvers. Based on this approach, an optimal control problem is defined for a berthing and an unberthing manoeuvre, which is successfully evaluated by simulations.