Mathematical model and simulation of cooperative manoeuvres among a ship and tugboats

Assisting harbour tugboats are essential for safe navigation in ports and for berthing/unberthing operations. Because the port infrastructure needs to be updated in the coming age of autonomous ships, autonomous tugboats or remotely controlled tugboats are expected to be part of the navigation assistance provided by future ports. Although there have been some studies on the design of cooperative control of tugboats, few studies have focused on the mathematical model of their cooperative manoeuvres. Particularly, in the case of pushing assistance, tugboats have often been treated simply as a kind of side thrusters attached to the assisted ship. Thus, we present a new framework of the mathematical model for cooperative manoeuvres that considers the coupled motions among tugboats and a ship as precisely as possible. Solving the dynamics of all tugboats as well as the assisted ship can render the model more advanced and realistic, and is the most significant contribution of this study. The simulation tool based on the proposed model can be used as a plant model in designing and verifying the tugboat’s manoeuvring control system in the future. In this study, as examples, considering a tentative control method, some unique scenarios were simulated to demonstrate the cooperative manoeuvres.