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In general, tugboats are used to convey many kinds of surface vessels, including unactuated vessels, such as barge ships and offshore structures. This requires an adequate model for tugboat operation to precisely take into account surge, sway, and yaw motions. We present an optimization method of tugboat operation for conveying a large surface vessel in the shipyard. An optimization problem that includes the interactions between the vessel and the tugboats is mathematically formulated. The procedure to solve this problem is composed of three steps. The desired control input, which should act on the vessel to track the desired path in the presence of environmental disturbances, is calculated every control interval. Second, the optimization problem is solved by using an optimization algorithm to find the thrust force and tug force direction for each tugboat. Finally, based on the three-degrees of freedom (DOF) horizontal model, the position and velocity of the vessel in the next step are calculated. There are three advantages to this study. First, the proposed method considers the thrust force and the direction of the tugboats at the same time, and the number of tugboats can also be changed. Second, it is possible to control the tugboats through realistic time intervals. Finally, the practical external force is considered in the application. The proposed method is applied to the conveying of a mega floating crane, one of the large surface vessels, in various environmental conditions, such as waves, winds, and currents, and the applicability of the method was evaluated.

An optimization model of tugboat operation for conveying a large surface vessel