Mathematical modeling of the trajectory of a ship as a control object in local planning

Odessa National Maritime University, Department “Navigation and Marine Safety”, Mechnikova str, 34, 65029, Odessa, Ukraine

^* Corresponding author: kupraty@ukr.net

Abstract

In the article proposes the decomposition of the global planning task in local planning. It is proposed to combine the segment method and the sector method of division of the circle to construct the ship’s trajectory in local planning. Corrective coefficients were selected for the correct geometry of the turning trajectory, combining the segment method and the sector method of constructing the ship’s trajectory. The article uses formulas of spherical trigonometry; the trajectory of the turn depends on the rudder angle, which in turn depends on the turning ability of the vessel under the given conditions. In determining the value of the angle of the rudder, the control device must take into account the ship’s turning ability in the conditions set, the value of the angle of the turn and the constrained water area. The combination of all factors allows to differentiate the ship’s turning ability such as: high HG, middle MD or low LW with regard to passage area. The ME shifting operating modes matrix proposed in the article works as a filter of modes of operation and is completely dependent on the readings of pressure, temperature and vibration sensors. The ship’s trajectory is constructed using calculations in MS Excel and graphic simulations in the MATLAB environment.