Method for calculating the positions of specific points on the multifocal ship’s domain

The concept of approximating of a ship’s domain on the ground of the continuous deformable media is considered as a continuous set of points of the multifocal ellipse. It is also applicable in the navigational hazards clearing problem. The configuration of the multifocal ellipse ship’s domain allows to present more accurately the information of the various kinematic and dynamic parameters of the vessel’s motion and generate the control actions to ensure safety of navigation. If ship’s domain is formalized as the multifocal ellipse safety of navigation requires the development of the principles of control actions on the kinematic level. The non-trivial problem of determining the positions of the special points on the ship’s domain: the closest point on the ship’s domain to the navigational hazard, intersection point with the relative motion line, and the “extreme” points arises. Due to the nonlinearity of the multifocal ellipse equation, variations of the size and shape of the ship’s domain caused by the ship’s movement and the current navigation situation, the represented results are grounded on the classical navigational position fix method — the generalized method of the position lines. The general provisions of the research are supported by the infographics and are brought to practical application. The formalization of the proposed methods in the automatic navigation or in autonomous ship’s control systems will enable the navigator on board or operating the vessel remotely to solve the various navigation problems on a new level and in interconnection with traditional methods of safety of navigation monitoring.