Application of the proportional navigation method in solving problems of navigation

Abstract

The development of methods and algorithms for ship control when maneuvering relative to a moving object and the creation of automated control systems based on these developments is an urgent task of navigation. The most optimal way to implement control of a moving object relative to another moving object is based on using the proportional navigation method. As applied to navigation problems, this method has been studied at the level of describing the kinematics of the movement of two points. The mathematical model provides for a preliminary calculation of the extrapolated ship coordinates. The construction of ship motion trajectories for any given proportionality factor is carried out taking into account the dynamics of the ship and makes it possible to obtain the law of rudder shift, as well as to predict changes in the process of maneuvering such ship parameters as angular velocity and drift angle. The proposed mathematical model can be used for algorithmic and software support for automated ship control systems when maneuvering relative to a moving object.