Auxiliary Function Gradient Approach to Marine Vehicle Path-Following Control

Abstract

This paper develops an approach to solving the problem of controlling the movement of a ship along a route. It is assumed that the route is specified using waypoints connected by line segments. The main idea of ​​the developed approach is to construct a set of auxiliary smooth functions having an extremum (maximum) on the corresponding sections of the route. The gradient vectors of the selected auxiliary functions are directed towards the corresponding section of the vessel's route. The sum of the vectors of the gradient of the auxiliary functions and the vector that specifies the direction on the selected section of the route determines the desired course of the vessel movement. It is shown that the chosen constructing algorithm for the desired vessel course ensures its output to the given trajectory.