NEW APPROACH TO THE COLLISION AVOIDANCE PROBLEM FOR A SHIP

Abstract

A new algorithm is developed to solve the collision avoidance problem for a host ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. The objective of the collision avoidance maneuver is to maximize with respect to the state and control history the timewise minimum distance between a host ship and an intruder ship. Two limiting cases are considered: (i) the intruder ship is uncooperative and keeps its course unchanged during the encounter; (ii) the intruder ship is cooperative. In both cases, a differential game formulation is avoided and the collision avoidance problem is formulated as a maximin problem of optimal control. Four problems are investigated and their solutions compared: Problems P1 and P2 deal with uncooperative collision avoidance, while Problems P3 and P4 deal with cooperative collision avoidance. Numerical results show that the optimal control histories always involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values.