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Collision avoidance for encounters between several ships and installations in the open sea, is treated as a problem of optimal control, using the theory of differential games. Each ship is, in this idealized model, assumed to have two controls corresponding to rudder angle and engine setting. The objective function, which the shipmasters try to minimize in an optimal evasive manoeuvre, is defined as the collision risk. Numerical solutions for the M-ships and I-installations optimal evasive manoeuvre problem, can be found by the ping-pong algorithm. Numerical examples are given for up to five ships and two installations

Optimal Evasive Maneuver for a Ship in an Environment of Fixed Installations and Other Ships