Algorithms for the ship trajectory planning and its tracking in the collision avoidance process

The paper presents a formalization of the collision avoidance problem, involving two ships at sea, in terms of nonlinear optimal control theory with state space constraints. The optimal rudder ship control and the corresponding avoidance trajectory is then found via properly chosen, task-specified numerical method based on Pontryagin's maximum principle. In the second part, the tracking problem of the previously determined trajectory is considered. The proposed tracking control system is based on linear Nomoto model of ship dynamics complemented by linearized equations of ship motion kinematics (Fossen, 1994). As the method of control synthesis the time varying LQ controller of Bryson and Ho (1969) is adopted. The obtained optimal solution is a combination of a time varying feed forward plus a state feedback controller. This form of controller makes it possible to take into account also measurable sea load disturbances as e.g. current and/or wind influence. The simulations of both collision avoidance process' as well as optimal trajectory tracking are presented. Copyright (C) 2001 IFAC.