The Optimal Steering Calculation Method of Passing through Several Waypoints

Abstract

The authors made the analytical solution of ship trajectory by simple zigzag maneuver with equal time-alternative steering in their previous study. It is found, in this study, that 1) Lateral deviation remains even after the helm returns to midship, 2) The bigger the T(index of stability on course and quickness in responding to steering) becomes, the longer the maximum lateral deviation is delayed. These facts indicate it is hard to predict ship trajectory even by the simple steering. It is more difficult, consequently, to search the steering of passing through some waypoints. This report describes how to compute the optimal steering for passing through several waypoints by linear theory with constant velocity. The steering function is expressed as Fourier sine series with coefficients which are fixed by calculus of variations under the restriction on passing through all waypoints. A frigate and a container, as examples, are analyzed along with the target course represented by three waypoints. The analysis shows that ship length and Nomoto's steering quality indices have strong influence on both capability of passing through waypoints and lateral deviation from the target course.