3. EFFECTIVENESS OF MINIMUM TIME MANEUVERING SOLUTION
In this section, we will show one of the actual results on the minimum time berthing maneuvering to demonstrate that the optimal maneuvering command numerically calculated under the above minimum time control formulation is also realizable and effective in the actual maneuvering phases. Table 1 shows the principal dimensions of the ship used in the actual sea test.
Table 1 Principal dimensions of the target ship
The maneuvering problem treated with this paper is generally shown in Figure 2.
Fig.2 Minimum time maneuvering problem
When the ship's velocity is vanished at the terminal point, it is called by 'Berthing Problem'. When the velocity is maintained at the initial speed, it is called by 'Course Changing Problem'. In this section, we treat the former problem whose solution has been already obtained in the latest paper.
It is difficult to use numerical solution directly for controlling ship at the real sea, because of various disturbances. Therefore, in order to track to the trajectory gained by calculation as faithful as possible, we provided a feedback controller shown in Figure 3.
Fig.3 Outline of tracking control system
3.3 Result of Actual Sea Test
Fig.4 The result of the actual sea test
Figure 4 shows the results of the actual sea test. The actual trajectory of the ship is indicated by solid line and the path of numerical solution is drawn by dot line.
This result clearly shows that the minimum time maneuvering method obtained by calculation is actually able to track with appropriate controller and yields reasonable and rigorous maneuvering method from the view point of the ship handling theory.