## 4 Experimental Validation
### Calm Water Area  
The validation in calm water was conducted by navigating the Quadmaran vessel automatically in a DP posture using various initial conditions of position and heading angle. The GPS system, ichimill, recorded the location information every 2 s [23], and was confirmed to be accurate with an error within centimeters through tests. In addition, the recorded rotation speed value of the four propellers was used in the calculation. Moreover, in this study, to avoid machine time delays and accurately grasp the direction of rotation of the propeller, we decided to operate the propellers only in the forward direction. In the tests, out of the four propellers, we only operated the two that rotate in the forward direction.  
Figure 15 shows the running test scene in the pool while in DP. The wind was weak on the test day and was ignored. Figure 16 shows the recorded DP trajectories of the Quadmaran vessel in the calm water area with the heading angle set to 0, 45, and 90 degrees from a specific starting position with no initial speed and yaw rate. From the recorded DP trajectory, we can see that the Quadmaran vessel navigated to the designated reference point, no matter the initial heading angle. Moreover, after arriving at the target, it remained within roughly 1 m of the designated reference point.  
Here, we employed the developed motion prediction model and compared it with the calm water experiment results. Figures 17-19 compare the experiment and simulation results when the initial heading angle was 0, 45, and 90 degrees. From the results, we can see that the model predicted the motion of a Quadmaran vessel during DP with an accuracy of roughly 2 m. However, the trajectory of the path of the vessel was different and varied depending on the initial heading angle and loads acting on the vessel. Especially in the case of an initial heading of 45 degrees (Figure 18), the trajectory demonstrated the effect of moment generated due to parallel motion. As discussed previously in Figure 10a, moment generated fluctuated between 20 and 45 degrees, and it was relatively challenging to predict the motion while in DP. The error in position prediction could be further reduced if the moment generated in parallel motion can be accurately assessed. Propeller deformation due to long-term use and GPS error are other sources of error in prediction for all the simulations. However, for practical purposes, an accuracy of 2 m is small, and it can be said that the developed computational model predicted the trajectory motion very well.  
Figure 16: The trajectory of the running tests in calm water.  
Figure 15: Running test scene in calm water.  
point was within 10 m. Further, once the reference point was within 2 m, a one-minute timer was turned on. Within this one minute, the vessel arrived at the reference point in DP model. After the timer ended, the vessel switched back in to straight navigation mode and proceeded to the next point.  
At P1-P5, all propellers were operated. As in the calm water area tests, only two propellers that rotate forward were operated at P6-P10. The overall recorded route of the Quadmaran vessel is depicted in Figure 21.  
The wind speed measured on the test day varied between 2 and 4 m/s. From Figure 21, we can see that the Quadmaran vessel sailed well under such wind conditions and followed  
Figure 21: The route of the navigation tests in the actual sea area.  
Figure 20: Validation tests in the actual sea area.  
In addition, from the validation results in the calm water area and actual sea area, we found that slow motions can be captured well through oblique towing tests and static turning tests based on the quasi-static motion assumption. Through the computational model, we now have a deeper understanding of the motion characteristics of the Quadmaran vessel while in DP. The method can be used as a basis for multi-hull navigation vessels to predict and improve the DP performance.