Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019


Calculating via equation 5, the only unknown variable in the 2 −4 = 0, reveals the new course which is optimal to avoid collision. In this case which provides the optimal course, there are four routes in which the TS passes through the tangent of the domain as illustrated in Figure 6 which is created with GeoGebra software. Three unsuitable ones from these routes are shown in red colour. Routes marked with C and D are not suitable solutions since they are tangent at negative time. Besides, route marked with A which passes through the head of the TS is also not a suitable solution due to the requirements of COLREGs. Only the route marked with B shown in green colour is obtained as a suitable solution.


Table 2. Navigational data identified in the cases. Navigational Data of Ships


Encounter Type


Cos [o]


Own Ship Vos


SD [kn]


1 Crossing 000 15 2 Overtaking 000 17 3 Head-on 088 14 4 Crossing 000 14 5 Crossing 000 14


2 2


RD


[Nm] [Nm] 2


Cts [o]


Target Ship Vts Dos-ts


[kn]


15 270 15 23 340


9


2 19.45 240 15 2 3.82 240 15


Table 3. Results of the experimental tests. Course


Length of Trajectory [Nm]


1 15.77 2 23.34 3 22.36 4 20.02 5


4.53 4.1 Extra


Navigating Distance [Nm]


0.77 0.34 0.36 0.57 0.71


Optimum Anti-


Collision Course [o]


028.96 012.34 095.10 005.12 043.20


Alteration to Return


Original Route [o]


-042.68 -022.83 -018.37 -051.44 -071.11


CASE 1: CROSSING SITUATION


Figure 6. Cluster of routes that the TS passes through the tangent of the ship domain


4. EXPERIMENTAL TESTS


The purpose of the experimental test is to reveal the performance of the proposed method. The experiment deals with various cases which include head-on, crossing and overtaking encounter situation. In all cases, the different parameter settings are used and the OS is approaching to the TS critically which will cause a collision if there is no course alteration. The experimental results are illustrated in figures representing the situations. Calculations have been conducted with the use of a PC characteristic with an Intel Core i5-3470 3.20Ghz processor, 4GB RAM, 64-Bit Windows 10 Pro. Many cases have been implemented, but three of them have been selected to be shared in this study. Two more cases which are presented at the end of this section as a Case 4 and Case 5 are also implemented to make a comparison with other methods and systems. The navigational data of ships identified in the cases and the results of the cases are listed in Table 2 and Table 3, respectively. In all these cases, the OS proceeds at constant speed, and collision avoidance action is performed via course alteration.


©2019: The Royal Institution of Naval Architects


In Case 1, the TS is approaching to OS from its starboard bow and the current motion of the ships lead to collision, so the OS should take action to eliminate the risk of collision. It is assumed that the navigational data of the ships comes from ARPA and AIS, the initial course of the OS is 000o, the course of the TS is 270o, the speed of both ships are set at 15 knots, the relative bearing of the TS is 045o, the distance between two ships is 8 Nm, the return distance to original route of the OS is 15 Nm and ship domain radius is set at 2 Nm. Figure 7 and Figure 8 show the time passed (T1, T2, T3, T4) of dynamic simulation of collision avoidance route in relative motion and true motion, respectively since the beginning of the simulation.


Computational Time [s]


≈ 0.02 ≈ 0.02 ≈ 0.02 ≈ 0.02 ≈ 0.02


[Nm] 8


6


RBts [o]


045 020


22 263 12 25.4 357 32


030 4 021.90


Figure 7. Dynamic simulation of collision avoidance route in relative motion for case 1


A-351


Case


Case


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