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


the TS are known. On the other hand, the initial position of the TS(, ) is determined by the user using the web-based user interface shown in Figure 4. The interface for data receiving also provides the following information:


• course () and speed () of the OS, • course (), speed (), relative bearing (RBts) of the TS and distance between ships (Dos,ts),


• ship domain size in radius (SD), • a final point distance to return the OS to its original route (RD).


The web-based user interface developed with the "JavaScript" programming language on the "Processing" software platform is created for a practical collision avoidance decision support function. The reason why the web-based implementation has been developed is that it is easily accessible and does not require installation. The lower side of the interface shows the spatial operation and displays the simulation of the optimal collision avoidance route. The red lines represent the routes of the ships, the green line represents the relative motion line, the yellow area represents the ship domain of the OS that must not be violated by other objects, the green point represents the return point of the OS to its original route. The horizontal bar with red and green colour indicates the distance between ships during the process. The red side represents the ship domain. The upper side of the interface provides the course, speed, safety domain area and return distance to original route of the OS, the relative bearing, distance, course and speed of the TS. The interface can simulate relative motion and true motion of the collision avoidance process.


to achieve this situation, the following quadratic equation (equation 4) can be formed.


() = = √(() − ())2 + (()− ())2


(4)


When the quadratic equation is solved, the t1 and t2 roots are obtained by the function 5.


According to the values of ∆, there are three different cases;


If ∆< 0 then, there is no real root which means that there is no violation to ship domain. In this case, there is no risk of collision, so no calculation is conducted.


If ∆> 0 then, risk of collision exists and the t1 and t2 roots to be obtained from the equation gives the entrance and exit moments to the ship domain.


If ∆= 0 then, roots are equal to each other (t1 = t2) and it represents that the TS passes through the tangent of the ship domain.


= () = ()


1 = − −√∆ 2


= 2 +


2 = − + √∆ 2


2 + 2 + + )


= 2(((0)+ (0)) − ((0)+(0)))


= (0)2 + (0)2 −2 ∆= 2 − 4


2 − 2( (5)


Figure 4. Web-based user interface


The aim of the collision avoidance path planning is to keep free the ship domain of the OS from the obstacles. It means that the distance between ships at the Closest Point Approach (CPA) should be large enough from the ship domain radius (() ≥ ). In the opposite case (() < ), the ship domain is violated and there are moments of entry to (t1) and exit from the domain (t2). Ultimately, in order to provide optimal trajectory which has the shortest length, the distance has to be equal to ship domain radius (() = ). In this case, the moment t1 = t2 represents that the TS passes through the tangent of the ship domain illustrated in Figure 5 which is an exemplary encounter situation. In order


A-350


Figure 5. An exemplary pattern of an encounter situation ©2019: The Royal Institution of Naval Architects


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