1 INTRODUCTION

According to classification societies, ship collisions

account for several to more than ten percent of total

tonnage lost due to incidents such as sinking, fire,

mechanical failure, or other breakdowns. As maritime

traffic grows—with the speed and size of ships

increasing—the need for effective collision avoidance

strategies becomes increasingly critical. Ship collisions

account for approximately 20% of all maritime

accidents. In the 2023 Maritime Accident and Incident

Statistics Report (EMSA 2024), the number of incidents,

lost ships, and fatalities and injuries was similar or

lower than in the previous period. This year, 2,676

maritime accidents and incidents were reported,

representing an increase of approximately 1.8%

compared to 2022 and a decrease of 2.5% compared to

2021. The number of fatalities at sea was 45 in 2023, 18%

less than in 2022, indicating a downward trend.

Despite this optimistic downward trend, we are not

exempt from searching for the best solutions and

methods to improve maritime safety standards. It is

estimated that more than half of these collision-related

losses could be prevented by more advanced computer

systems for managing the safe navigation of ships [1],

[2], [3], [4], [5]. Due to the important role that maritime

transport plays in global transport, some researchers

have conducted a comparative study of sea and rail

transport [6].

In recent years, we have observed a very intensive

development of artificial intelligence technologies in

connection with the control of ships in maritime traffic

[7], [8], [9], [10], [11] . Many scientists are trying to

improve and introduce new solutions to ship systems

responsible for maritime navigation to make the units

increasingly safer, more economical, and even, to some

extent, autonomous [12] [13]. Implemented automatic

control methods can facilitate the work of navigators

by performing calculations, estimating the safety of the

Decision Support System Using Modern Methods

of Collision Avoidance in Collision Situations at Sea

M. Mohamed-Seghir

Gdynia Maritime University, Gdynia, Poland

ABSTRACT: Due to the rapid growth of maritime transport, many researchers have developed advanced

methods aimed at increasing navigation safety and reducing operating costs, while maintaining compliance with

the International Regulations for Preventing Collisions at Sea (COLREGs). Navigating a ship in potential collision

situations requires decision-making under conditions of uncertainty and ambiguity – particularly with respect to

concepts such as collision risk and safe speed. These concepts are subjective and not clearly defined. In response

to these challenges, this paper presents an artificial intelligence-based method that takes into account the

navigator's role as a decision-maker. The proposed solution is designed for integration with existing collision

avoidance systems. A universal simulator was developed to evaluate the effectiveness of an algorithm for

determining a safe ship trajectory in collision situations. Example navigation scenarios were conducted and

presented using this simulator.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 20

Number 1

March 2026

DOI: 10.12716/1001.20.01.07

selected sea route, taking control of the ship and

making the most optimal decisions, or supporting the

crew in operating the ship's infrastructure during

normal operation during a sea voyage [14].

Rapid technological advances and artificial

intelligence, along with the growing need to improve

maritime safety, have led to the development of

devices to assist navigators in their duties. Specialized

collision avoidance systems have emerged on the

market. These systems provide crucial information on

the position, course, speed, and destination of nearby

objects, as well as other threats [15], [16], [17], [18].

Modern navigation systems integrate all navigational

instruments into a unified information network that

offers real-time data on ship motion parameters. These

systems significantly support navigators by providing

accurate information, enabling them to make informed

decisions that ensure safe sea travel. Despite these

technological advances, maritime collisions still

occur—often due to human error. Many of these

accidents could be prevented by developing and

implementing advanced computer-assisted methods

for safe ship navigation. Artificial intelligence-based

techniques offer promising solutions. Improvement of

these computational methods can lead to automatic

tracking of objects based on data from onboard

collision avoidance systems. Such methods can be used

to support the navigator's decision-making process or

improve the automatic control of the ship during

potential collision scenarios [19], [20], [21]. Correct

selection of an appropriate evasive maneuver can

eliminate human error and significantly improve

navigation safety, taking into account the

Intergovernmental Maritime Regulations [22], [23] .

Taking the above into account, the aim of this work can

be defined as developing a method for determining the

optimal and safe ship trajectory in multiple-object

collision situations. This method should take into

account the provisions of the International Maritime

Traffic Code (COLREGs), the ship's maneuvering

characteristics, and the subjective characteristics of the

navigator, who makes the final decision regarding the

maneuver. This paper presents a method for

determining a ship's optimal course in each phase of a

planned route, using a kinematic model that assumes

targets move in straight lines at constant speed. Given

the uncertainty and subjective judgments of individual

navigators, decisions about maintaining a safe distance

and maneuvering to avoid collisions are inherently

inaccurate. To address this issue, this study proposes a

fuzzy dynamic programming approach for calculating

safe ship trajectories in potential collision scenarios

[24], [25], [26], [26] (Figure 1).

Figure 1. Block diagram of decision support system in a

fuzzy environment

2 PROCESS MODEL

To describe a ship's safe trajectory, the ship's motion

returning to the helm in deep water was described. The

ship's dynamic properties were assessed using the

transition function, i.e., the lead time tw and the

maximum angular velocity . The maneuver

parameters were selected based on the ship's dynamics

in operational conditions. They depend on the rudder

angle, speed, rudder angle, load, and environmental

conditions (Figure 2).

Typically, a ship's maritime maneuver in a collision

situation consists of two phases:

1. target tracking based on CPA and TCPA to assess

collision risk,

2. anti-collision maneuver in accordance with

COLREGs, in which determining the ship's safe

trajectory can be reduced to multi-stage decision-

making in a fuzzy environment.

The quality of the decision is assessed based on the

fuzzy decision, which is an aggregation of fuzzy targets

and the fuzzy environment. The anti-collision system

processes radar signals and generates information

about the relative and actual motion of tracked objects.

The signal processing system performs primary and

secondary processing. The first process processes radar

signals, which are synchronized with the radar antenna

rotation. This process determines the polar

coordinates: azimuth and distance between the ship

and the objects (Figure 2). The second process

correlates the object's position coordinates during

subsequent radar antenna rotations, estimates motion

parameters, and approximates detected objects relative

to the ship.

Figure 2. The ship passing situation with j-th target in a

rectangular coordinate system

3 SHIP CONTROL PROCESS SYNTHESIS IN A

FUZZY ENVIRONMENT

The process of steering a ship in collision situations

involves imprecise and poorly defined concepts, such

as safe speed, collision risk, and the deadline for taking

action to avoid a collision early enough. These terms

are subjective and imprecise, and largely depend on

the circumstances and navigation conditions. The

steering process, characterized by uncertainty, can be

represented as a multi-stage model of decision-making

and control in a fuzzy environment (Figure 1).

The model of safe ship trajectory can be represented

by the state equation

( )

, , 1,2, ,

k k k

X f X S k N

= = 

(1)

where:

1 0 0 1 1

, { , , ..., , , , ,

k k p p p N

X X X a a a a a a

+ − +

 = 

- set of real ship

position coordinates,

 

, , ,

S c c c=

- control set.

 

, ,

p p N

a a a

(2)

 

, ,

opt z opt z R Rsafe

   

= = 

(3)

where:



opt - optimal corse,

Vopt - optimal speed,



R -membership function of fuzzy set collision risk.

To solve the problem formulated above, a method

based on an artificial neural network was proposed, as

below.

3.1 Membership function of the fuzzy collision risk

Ships that participate in a collision situation should be

sorted according to the degree of danger [25] . It is used

an indicator of collision risk. This indicator is defined

by referring to the current approximation situation,

described by the CPA and TCPA parameters, to a safe

situation predetermined by a safe proximity distance

and the safe time required to avoid a collision

avoidance maneuver. The ship's domain is treated as a

collision risk assessment by many scientists. The

membership function of the fuzzy collision risk was

used in this work as collision risk assessment.

( ) ( )

( , ) ( , )

( , ) exp

for 0

RD j RT j

k j CPA k j TCPA

TCPA











=−



(4)

3.2 Membership function of the fuzzy goal

Anti-collision maneuver, that is, action taken to avoid

collision with another ship, should be done in such a

way that two objects have passed a safe distance. The

effectiveness of the maneuver should be monitored

until the other ship has passed and departed. A variety

of safety assessments made by navigators can be

described as a membership function of the fuzzy goal,

allowing for a subjective assessment.

( )

),(

exp1),(

CPAjk





−−=

(5)

3.3 Membership function of the fuzzy constraints

Each anti-collision maneuver causes a change in the

course navigator's intent. The consequence of course

change is the length of the ship's path, resulting in

additional waste of time and fuel. The task of the

navigator is to perform the safe operation of passing a

foreign object at a safe distance with the optimum

trajectory to minimize the loss. While, the membership

function of the fuzzy constraints can be defined as

constraints of maneuver at each stage.

The above functions have been described in detail

in other works by the author of this article and are

included in the algorithm in the form of pseudocode.

To answer the above problem, a method based on

fuzzy dynamic programming is proposed, as

presented below.

( )

)1(cos)(cos)(

exp)(

tkVkVk

−−

−=





(6)

where:

CPA - Closest Point of Approach,

TCPA - Time to Closest Point of Approach,



RD,



RT - navigator subjectivity parameters in ship

collision risk assessment,



D - parameter of the navigator's subjectivity in

assessing the ship's safety,



C - parameter of subjectivity of the navigator in

assessing the loss of the way.

To identify the properties of a fuzzy process that

reflect the process of determining a safe trajectory in

collision situations, it is necessary to determine the

subjective parameters of the navigator making a

decision in a given situation. To this end, empirical

studies were conducted to identify and select the types

of decisions used in a multi-stage decision-making

model. The rationale for using this approach is that

humans have a remarkable ability to determine the

degree of belonging to a given element without

conscious reasoning about how to achieve this degree.

Although it is difficult to study every real-world

navigational situation, each situation can be treated as

the result of several basic situations, based on the

principle of superposition. Basic situations can be

distinguished based on the angle and difference of

course, as well as the ship's speed, the speed of the

object, the ship's dynamic properties, and visibility

conditions.

3.4 Fuzzy dynamic programming algorithm

The aim of this study is also to develop solutions to

ensure safe control of the vessel in collision risk

situations [18], [19]. This problem is solved using an

artificial intelligence based method. In this part of the

presented work, a dynamic fuzzy programming

algorithm for determining the safe route of own ship at

sea is presented. The algorithm is written in the form

of pseudocode and presented below. In order to verify

the adequacy of the proposed model and the

correctness of the algorithm operation, a series of tests

were conducted. This part presents one example of a

navigation situation in which own ship passes 20

moving and stationary objects. In addition, a

sensitivity analysis of the safe ship control process was

performed.

Algorithm - Pseudocode

BEGIN

1-Input parameters;

2- Initialization of variables, array and structures;

3- Determine the value of the coefficients λ ;

4- Calculation the CPA, TCPA, and membership

functions μ;

5- If safe situation is true go to position 13 else continue;

6- Finding the most dangerous object R

( ) ( )

0exp),(

),(

−=













TCPAforjk

jRTjRD

TCPACPAjk





7-Finding the coordinates of your own ships in the last

stage N;

8- Set the following courses in stage N, which are intended

to avoid collisions;

9- Selecting the optimal rate at stage N based on

membership functions μC and μG;

( )

( ) cos ( ) cos ( 1)

( ) exp

( , ) 1

( ( ) )

k V k V k t

exp λ k, j CPA

  



−−

=−

;

10- Return to the previous stage according to the desired

course N:=N-1;

11- If N = 0 is false go to point 8 else continue ;

12- Designate a safe route based on selected optimal courses

at each stage;

13- Calculate the ship coordinates at each stage;

14- Draw a safe route and paths for encountered objects.

END

4 RESULTS OBTAINED WITH THE PROPOSED

METHOD

In the initial phase of simulation studies on the optimal

and safe ship trajectory, two passing scenarios were

analyzed – with both moving and stationary objects –

taking into account both good and limited visibility

conditions.

In the first scenario, the object was located on the

ship's starboard side and moved so that it crossed its

course at a 90-degree angle. The second scenario

analyzed a situation in which two ships were sailing

perpendicular to each other, also in conditions of

varying visibility.

The simulations were conducted for a mid-class

ship, taking into account applicable COLREG

regulations. Due to their simplified nature, the

described situations are not presented in detail in this

study.

To further verify the accuracy of the applied

algorithm, tests were conducted with a larger number

of objects participating in potentially conflicting

maneuvers. The developed algorithm allows for the

analysis of situations with any number of ships. The

tests were limited to 60 objects – in line with the

maximum number that the ARPA (Automatic Radar

Plotting Aid) system can track.

Figure 3 illustrates two example scenarios using the

fuzzy dynamic programming algorithm in the safe

ship control process:

− A: passing 20 objects (moving and stationary),

− B: passing 60 objects (moving and stationary).

Figure 3. The result of the collision situation in passing with

20 objects (A) and passing 60 objects (B).

As shown in Figure 3A, the anti-collision procedure

was carried out safely. After generating a trajectory in

10 steps, the simulation program proposed expanding

it to 12 steps. Due to the length of the collision

avoidance maneuver, the path was ultimately divided

into 12 steps. The most dangerous objects – designated

18, 16, and 17 – were avoided while maintaining safe

distances.

The trajectory calculation algorithm allows for a

return to the so-called main course (public course),

even when intersecting with another trajectory – for

example, the course of object 20, which is moving in a

straight line. In such a case, the algorithm ensures safe

passage of the vessels by maintaining the CPA (Closest

Point of Approach) value at 0.75 nautical miles.

Based on the analysis of the simulation test results

of the algorithm for calculating a safe trajectory in a

fuzzy environment, the following conclusions can be

drawn:

The optimal vessel path depends largely on

visibility conditions. The poorer the visibility, the

sooner or longer the avoidance maneuver takes.

In the presented fuzzy model, the vessel follows a

trajectory that minimizes deviation from the main

course while allowing for obstacle avoidance at

varying distances.

The algorithm assumes a constant collision risk,

meaning that navigational decisions are based on the

navigator's assessment of the situation, rather than on

a fixed minimum distance from the object..

5 SENSITIVITY ANALYSIS OF THE SAFE SHIP

CONTROL PROCESS

When constructing utility models for solving control

tasks, the choice of model is largely arbitrary, being the

result of a trade-off between the required accuracy and

the effort needed to collect more experimental data and

establish a more accurate model. Since fully accurate

models are not used, the problem of the influence of

model inaccuracy on the consequences of a decision

based on that model becomes of fundamental

importance.

5.1 Sensitivity of the process model

Sensitivity analysis is the study of the impact of model

inaccuracy on the results of applying the resulting

control law. Changes in the parameters of the ship

control model concern: maximum angular velocity of

the turn, time of maneuver progress, subjective

navigator coefficients, ship speed, distance between

ships and time of maneuver execution. All these

parameters appear in the fuzzy set membership

functions: "safe maneuver", "start of route" and

"collision risk". In order to estimate sensitivity, the

sensitivity measure was assumed as the relative

increase in the fuzzy set membership function.

5.2 Control Sensitivity

Sensitivity tests were performed on two selected

navigational situations. In the first situation, the ships'

courses intersect at a small angle, and the encountered

object is on the port side. In the second situation, the

courses intersect at a convergent angle, and the

encountered object is on the starboard side. The

following quantities were tested:

− the sensitivity of the "collision risk" membership

function



− the sensitivity of the "safe maneuver" membership

function



− the sensitivity of the "start of voyage" membership

function



The test results are presented as sensitivity curves

for each parameter change and input data inaccuracy.

Input data errors are expressed as percentages and are

the result of the combined measurement error of the

navigation equipment and changes in the model

parameters.

5.3 Sensitivity to the accuracy of process status

information

To estimate the sensitivity to the accuracy of

information about the process state, the relative

increase of the fuzzy set membership function was

taken as the sensitivity measure.

( ) ( )

()

K rl K pl

K pl





−

(7)

where:

K = 1, 2, 3, … , l = 1, 2, 3, …, 6

Lpl – vector of basic information from the anti-collision

system,

Lpl ={Dj, Nj,



j, Vj},

Lrl – vector of information affected by measurement

errors.

Figure 5. Sensitivity characteristics of the safe ship control

process model

5.4 Sensitivity to changes in process parameters

To estimate sensitivity to changes in process

parameters, the sensitivity measure was assumed to be

the relative increase in the fuzzy set membership

function.

( ) ( )

()

K rl K pl

K pl





−

(5)

where:

K = 1, 2, 3, … , l = 1, 2, 3, …, 6

Mpl – vector of basic information from the anti-collision

system,

Mpl = {

RTRDCD



,,,

}

Mrl – vector of information affected by measurement

errors.

Figure 6. Sensitivity to changes in process parameters.

Sensitivity tests of the ship control process in

collision situations in a fuzzy environment showed

that:

− the model is not sensitive to changes in the

parameters

D RD RT

  

, when DCPA = 0 or TCPA

= 0, it is not sensitive to changes in



, in the

absence of maneuvering (V = 0 or = 0), and also

when the navigator is more risky or the object poses

a lower collision risk, i.e.,





> 0,





> 0 and





< 0, the model is less sensitive to changes in

the parameters



, and



, and vice versa

in the case of





< 0,





< 0, and



> 0,

− the sensitivity changes for different signals

measurement and parameters characterizing the

subjectivity of the navigator's decisions,

− sensitivity varies for different navigational

situations,

− sensitivity is in some cases asymmetric relative to

the sign of the measurement error.

6 CONCLUSIONS

Analysis of the algorithm's effectiveness in

determining an optimal and safe trajectory in collision

situations, in a fuzzy logic-based environment, allows

for the following conclusions:

The developed model faithfully reproduces the

actual conditions for safe ship control in collision

situations. It takes into account factors such as water

level, visibility conditions, ship maneuverability, the

movement of other vessels, and the navigator's

maneuvering decisions made in accordance with the

provisions of the COLREG convention. This allows the

model to more accurately describe the analyzed

problem.

Introducing the collision risk set membership

function as a criterion for situation assessment is

beneficial because it allows for the consideration of

subjective factors influencing the navigator's decisions.

The task of determining the optimal ship trajectory

can be effectively accomplished using a dynamic

programming algorithm.

The algorithm is capable of handling more complex

collision scenarios. Although in some cases it may

generate maneuvers leading to unnecessary losses

(e.g., extending the route), its significant advantage is

the automatic return of the ship to its original course

after passing the hazard. In summary, the designed

algorithm provides a valuable tool to support

navigators in making decisions at sea. The simulation

results are promising and confirm the algorithm's

significant potential for practical application in

ensuring safe navigation.

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