13th

Congress of Intl. Maritime Assoc. of Mediterranean

IMAM 2009, Istanbul, Turkey, 12-15 Oct. 2009, Page 1121-1128

Decision making system for the collision avoidance of marine vessel

navigation based on COLREGs rules and regulations.

L. P. PERERA Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon,

Instituto Superior Técnico, Lisbon, Portugal

J. P. CARVALHO INESC-ID, Technical University of Lisbon, Instituto Superior Técnico, Lisbon, Portugal

C. GUEDES SOARES Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon,

Instituto Superior Técnico, Lisbon, Portugal

ABSTRACT: A fuzzy-logic based decision making (DM) system to facilitate the collision avoidance

capabilities for marine vessels during ocean navigation is presented in this paper. The collision avoidance of

the target vessel with respect to the vessel domain of the own vessel has been analyzed and fuzzy

membership functions have been derived in this study. Fuzzy rule based (IF-THEN) decision making system

has been formulated, implemented and results are summarized. Further, decisions on the DM system are

formulated in accordance with the International Maritime Organization (IMO) rules and regulations

(COLREGs) of ocean navigation to avoid conflict situations.

1 INTRODUCTION

Conventional marine vessel navigational systems

consist of human guidance, hence 75-96% of marine

accidents and causalities are affected by some types

of human errors (Rothblum et al. 2006, Antão and

Guedes Soares 2008). Therefore implementation of

an intelligent DM system during the ocean

navigation is a mandatory requirement to achieve

higher maritime safety standards. This reality has

been characterized as e-Navigation (eNAV 2008).

Furthermore, to have Autonomous Guidance and

Navigation capabilities in ocean navigation, such as

the system described in Moreira et al (2007), it is

necessary to have a decision making system onboard

vessels to avoid collision situations. This application

area is bound to become more important in the

future ocean navigation (Fossen, 1999) due to its

cost reduction and requirements of maritime safety.

This paper focuses on a fuzzy logic based

Decision Making (DM) system to implement on

vessel navigation to improve safety of the vessel by

avoiding the collision situations. The rules and

regulations with respect to the collision avoidance

conditions, i.e., Convention on the International

Regulations for Preventing Collisions at Sea

(COLREGs) (IMO 1972), were formulated by the

International Maritime Organization (IMO) that

represents the importance of regulated prevention of

the collisions in ocean navigation.

Decision making process and strategies in

interaction situations with respect to the collision

avoidance conditions were presented by Chauvin et

al. (2008). The analysis of quantitative data

describing the maneuvers undertaken by ferries and

cargo-ships and the behavior of the 'give way' and

'stand on' vessels with respect to the verbal reports

on-board recorded in a car-ferry in the Dover Strait

were also presented in the same work.

The two main terminologies that were used in

recent literature with respect the collision avoidance

conditions could be presented as “Own vessel” (the

vessel with the DM system) and “Target vessel” (the

vessel that need to be avoided). Similar definitions

have been considered during the formulation of

collision situations in this study. The detection of a

target vessel location and velocity are two important

factors in the decision making process of the

collision avoidance. The combination of radar and

infrared imaging to detect the other vessel conditions

were proposed by Sato et al. (1998) as a part of the

collision avoidance system. The method of

measuring course of the target vessel and the

evaluation of the risk of the collision situations by

image processing are further proposed as

improvements of collision avoidance conditions in

the same work.

The defined region of vessel domain that was

bounded for dynamics of the marine vessel is an

important factor to define the collision conditions.

The vessel domain, in a collision situation, that

depends on parameters of the vessel size, vessel

course and heading angles of the encountered

vessels has been proposed by Pietrzykowski et. al

(2006) and fuzzy logic based domain determination

system has been considered. Similarly neural-

classifiers have been proposed by Lisowski et. al

(2000), as an element that is supporting the

navigator in the process of determining the ship's

domain where the area around the vessel should be

free from stationary or moving navigational

obstacles.

The calculations based on the kinematics of two-

ship collision encounters conjunction with the

equations of motion were presented by Kwik (1989).

The analysis of a collision avoidance situation was

illustrated with respect to the vessel velocity, turning

rate and direction, and the desired passing distance

in the same work. The collision avoidance

conditions among ships, shore installations and other

obstacles were considered by Yavin et al. (1995). In

addition a case study of a ship moving from one

point to another in a narrow zigzag channel was

considered and a computational loop command

strategy for the rudder control system associated

with the numerical differential equation solver was

proposed in the same study.

Ship trajectories are normally simulated by

mathematical models based on maneuvering theory

(e.g. Sutulo et al, 2002) although approaches based

on neural networks have also been proposed

(Moreira, and Guedes Soares, 2003). Modeling of

ship trajectory in collision situation by an

evolutionary algorithm was presented by

Smierzchalski et. al (2000) and comparison of

computational time for trajectory generation with

respect to the other maneuvering algorithms were

also illustrated. Static and dynamic constrains were

considered for the optimization process of the safe

trajectory in the same work.

2 COLREGs RULES AND REGULATIONS

It is observed that the COLREGs rules and

regulations with respect to collision situations in

ocean navigation were ignored by most of the recent

literature. The negligence of the IMO rules may lead

to conflicts during collision situations. Therefore the

methods ignoring COLREGs rules and regulations

should not be implemented.

On the other hand there are practical issues in the

implementation of the COLREGs rules and

regulations during the ocean navigation. As an

example, there will be implementation issues of

"give way” and “stand on" vessels of the COLREGs

rules during the vessel navigation in a situation

where the moving vessel or moving obstacle with

very low or very high speeds with respect to the own

vessel. Hence smart DM system must be

implemented to be consistent with the COLREGs

rules and regulations and also to eliminate

previously mentioned implementation conflicts.

Similarly considerable amount of recent research has

been focused on design and implementation of

optimization algorithms to find the safest path to

avoid collision situations. It is observed that some

optimization algorithms always find the safest path

behind the target vessel which may lead to a conflict

with the COLREGs rules and regulations.

Similarly some algorithms are enforcing the own

vessel to navigate away from the target vessel or

obstacle by repulsive forces from the vessel or the

obstacle during the collision situations. This concept

may lead to a conflict situation when the moving

vessel with very low speed or very high speed with

respect to the own vessel. In addition, complex

orientation of obstacles may lead to unavoidable

collision situations. Further, the concepts of "give

way” and “stand on" vessels that were derived on the

COLREGs rules and regulations during the vessel

navigation will not be honored in by the repulsive

forces based algorithms. Hence optimizations

algorithms integrated with a smarter DM system

should be considered to overcome the above

problems.

The consideration of course changes and/or speed

changes of vessels in ocean navigation must be

formulated in order to avoid critical collision

situations. However some of the recent collision

avoidance applications have been focused on

specific controllability of either course change or

speed change. According to the COLREGs rule 8(b).

“Any alteration of course and/or speed to avoid

collision shall, if the circumstances of the case

admit, be large enough to be readily apparent to

another vessel observing visually or by radar; a

succession of small alterations of course and/or

speed should be avoided”.

Hence integrated controls of course changes

as well as speed changes should be implemented

during the vessel navigation to avoid collision

situations. Similarly special measures should be

considered during integrations of course and speed

controls due to the fact that the vessels may not

response to required changes in course or speed.

3 COLLISION SITUATION

Two vessels in a collision situation are presented in

Figure 1 and the following description has been

illustrated with respect to the collision conditions.

The own vessel that has implemented the DM

system is located at the point O (Xo, Yo), and the

target vessel, the vessel need to be avoided is located

at the point A (Xa, Ya). The own and target vessels

velocities of Vo, Va and course of ψo, ψa respectively

are also presented in the same figure. The relative

velocity of the target vessel with respect to the own

vessel was defined as Va,o and relative speed |Va,o| →

Va,o and course of ψa,o could be calculated from

Va,o = Va - Vo (1)

Figure 1. Vessel collision situation.

In addition the relative distance and angle of the

target vessel with respect to the own vessel are

derived as the |AO| and θo respectively. All angles

have been measured with respect to the positive Y-

axis as presented in Figure 1 and 2. The curve AB

represents the relative path of the target vessel with

respect to the own vessel and the collision encounter

angle is presented by θa,o. The vessel relative

collision situation that is similar to a Radar plot is

presented in Figure 2. As presented in the figure the

collision regions with respect to the own vessel have

been divided into eight regions: I, II, III, IV, V, VI,

VII, and VIII.

Figure 2. Vessel relative collision situation.

These regions have been separated by the

discontinue lines that are coincided with the fuzzy

regions as formulated in the fuzzy membership

function in Figure 4. It is assumed that any target

vessels should be located within these eight regions

and the decisions were formulated accordance to

each region. The gray circular region represents the

vessel domain with the radius of Rvd ( Figure 1). The

white circular region represents the critical collision

risk region due to the target vessel orientation.

As presented in Figure 2, the target vessel

position at the region II has been divided into eight

divisions of target vessel orientations with respect to

the relative course regions: II-a, II-b, II-c, II-d, II-e,

II-f, II-g and II-h. These divisions have been

separated by the discontinue lines that are coincided

with the fuzzy collision risk regions presented later.

4 COLLISION AVOIDANCE METHODOLOGY

4.1 Identification of Obstacles

The stationary and moving obstacles in the ocean

navigation can be identified by several instruments

and systems: Eye / camera, radar / Automatic Radar

Plotting Aid (ARPA), and Automatic Identification

System (AIS). ARPA provides accurate information

of range and bearing of nearby obstacles and AIS is

capable of giving all the information on vessel

structural data, position, course, and speed

(Hasegawa 2009). The collection of radar data has

been considered as the method of identifying

stationary and moving obstacles during this study.

4.2 Collection of Navigational Information

The navigational information could be categorized

into three sections: static information, dynamic

information and voyage related information.

Collection of navigational information is an

important part of the decision making process of the

collision avoidance in ocean applications. However

it has not been emphasized on the navigational

information of the target vessels at this stage of the

study.

4.3 Analysis of Navigational Information

The collected target vessel information should be

considered for further analysis of navigational

information. Three distinct situations that are

involving risk of collision with respect to the ocean

navigation have been recognized by the recent

literature (Smeaton, et. al 1987), overtaking, head-on

and crossing, and same situations have been

highlighted in this study. However in ocean

navigation, complex collision situations involving

combinations of the above situations could occur

and identification of each situation with respect to

the each collision conditions will be helpful for the

overall decisions on vessel navigation.

4.4 Assessments on the Collision Risk

The analysis of navigational information will be able

to predict the collision risk assessments. Therefore

the assessment of the collision risk should be

continuous in the navigational system for safety of

the own vessel. As presented in recent literature, the

mathematical analysis of collision risk detection

could be divided into two categories: 2D methods

and 3D methods. Both methods consist of locations

of each vessel in 2D coordinate system and the 3D

method consists of an addition time axis. However

analysis of 2D method in real-time is proposed in

this study to capture the time axis effects.

The summarized collision risk assessments

including the fuzzy linguistic variables are presented

in the Table 1. The first column represents the

collision regions with respect to the own vessel and

the second column represents the divisions of the

target vessel orientations. Furthermore the third

column represents the risk assessment with respect

to each collision region and that have been divided

into three sections: Low risk (Low), Medium Risk

(Mid.) and High risk (High). The respective

COLREGs rules and regulations are presented in the

fourth column. Target vessel relative speed

conditions are presented in the fifth column. Finally

the decisions that need to be taken to avoid the

collision situations with respect to the COLREGs

Table 1. Collision Risk Assessment and Decisions

Reg. Division Risk Rule Condition Decision

I d Mid. 13 NA NA

e High 14 Va,o << 0

Va,o ≈ 0

Va,o >> 0

δψ > 0

δψ > 0

δψ > 0

f Mid. NA NA

II e Mid 15 NA NA

f High 16 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δψ > 0

δψ > 0

g Mid. 17 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δψ > 0

δψ > 0

III f Mid. 15 NA NA

g High 16 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δVo<< 0

δVo<< 0

h Mid. 17 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δVo < 0

δVo < 0

IV a Mid. 17 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δVo < 0

δVo < 0

g Mid. 15 NA NA

h High 16 Va,o << 0

Va,o ≈ 0

Va,o >> 0

NA

δVo<< 0

δVo<< 0

V a High 14 NA* NA*

b Mid. NA* NA*

h Mid. 13 NA* NA*

VI a Mid. 15 NA* NA*

b High 16 NA* NA*

c Mid. 17 NA* NA*

VII b Mid. 15 NA* NA*

c High 16 NA* NA*

d Mid. 17 NA* NA*

VIII c Mid. 15 NA* NA*

d High 16 NA* NA*

e Mid. 17 NA* NA*

* Target vessel should take actions to avoid the collision situations.

NA : Not Applicable

rules and regulations are presented in the last

column.

With respect to the COLREGs rules and

regulations the vessel coming from the starboard

side has the priority for the navigation. Hence, as

noted from the table, the collision avoidance

appropriate actions from own vessel have been

limited for the regions of I, II, III and IV. As

presented in Table 1, δψ > 0 represents the decision

to increase of own vessel course to the starboard

side, and δVo < 0 and δVo << 0 represent decrease of

own vessel different speed levels respectively.

4.5 Decisions on Navigation

The decisions of collision avoidance in ocean

navigation should be based on several factors: Speed

and Course of each vessel, distance between two

vessels, Distance of the Closest Point of Approach

(DCPA) RDCPA (see Figure 1), time to DCPA,

neighboring vessels and other environmental

conditions. The initial decisions of collision

avoidance can be categorized into three stages for

each vessel.

− When both vessels are at non collision risk range,

both vessels have the options to take appropriate

actions to avoid collision situation.

− When both vessels are at collision risk range,

'give way' vessel should be taken appropriate

actions to achieve safe passing distance

accordance with the COLREGs rules and

regulations and 'stand on' vessel should keep the

course and speed.

− When both vessels are at critical collision risk

range, 'give way' vessel should not be taken

appropriate actions to achieve safe passing

distance accordance with the COLREGs rules,

then 'stand on' vessel should be taken appropriate

actions to avoid the collision situation.

In this study it is assumed that both vessel take

appropriate actions to avoid the collision situations

to with the respect to the COLREGs rules and

regulations.

4.6 Implementation of Decisions on Navigation

As the final step, it is assumed that the decisions on

vessel navigation will be formulated with respect to

the collision risk assessments. The actions were

taken by own vessel are proportional to target vessel

behavior as well as the COLREGs rules and

regulations. The expected own vessel and target

actions of collision avoidance situations could be

divided into two categories.

− Own vessel course change and/or speed change.

− Target vessel course change and/or speed change

5 FUZZIFICATION & DEFUZZIFICATION

The Fuzzy-logic based DM system, which is

formulated for human type thinking, has created a

human friendly environment to facilitate the

collision avoidance capabilities for marine vessels.

Furthermore, a proper formulated fuzzy logic based

DM system has an advantage of simulating the

actions of an experienced helmsman in ocean

navigation.

5.1 Fuzzy sets and membership functions

Fussy sets are described by the membership

functions that are mappings from one given universe

of discourse to a unit interval. It is conceptually and

formally different from the fundamental concept of

the probability (Pedrycz et. al 2007). Three fuzzy

input membership functions have been considered

during this study: Collision Regions µA (Figure 3),

Relative Speed µVa,o (Figure 4) and Relative Course

µψa,o (Figure 5). Similarly two fuzzy output

membership functions have been considered: Speed

Change µδVo (Figure 6) and Course Change µδψo

(Figure 7).

Figure 3. Collision Regions Fuzzy Membership Function.

Figure 4. Rel. Speed Fuzzy Membership Function.

Figure 5. Rel. Course Fuzzy Membership Function.

Figure 6. Speed change Fuzzy Membership Function.

Figure 7. Course Angle change Fuzzy Membership Function.

The Core of the fuzzy set A is defined as the set

of all elements of the universe that are typical to A

that are associated with the membership value of 1,

that could be written as

{ }1)(|)( =∈= xAXxACore (2)

where x is a generalized variable. The Support of the

fuzzy set is defined as the set of all elements of X

that have non-zero membership degree in A, that

could be written as

{ }1)(|)( ≥∈= xAXxASupp (3)

The Core and Supp values for the three input and

two output fuzzy membership functions was

formulated using the given variables in the

respective Figures 3 to 7. Mamdani type IF

<Antecedent > THEN <Consequent> rules based

system has been considered and inference via

Min/Max norm has been proposed. Finally the

defuzzification has been calculated by the center of

gravity method.

5.2 Fuzzy inference system

The block diagram for fuzzy inference system with

integration of the instruments as well as the data

acquisition system is presented in Figure 8.

Figure 8. Rel. Block diagram for fuzzy inference system

The initial step of the fuzzy inference system

consists of collection of the target vessel position

and velocity data. The next step is the calculations of

the relative positions, speed and course which have

previously been formulated. Then, the data is

fuzzified by membership functions in the Figures 3

to 5. The fuzzy rules were developed respecting the

COLREGs rules and regulations in Table 1. The

output of the rules based system could be

categorized as the collision risk assessment and the

fuzzy decisions. Finally the fuzzy decision will be

defuzzified (see Figure 6 and 7) to obtain the control

actions and that will be executed on own vessel

navigation.

6 COMPUTATIONAL SIMULATIONS

The implementation of the DM system has been

formulated by using the software MATLAB.

MATLAB supports for the fuzzy logic schemes of

Mamdani and Sugeno Types (Sivanandam et. al

2007). However this work has been implemented on

the GUI for fitting Mamdani based Fuzzy Inference

System (FIS).

The Mamdani type fuzzy logic inference

system consists of utilizing membership functions

for both inputs and outputs. As previously

mentioned If-Then rules are formed by applying

fuzzy operations into these membership functions

for given inputs: Collision regions, Relative Speed,

and Relative Course (see Figures 3 to 5).

The resulting output membership functions,

vessel speed change and course change (see Figures

6 & 7) have been calculated by the Fuzzy min-max

configurations. The MATLAB simulation results

with respect to the above formulation have been

presented in Figures from 9 to 15. These figures

contain the start and end positions of the both

vessels with respect to the equal time intervals. In

addition navigational trajectories for both vessels are

also presented in the same figures.

The simulations of two vessels crossing situation

with respect to different speeds and course

conditions in the Cartesian coordinate space have

been presented in Figures 9, 10 and 11. As presented

in Figure 9, for the speed condition of Vo ≈ Va, the

DM system made the proper decision and turned the

own vessel into the starboard side. However the

speed conditions of Vo >> Va and Vo << Va , in Figures

10 and 11, the DM system did not make any

decisions as formulated in the design phase. This is

one of the advantages in the fuzzy logic based DM

system that has not been addressed by recent

research on collision avoidance.

The avoidance of collisions with respect to

overtake and heading situations are presented in

Figures 12 and 13 respectively. Further angular

heading and angular overtake situations are

presented in Figures 14 and 15. The majority of the

collision situations have been avoided by changing

the course angle of the own vessel as preferred by

the navigators.

In an angular overtake situation (in Figure 15),

the initial speeds of both vessels are equal and the

final speed of the own vessel has been reduced by

the DM system to avoid the collision situation. This

is one of the special situations where the speed

change has been considered and the course changes

could not be implemented to avoid collisions.

Figure 9. Crossing situation with High Collision Risk

Figure 10. Crossing situation with No Collision Risk

Figure 11. Crossing situation with No Collision Risk

Figure 12. Overtake situation with High Collision Risk

Figure 13. Heading situation with High Collision Risk

Figure 14. Ang. heading situation with High Collision Risk

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Figure 15. Ang. overtake situation with High Collision Risk

7 CONCLUSION

This paper introduces a new DM system for ocean

navigation based on the fuzzy logic and human

expert knowledge. Although successful

computational results were obtained, it is assumed

that more complex collision situations can possibly

occur and unexpected actions of target vessels could

be experienced; hence higher capabilities should be

formulated into the DM system to overcome similar

situations. As mentioned before, the own vessel

collision avoidance actions have been limited for the

Regions of I, II, III and IV to eliminate the

navigational conflicts. However critical collision

situations with respect to the other regions should

considered and further study should be formulated.

8 ACKNOWLEDGEMENT

The research of the first author has been supported

by a Research Fellowship of the Portuguese

Foundation for Science and Technology (Fundação

para a Ciência e a Tecnologia) under contract

SFRH/BD/46270/2008. This work is done within the

project of “Methodology for ships manoeuvrability

tests with self-propelled models”, which is being

funded by the Portuguese Foundation for Science

and Technology, under contract

PTDC/TRA/74332/2006.

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