Fuzzy logic based decision making system for collision avoidance of ocean navigation under critical...

ORIGINAL ARTICLE

Fuzzy logic based decision making system for collision avoidanceof ocean navigation under critical collision conditions

L. P. Perera • J. P. Carvalho • C. Guedes Soares

Received: 27 September 2009 / Accepted: 12 August 2010 / Published online: 7 October 2010

� JASNAOE 2010

Abstract This paper focuses on a fuzzy logic based

intelligent decision making system that aims to improve the

safety of marine vessels by avoiding collision situations. It

can be implemented in a decision support system of an

oceangoing vessel or included in the process of autono-

mous ocean navigation. Although Autonomous Guidance

and Navigation (AGN) is meant to be an important part of

future ocean navigation due to the associated cost reduction

and improved maritime safety, intelligent decision making

capabilities should be an integrated part of the future AGN

system in order to improve autonomous ocean navigational

facilities. In this study, the collision avoidance of the

Target vessel with respect to the vessel domain of the Own

vessel has been analyzed and input, and output fuzzy

membership functions have been derived. The if–then rule

based decision making process and the integrated novel

fuzzy inference system are formulated and implemented on

the MATLAB software platform. Simulation results are

presented regarding several critical collision conditions

where the Target vessel fails to take appropriate actions, as

the ‘‘Give way’’ vessel to avoid collision situations. In

these situations, the Own vessel is able to take critical

actions to avoid collisions, even when being the ‘‘Stand

on’’ vessel. Furthermore, all decision rules are formulated

in accordance with the International Maritime Organization

Convention on the International Regulations for Preventing

Collisions at Sea (COLREGs), 1972, to avoid conflicts that

might occur during ocean navigation.

Keywords Autonomous Guidance and Navigation �Collision avoidance � IMO rules and regulations �COLREGs � Fuzzy logic � Intelligent systems �Decision making process � Crash stopping

1 Introduction

Autonomous Guidance and Navigation (AGN) Systems

and their applications have been in the dreams of ship

designers for several decades. The development of com-

puter technology, satellite communication systems and

electronic devices, including high-tech sensors and actua-

tors, have turned these dreams into a possible reality when

designing the next generation ocean AGN systems.

The main functionalities of the Multipurpose Guidance,

Navigation and Control (GNC) systems are summarized by

Fossen [1] in a paper that focuses not only on course-

keeping and course-changing manoeuvres (a conventional

auto pilot system), but also on integration of digital data

(digital charts and weather data), dynamic position and

automated docking systems. Recent developments of

design, analysis and control of AGN systems are also

summarized by Ohtsu [2], and several ocean applications

of AGN systems have been further studied, theoretically as

well as experimentally, by Healey and Lienard [3], Do and

Pan [4] and Moreira et al. [5, 6]. This area is bound to

become increasingly important in the future of ocean

navigation due to the navigational cost reduction and

improved maritime safety [1].

An intelligent decision making process is an important

part of the future AGN systems in ocean navigation.

L. P. Perera � C. Guedes Soares (&)

Centre for Marine Technology and Engineering (CENTEC),

Technical University of Lisbon, Instituto Superior Tecnico Av.

Rovisco Pais, 1049-001 Lisbon, Portugal

e-mail: [email protected]

J. P. Carvalho

INESC-ID, Technical University of Lisbon, Instituto Superior

Tecnico Av. Rovisco Pais, 1049-001 Lisbon, Portugal

123

J Mar Sci Technol (2011) 16:84–99

DOI 10.1007/s00773-010-0106-x

However, conventional ocean navigational systems consist

of human guidance and, as a result, 75–96% of marine

accidents and casualties are caused by some type of human

error [7, 8]. Since many of the wrong judgments and

missed operations of humans at the ocean end in human

casualties and environmental disasters, limiting human

subjective factors in ocean navigation and replacing them

by an intelligent decision making (DM) system for navi-

gation and collision avoidance could reduce maritime

accidents and their respective casualties. However, devel-

opment of collision avoidance capabilities into the next

generation AGN systems in ocean navigation is still in the

hands of future researchers; this formation of the intelligent

AGN systems has been characterized as eNavigation [9].

A block diagram for the main functionalities of an AGN

system integrating collision avoidance facilities is pre-

sented in Fig. 1. The terminology used in recent literature

regarding the collision avoidance conditions designates the

vessel with the AGN system as the ‘‘Own vessel’’, and the

vessel that needs to be avoided as the ‘‘Target vessel’’.

These definitions have been considered during the formu-

lation of collision situations in this work.

Many techniques have been proposed for avoidance of

collision situations in recent literature, but in general those

techniques ignore the law of the sea as formulated by the

International Maritime Organization (IMO) in 1972 [10].

These rules and regulations are expressed in the Conven-

tion on the International Regulations for Preventing

Collisions at Sea (COLREGs). The present convention was

designed to update and replace the Collision Regulations of

1960, which were adopted at the same time as the Inter-

national Convention for Safety of Life at Sea (SOLAS)

Convention [11].

The decision making process and strategies in inter-

action situations in ocean navigation, including collision

avoidance situations, are presented by Chauvin and

Lardjane [12]. The same work also presents the analysis of

quantitative data describing the manoeuvres undertaken by

ferries and cargo-ships and behaviour of the ‘‘Give way’’

and ‘‘Stand on’’ vessels with respect to verbal reports

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

paper further analyzes critical collision situations, where

the ‘‘Give way’’ vessel failed to take action and the ‘‘Stand

on’’ vessel had to take action to avoid collision conditions,

with respect to the decision making process.

Detection of the Target vessel’s position and its velocity

are two important factors assessing the collision risk in

ocean navigation as illustrated in this study. Sato and Ishii

[13] proposed combining radar and infrared imaging to

detect the Target vessel conditions as part of a collision

avoidance system. In the same work, collision risk was

presented with respect to the course of the Target vessel

and the proposed image processing based course mea-

surement method.

The size and shape of the vessel domain, the area

bounded for dynamics of the marine vessel, are other

important factors in assessing the collision risk in ocean

navigation. Lisowski et al. [14] used neural-classifiers to

support the navigator in the process of determining the

vessel’s domain, defining that the area around the vessel

should be free from stationary or moving obstacles. In a

similar approach, Pietrzykowski and Uriasz [15] proposed

the notion of vessel domain in a collision situation as

depending on parameters such as vessel size, course and

heading angle of the encountered vessels in the same study.

Fuzzy logic based domain determination system has been

further considered in the same work.

Kwik [16] presented the calculations of a two-ship

collision encounter based on the kinematics and dynamics

of the marine vessels. The analyses of collision avoidance

situations are illustrated regarding the vessel velocity,

turning rate and direction, and desired passing distance.

Yavin et al. [17] considered the collision avoidance con-

ditions of a ship moving from one point to another in a

narrow zig-zag channel, and propose a computational open

loop command strategy for the rudder control system

associated with the numerical differential equation solver.

Most restricted waters and channels have their own rules

and regulations for navigation. One of the disadvantages in

this approach is insufficient flexibility to implement rules

and regulations in navigation.

The design of a safe ship trajectory is an important part

of the collision avoidance process, and it has normally been

simulated by mathematical models based on manoeuvring

Fig. 1 Autonomous Guidance and Navigation system

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theory [18]. An alternative approach based on neural

networks has also been proposed by Moreira and Guedes

Soares [19]. Modelling of ship trajectories in collision

situations by an evolutionary algorithm is presented by

Smierzchalski and Michalewicz [20], where comparison of

computational time for trajectory generation with respect to

other manoeuvring algorithms, and static and dynamic

constrains for the optimization process of the safe trajec-

tories, are also illustrated.

The intelligent control strategies implemented in colli-

sion avoidance systems can be categorized as automata,

hybrid systems, Petri nets, neural networks, evolutionary

algorithms and fuzzy logic. These techniques are popular

among machine learning researchers due to their intelligent

learning capabilities. The soft-computing based artificial

intelligence (AI) techniques, evolutionary algorithms,

fuzzy logic, expert systems and neural networks and

combinations of them (hybrid expert systems), for colli-

sion avoidance in ocean navigation are summarized by

Statheros et al. [21].

Ito et al. [22] used genetic algorithms to search for safe

trajectories on collision situations in ocean navigation. The

approach is implemented in the training vessel ‘‘Shioji-

maru’’, integrating Automatic Radar Plotting Aids (ARPA)

and a Differential Global Position System (DGPS). ARPA

system data, which can be formulated as a stochastic pre-

dictor, is designed such that the probability density map of

the existence of obstacles is derived from the Markov

process model before collision situations, as presented by

Zeng et al. [23] in the same experimental setup. Further,

Hong et al. [24] have presented collision free trajectory

navigation based on a recursive algorithm that is formu-

lated by analytical geometry and convex set theory.

Similarly, Cheng et al. [25] have presented trajectory

optimization for a ship collision avoidance system based on

a genetic algorithm.

Liu and Liu [26] used Case Based Reasoning (CBR) to

illustrate the learning of collision avoidance in ocean

navigation from previous recorded data of collision situa-

tions. In addition, a collision risk evaluation system based

on a data fusion method is considered and Fuzzy Mem-

bership Functions (FMF) for evaluating the degree of risk

are also proposed. Further intelligent anti-collision algo-

rithms for different collision conditions have been designed

and tested on the computer based simulation platform by

Yang et al. [27]. Zhuo and Hearn [28] presented a study of

collision avoidance situations using a self learning neuro-

fuzzy network based on an off-line training scheme. The

study is based on two-vessel collision situations, and a

Sugeno type fuzzy inference system (FIS) is proposed for

the decision making process of the collision avoidance.

However, the work presented in this paper is formulated

with respect to the Mamdani type FIS.

Fuzzy-logic based systems, which are formulated for

human type thinking, facilitate a human friendly envi-

ronment during the decision making process. Hence,

several decision making systems in research and com-

mercial applications have been presented before [29].

Automatic collision avoidance systems for ship systems

using fuzzy logic based control systems have been pro-

posed by Hasegawa [30]. The conjunction of human

behaviour and the decision making process has been for-

mulated by various fuzzy functions in Rommelfanger [31]

and Ozen et al. [32]. A fuzzy logic approach for collision

avoidance with the integration of a virtual force field has

been proposed by Lee et al. [33]. However, the simulation

results are limited to the two-vessel collision avoidance

situations.

Behaviour based controls formulated with interval pro-

gramming for collision avoidance of ocean navigation are

proposed by Benjamin et al. [34]. The collision avoidance

behaviour is illustrated accordance with the Coast Guard

Collision Regulations (COLREFGS-USA).

Benjamin and Curcio [35] present the decision making

process of ocean navigation based on an interval pro-

gramming model for multi-objective decision making

algorithms. The computational algorithm based on if–then

logic is defined and tested under simulator conditions by

Smeaton and Coenen [36] regarding different collision

situations. Further, this study focused on a rule-based

manoeuvring advice system for collision avoidance.

Cockcroft and Lameijer presented detailed descriptions

of collision avoidance rules, how the regulations should be

interpreted and how to avoid collision [11]. Further, the

complexity of autonomous navigation, not only in the sea

but also in the ground, has been discussed by Benjamin and

Curcio [34] who, in the same work, discuss the legal

framework, rules and regulations, and the importance

of collision avoidance within a set of given rules and

regulations.

This paper focuses on a fuzzy logic based DM system to

be implemented in ocean navigation to improve safety of

the vessel by avoiding collision situations under critical

collision conditions; the system is a continuation of the

study of Perera et al. [37]. The experienced helmsman’s

actions in ocean navigation can be simulated by fuzzy logic

based decision making process, and that could be one of

the main advantages in this proposal. Even though similar

approaches have been identified in the recent literature

[30], some of the drawbacks of those studies are the

ignorance of the COLREGs rules and regulations and of

expert knowledge in ocean navigation (i.e. crash stopping

manoeuvres) that have been extensively considered in this

study. Further discussion on COLREGs rules and regula-

tions and their importance in ocean navigation can be

found in Sect. 2.

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2 COLREGs rules and regulations

The COLREGs [10] include 38 rules that have been divi-

ded into Part A (General), Part B (Steering and Sailing),

Part C (Lights and Shapes), Part D (Sound and Light

signals), and Part E (Exemptions). There are also four

Annexes containing technical requirements concerning

lights and shapes and their positioning, sound signalling

appliances, additional signals for fishing vessels when

operating in close proximity, and international distress

signals. However, the main focus in this study is the

COLREGs Part B, concerning Steering and Sailing rules.

It is a fact that the COLREGs rules and regulations

regarding collision situations in ocean navigation have

been ignored in most of the recent literature. The negli-

gence of the IMO rules may lead to conflicts during ocean

navigation. As for the reported data of maritime accidents,

56% of major maritime collisions include violations of

the COLREGs rules and regulations [20]. Therefore, the

methods proposed by the literature ignoring the COLREGs

rules and regulations should not be implemented in ocean

navigation. On the other hand, there are some practical

issues regarding implementation of the COLREGs rules

and regulations during ocean navigation. The Own vessel

Head-on and Overtake situations are presented in Figs. 2

and 3. Consider the Crossing situations where the Own

vessel is in ‘‘Give way’’ situations in Figs. 4, 5, 6, and 7

and in ‘‘Stand on’’ situations in Figs. 8, 9, 10 and 11, there

are velocity constrains in implementing COLREGs rules

and regulations of the ‘‘Give way’’ and ‘‘Stand on’’ vessel

collision situations when the Target vessel has very low or

very high speed compared to the Own vessel. Furthermore,

the Target vessel overtake situation is presented in Fig. 12.

On the other hand, a considerable amount of recent

research has been focused on design and implementation of

optimization algorithms to find the safest path to avoid

Fig. 2 Head-on (Own vessel)

Fig. 3 Overtake (Own vessel)

Fig. 4 Crossing (Own vessel ‘‘Give Way’’)


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stationary and moving obstacles. These optimization

algorithms always find the optimum solution for the safe

trajectory based on assumptions; hence the optimum

solutions may not be realistic and may not have intelligent

features. As an example, it is observed that some of the

optimization algorithms always find the safest path behind

the Target vessel, which may lead to a conflict situation

with the COLREGs rules and regulations where the Own

vessel is in ‘‘Stand on’’ vessel situation.

On the popular collision avoidance approach of repul-

sive force based optimization algorithms, the Own vessel is

kept away from the obstacles by a repulsive force field.

This concept may not be practical in situations of moving

obstacles with very low speed or very high speed when

compared to the Own vessel’s speed. In addition, a com-

plex orientation of obstacles may lead to unavoidable

collision situations. On the other hand, repulsive force

based optimization algorithms are tasked with finding a

Fig. 6 Parallel-crossing (Own vessel ‘‘Give Way’’)


Fig. 8 Crossing (Own vessel ‘‘Stand On’’)

Fig. 9 Parallel-crossing (Own vessel ‘‘Stand On’’)



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globally safe trajectory for Own vessel navigation, and this

might not be a good solution for the localized trajectory

search. In addition, the concepts of ‘‘Give way’’ and

‘‘Stand on’’ vessels that are derived in COLREGs rules and

regulations during the repulsive force based optimization

process are not taken into consideration, and therefore may

not be honoured.

Vessel course changes and/or speed changes in ocean

navigation must be formulated in order to avoid collision

situations. However, some of the recent collision avoidance

applications have been focused specifically on controlla-

bility of either course or speed change. According to the

COLREGs rule 8(b) [10]:

‘‘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, as well as speed

changes, should be implemented during ocean navigation

to avoid collision situations. Similarly, special measures

should be considered for integration of course and speed

controls due to the fact that the Own vessel may not

respond to the required changes of course or speed. The

problems and suggestions that are discussed in this section

have been further illustrated in the design process of the

DM system in this study. Consider critical collision con-

ditions, where the ‘‘Give way’’ vessel does not take any

appropriate actions to avoid collisions, so therefore the

‘‘Stand on’’ vessel is forced to take actions to avoid colli-

sion situation; according to COLREGs rule 17(b) [10]:

‘‘When, from any cause, the vessel required to keep

her course and speed finds herself so close that col-

lision cannot be avoided by the action of the ‘‘Give

way’’ vessel alone, she shall take such action as will

best aid to avoid collision’’

However, the decision making process of the Own

vessel in a critical collision situation should be carefully

formulated, because the collision avoidance in this situa-

tion alternatively depends on the ‘‘Stand on’’ vessel’s

manoeuvrability. Further, this situation might lead to a

‘‘Crash stopping’’ manoeuvre of the ‘‘Stand on’’ vessel due

to a lack of distance for speed reductions. Hence, this study

is focused on the critical collision conditions in which the

Own vessel, even as the ‘‘Stand on’’ vessel, has to take

actions to avoid the collision due to absence or negligence

of actions from a ‘‘Give way’’ Target vessel.

3 Collision conditions

Figure 13 presents two vessels in a collision situation. The

Own vessel is initially located at the point O (xo, yo), and

the Target vessel is located at the point A (xa, ya). The Own

and Target vessels’ velocity and course conditions are

represented by Vo, Va and Wo, Wa. The speed and course of

the Target vessel with respect to the Own vessel can be

estimated using the range and bearing values in a given

Fig. 12 Overtake (Target vessel)

Fig. 13 Vessel collision situation

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time interval. It is assumed that the Target vessel maintains

constant speed, |Va| ? Va, and course Wa conditions. The

relative speed and course of the Target vessel with respect

to the Own vessel are defined as |Va,o| ? Va,o and Wa,o,

and can be calculated from

Va;o ¼ Va � Vo ð1ÞThe relative trajectory of the Target vessel has been

estimated from the Eq. 1 with the derivation of the relative

speed Va,o and relative course Wa,o. In addition, the relative

range and bearing of the Target vessel with regard to the Own

vessel are derived as |AO| and ho, respectively. All angles

have been measured regarding the positive Y-axis. The curve

AB represents the relative path of the Target vessel with

respect to the Own vessel and the collision encounter angle is

represented by ha,o. Further, it is assumed that both vessels

are power driven vessels (IMO categorization).

Figure 14 presents a relative collision situation in ocean

navigation that is similar to a Radar plot. The Own vessel

ocean domain is divided into three circular sections with

radius Rvd, Rb and Ra. The radius Ra represents the

approximate distance to the Target vessel identification;

this distance could be defined as the distance where the

Own vessel is in a ‘‘Give way’’ situation and should take

appropriate actions to avoid collision. The distance Rb

represents the approximate distance where the Own vessel

is in a ‘‘Stand on’’ situation, but should take actions to

avoid collisions, if necessary due to absence of the

appropriate actions from the Target vessel. The circular

region with the radius Rvd represents the vessel domain.

The distances of Rvd, Rb and Ra are formulated with the

Collision Distance FMF (see Fig. 15).

The Own vessel Collision Regions are divided into eight

regions from I to VIII (see Fig. 14). These regions are

separated by dotted lines that are coincident with the

Collision Regions (see Fig. 16) as formulated in the FMF.

It is assumed that the Target vessel will be located within

one of these eight regions and the collision avoidance

decisions are formulated in accordance to each region. As

represented in Target vessel position II in Fig. 14, the

Target vessel positions have been divided into eight

Fig. 14 Relative collision situation in ocean navigation

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divisions of vessel orientations regarding the relative

course (II-a, II-b, II-c, II-d, II-e, II-f, II-g and II-h). These

divisions are separated by dotted lines that are coincident

with the Relative Collision Angle FMF (see Fig. 18).

4 Collision avoidance methodology

4.1 Identification of obstacles

The stationary and moving obstacles in ocean navigation

can be identified by several instruments and systems such

as 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. The AIS simulator and marine traffic simulator have

been implemented on several experimental platforms for

design of safe ship trajectories [38]. The method of iden-

tifying stationary and moving obstacles in this model is the

collection of radar data.

4.2 Collection of navigational information

Navigational information can be categorized into static,

dynamic and voyage related information [39]. Static

information is composed of Maritime Mobile Service

Identity (MMSI), Call Sign and Name, IMO number,

length and beam, type of ship and location and position of

communication antenna. Dynamic information can be

divided into vessel position, position time stamp, course

over ground, speed over ground, heading, navigational

status and rate of turn. Finally, voyage related information

can be expanded into vessel draft, cargo type, destination

and route plan. Collection of navigational information is an

important part of the decision making process of the col-

lision avoidance in ocean navigation and can be achieved

by collaboration with the AIS. However, collection of the

navigational information of the Target vessel has not been

emphasized at this phase of the present work.

4.3 Analysis of navigational information

The collected obstacles’ information should be considered

for further analysis of navigational information. Three

distinct situations involving risk of collision in ocean

navigation have been recognized in recent literature [36]:

Overtaking (see Figs. 3, 12); Head-on (see Fig. 2) and

Crossing (see Figs. 4, 5, 6, 7, 8, 9, 10, 11). Therefore, these

three situations have been analyzed in this work. However,

in ocean navigation, complex collision situations involving

a combination of the above situations can occur, and

identification of each situation with respect to each of the

collision conditions will useful for the overall decisions of

ocean navigation.

4.4 Assessments of the collision risk

The analysis of navigational information will help to assess

the collision risk. The assessment of collision risk should

be continuous and done in real-time by the navigational

system in order to guarantee the safety of the Own vessel.

As illustrated in the literature, the mathematical analysis of

collision risk detection can be divided into two categories

[39]: the Closest Point Approach Method (CPA-2D

method) and the Predicted Area of Danger Method (PAD-

3D method). The CPA method consists of calculation of

the shortest distance from the Own vessel to the Target

vessel and the assessment of the collision risk, which can

be predicted with respect to the Own vessel domain.

However, this method is not sufficient to evaluate the

collision risk, since it does not take into consideration the

Target vessel size, course and speed. An extensive study of

the CPA method with respect to a two-vessel collision

situation has been presented by Kwik [16]. The PAD

method consists of modelling the Own vessel’s possible

trajectories as an inverted cone and the Target vessel’s

trajectory as a cylinder, being the region of both objects’

intersection categorized into the PAD. The Target vessel

size, course and speed can be integrated into the geometry

of the objects of navigational trajectories.

Tables 1 and 2 present the summarized collision risk

assessments and decisions of the two-vessel collision sit-

uation in Fig. 14. The first column of the Tables 1 and 2

represents the Collision Regions (Reg.) with respect to the

Own vessel, and the second column represents the Divi-

sions (Div.) of the Target vessel orientations. The third

column represents the Collision Risk (Risk) assessments

with respect to each of the Collision Regions, which have

been divided into three sections of Low Risk (Low),

Medium Risk (Mid.) and High Risk (High). The Target

vessel Relative Range (Range) from Rvd to Ra is presented

in the fourth column, and from Ra to Rb is presented in the

seventh column. The Relative Speed Ratio conditions (Sp.

Cond.) of Va,o/Vo are presented in the fifth and eighth

columns. The velocity conditions of Va,o/Vo�, & and �0

are represented by approximately less than, equal, and

greater than zero, respectively. Finally the decisions that

need to be taken to avoid collision situations with respect to

the COLREGs rules and regulations are presented in the

sixth and ninth columns.

The specific COLREGs rules and regulations that are

considered during the decision making processes with

respect to ocean navigation are Overtaking (Rule 13),

Head-on (Rule 14) and Crossing (Rule 15) situations. With

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respect to the COLREGs rules and regulations, the vessel

coming from the starboard side has high priority for the

navigation that had been called the ‘‘Stand on’’ vessel, as

mentioned before. As noted from Table 1, the appropriate

actions for collision avoidance from the Own vessel have

been formulated in the Regions I, II, III and IV with the

relative distance range of (Rvd Ra) and (Ra Rb). However,

respecting the COLREGs rules and regulations, the vessel

coming from the port side has low priority, so is known as

the ‘‘Give way’’ vessel. Further, noted from the Table 2,

the appropriate actions of collision avoidance from the

Own vessel have been formulated in Regions V, VI, VII

and VIII with the relative range of (Rvd Ra). The range (Rvd

Ra) represents the region in which the Own vessel, as the

‘‘Stand on’’ vessel, might take appropriate actions to avoid

critical collision situations.

Even though the main decision making process in this

study is based on the COLREGs rules and regulations, the

COLREGs do not account for critical collision condition

situations (see Table 2) in near proximity. Therefore the

Table 1 Collision risk assessments and decisions for regions I to IV

Reg. Div. Risk Range Sp. Cond. Decisions Range Sp. Cond. Decisions

I d Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 NA Va,o/Vo & 0 NA

Va,o/Vo � 0 NA Va,o/Vo � 0 NA

e High (Rvd Ra) Va,o/Vo � 0 dwo [ 0 (Ra Rb) Va,o/Vo � 0 dwo [ 0

Va,o/Vo & 0 dwo [ 0 Va,o/Vo & 0 dwo [ 0

Va,o/Vo � 0 dwo [ 0 Va,o/Vo � 0 dwo [ 0

f Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



II e Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dVo [ 0 Va,o/Vo & 0 dVo [ 0

Va,o/Vo � 0 dVo [ 0 Va,o/Vo � 0 dVo [ 0

f High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo [ 0, dVo \ 0 Va,o/Vo & 0 dwo [ 0, dVo \ 0

Va,o/Vo � 0 dwo [ 0, dVo \ 0 Va,o/Vo � 0 dwo [ 0, dVo \ 0

g Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo [ 0 Va,o/Vo & 0 dwo [ 0

Va,o/Vo � 0 dwo [ 0 Va,o/Vo � 0 dwo [ 0

III f Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



g High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dVo \ 0 Va,o/Vo & 0 dVo \ 0

Va,o/Vo � 0 dVo \ 0 Va,o/Vo � 0 dVo \ 0

h Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



IV a Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



g Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



h High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



NA not applicable

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decision making process under critical collision conditions

have been based on expert knowledge in navigation (i.e.

crash-stopping manoeuvres), as presented in Table 2.

4.5 Decisions on navigation

The decisions of collision avoidance in ocean navigation

are based on the speed and course of each vessel, distance

between two vessels, distance of the closest point approach

(RDCPA) (see Fig. 13), time to DCPA, neighbouring vessels

and other environmental conditions. The decision space of

collision avoidance can be categorized into three stages for

each vessel in an open ocean environment:

• When both vessels are at non-collision risk range, both

vessels have the options to take appropriate actions to

avoid a collision situation;

• When both vessels are at collision risk range, the ‘‘Give

way’’ vessel should take appropriate actions to achieve

safe passing distance in accordance with the COLREGs

Table 2 Collision risk assessments and decisions for regions V to VIII

Reg. Div. Risk Range Sp. Cond. Decisions Range Sp. Cond. Decisions

V a High (Rvd Ra) Va,o/Vo � 0 dwo \ 0 (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dwo \ 0 Va,o/Vo � 0 NA

b Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



h Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



VI a Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo [ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dwo [ 0 Va,o/Vo � 0 NA

b High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo [ 0, dVo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dwo [ 0, dVo \ 0 Va,o/Vo � 0 NA

c Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dVo [ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dVo [ 0 Va,o/Vo � 0 NA

VII b Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dVo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dVo \ 0 Va,o/Vo � 0 NA

c High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dVo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dVo \ 0 Va,o/Vo � 0 NA

d Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



VIII c Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dwo \ 0 Va,o/Vo � 0 NA

d High (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA

Va,o/Vo & 0 dwo \ 0, dVo \ 0 Va,o/Vo & 0 NA

Va,o/Vo � 0 dwo \ 0, dVo \ 0 Va,o/Vo � 0 NA

e Mid. (Rvd Ra) Va,o/Vo � 0 NA (Ra Rb) Va,o/Vo � 0 NA



NA not applicable

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123

rules and regulations and the ‘‘Stand on’’ vessel should

keep its course and speed;

• When both vessels are at critical collision risk range, and

the ‘‘Give way’’ vessel does not take appropriate actions

to achieve safe passing distance in accordance with the

COLREGs rules, then the ‘‘Stand on’’ vessel should take

appropriate actions to avoid the collision situation.

In this study it is assumed that the ‘‘Give way’’ vessel

does not take appropriate actions to avoid the collision

situations, therefore the ‘‘Stand on’’ vessel should take

appropriate actions to avoid the collision situation while

respecting the COLREGs rules and regulations.

4.6 Implementation of decisions on navigation

As the final step, the decisions on vessel navigation will be

formulated with respect to the collision risk assessments.

The actions that are taken by the Own vessel are propor-

tional to the Target vessel behaviour as well as the COL-

REGs rules and regulations. The expected Own and Target

vessel actions of collision avoidance can be formulated into

two categories:

• The Own vessel passage change (course change and/or

speed change);

• The Target vessel passage change (course change and/

or speed change).

The Own vessel Course Change (dWo) collision avoid-

ance decisions, as presented in columns six and nine of

Tables 1 and 2, dW[ 0 and dW \ 0, represent the change of

course to starboard and port side, respectively. Furthermore

dVo [ 0 and dVo \ 0 represent increment and decrement of

the Own vessel Speed Changes (dVo), respectively.

5 Fuzzification and defuzzification

The design process of the overall Fuzzy logic based DM

system can be categorized into the following six steps:

• Identification of the input FMFs.

• Identification of the output FMFs.

• Creation of the FMF for each set of inputs and outputs.

• Construction of if–then fuzzy rules to operate the

overall system.

• Formulation of the fuzzy rules to execute the actions.

• Combination of the fuzzy rules and defuzzification of

the output.

5.1 Fuzzy sets and membership functions

FMF describes fuzzy sets that map from one given universe

of discourse to a unit interval. This is conceptually and

formally different from the fundamental concept of prob-

ability [40]. The Core of the fuzzy set A is defined as the set

of all elements of the universe typical to A that are asso-

ciated with the membership value of 1 and that could be

written as

Core(AÞ ¼ fx 2 XjAðxÞ ¼ 1g ð2Þ

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 and that could be written as

Supp(AÞ ¼ fx 2 XjAðxÞ� 1g ð3Þ

The FMF for inputs, Collision Distance (R), Collision

Region (ho), Relative Speed Ratio (Va,o/Vo) and Relative

Collision Angle (Wa,o), are presented in Figs. 15, 16, 17

and 18 respectively. Figures 19 and 20 are formulated for

the output FMFs of Speed (dVo) and Course (dWo) change

of the Own vessel. The Core and Supp variables are listed

on the respective figures of inputs and outputs FMFs.

A Mamdani type IF \Antecedent[ THEN \Consequent[rule based system has been developed and inference via

Min–Max norm has been considered during this study.

Finally the defuzzification has been calculated by the

center of gravity method.

5.2 Fuzzy inference system

The block diagram for FIS with integration of naviga-

tional instruments is presented in Fig. 21. The initial step

of the FIS consists of data collection of the Target vessel

position, speed and course. In the next step, the relative

trajectory, relative speed and relative course of the Target

vessel are estimated, considering Eq. 1. Then, the data is

fuzzified with respect to the input FMF of Collision

Distance (see Fig. 15), Collision Region (see Fig. 16),

Relative Speed Ratio (see Fig. 17) and Relative Collision

Angle (see Fig. 18). The if–then fuzzy rules are devel-

oped (see Tables 1, 2) in accordance with the COLREGs

rules and regulations and using expert navigational

knowledge. The outputs of the rule based system are the

Fig. 15 Collision Distance FMF

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123

Collision Risk Warning and the fuzzy decisions. Finally

the fuzzy decisions are defuzzified by the output FMF of

Course Change (see Fig. 19) and Speed Change (see

Fig. 20) to obtain the control actions that will be executed

in the Own vessel’s navigation. The control actions are

further expanded as the Course Control Commands and

Speed Control Commands that can be implemented on

Speed and Course Control Systems, as presented in

Fig. 21.

6 Computational implementation

6.1 Fuzzy membership functions and variables

The Fuzzy logic based DM system has been imple-

mented on the MATLAB software platform. MATLAB

supports the fuzzy logic schemes of Mamdani and

Sugeno Types [41]. The Mamdani type fuzzy logic

scheme consists of utilizing membership functions for

both inputs and outputs. As previously mentioned,

if–then rules are formed by applying fuzzy operations to

the Mamdani type membership functions for given inputs

and outputs.

Following values are considered for the simulations.

Considering the Collision Distance FMF (see Fig. 15), the

assigned distance values are Rvd & 0.5 NM, Rb & 5 NM

and Ra & 10 NM. The variables of j1 & 10�, j2 & 80�,

j3 & 10�, and j4 & 80� have been considered for the

Collision Region FMF (see Fig. 16). The Relative Colli-

sion Angle FMF (see Fig. 18) variables have been assigned

as m1 & 10�, m2 & 10�, and m3 & 10�. Considering the

Fig. 17 Relative Speed Ratio FMF

Fig. 18 Relative Collision Angle FMF

Fig. 19 Course Change FMF

Fig. 20 Speed Change FMF

Fig. 16 Collision Region FMF

J Mar Sci Technol (2011) 16:84–99 95

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Relative Speed Ratio FMF (see Fig. 17), the assigned

values are v1 & 0.1 and v2 & 5. The output FMF of Speed

Change (see Fig. 20) has been derived with respect to the

variables of 01 & 2, 02 & 10, and 03 & 20. Finally, the

Course Change FMF (see Fig. 19) has been formulated by

the variables of i1 & 10�, and i2 & 40�.

6.2 Simulation results

Figures 22, 23, 24 and 25 present the MATLAB simula-

tions for two-vessel collision situations considering dif-

ferent speed and course conditions in the Cartesian

coordinate space. These figures contain the start and end

Fig. 21 Block diagram for fuzzy inference system

Fig. 22 Crossing situation Fig. 23 Crossing situation

96 J Mar Sci Technol (2011) 16:84–99

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positions of the Own and Target vessels and their naviga-

tional trajectories. The vessel initial speed condition is

Vo/Va = 0.5 and initial course of the Own vessel is

Wo = 0�. The start position of the Own vessel (0, 0) and

the collision point for both vessels (0, 5) are common to all

simulations. It is assumed that the speed and the course of

the Target vessel is always a constant.

Two front crossing situations of two vessels are pre-

sented in Figs. 22 and 23. In both situations, the Target

vessel is in the ‘‘Give way’’ situation and the Own vessel is

in the ‘‘Stand on’’ situation. However, in the simulation, the

Target vessel has not taken any appropriate actions to avoid

the collision situations. Therefore the Own vessel changed

its velocity and course to avoid the collision situation.

In Fig. 22, the Own vessel changed its speed ratio to

Vo/Va = 0.38 and course Wo = 2.7502� to the port side to

avoid the collision and the minimum distance between both

vessels is 0.2863 NM. Similarly, in the collision situation

represented in Fig. 23, the Own vessel changed its speed

ratio to Vo/Va = 0.4025 and course Wo = 2.2345� to port

side in order to avoid collision, and the minimum distance

between both vessels is 0.36792 NM.

Figures 24 and 25 present back crossing situations of

two vessels in ocean navigation. On Fig. 24, the Target

vessel is in the ‘‘Give way’’ situation and the Own vessel is

in the ‘‘Stand on’’ situation. However, in this simulation the

Target vessel has not taken any appropriate actions to avoid

the collision, hence the Own vessel has changed velocity

and course to avoid collision situations. In this case the

Own vessel changed speed ratio to Vo/Va = 0.4225 and

course Wo = 1.7189� to the starboard side to avoid the

collision, and the minimum distance between both vessels

is 0.4658 NM. On the collision situation represented in

Fig. 25, where the Target vessel overtakes the Own vessel,

the Own vessel did not change speed ratio to (Vo/Va) but

changed course Wo = 4.0107� to the port side to avoid the

collision. The minimum distance between both vessels is

0.29164 NM.

7 Conclusion

This paper presents a fuzzy logic based DM system for

collision avoidance of ocean navigation based on the

COLREGs rules and regulations and human expert

knowledge for critical situations. The critical collision

conditions where the Own vessel under ‘‘Stand on’’ con-

ditions take actions to avoid collision due to absence of

the safety actions from the Target vessel, have been

illustrated in the work. Even though crash stopping

manoeuvres of the Own vessel are expected under critical

collision conditions, it is observed that the DM system

could be able to overcome ‘‘Crash stopping’’ manoeuvres

by a fuzzy logic based smooth decision making process.

As presented in Figs. 22, 23, 24, and 25, proper change of

course and/or speed could overcome the ‘‘Crash stopping’’

manoeuvres in critical collision conditions, even within a

Fig. 24 Crossing situation

Fig. 25 Overtake situation

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short distance. Although successful computational results

are obtained under critical collision conditions, it is

assumed that more complex collision conditions in multi-

vessel situations can possibly occur, and unexpected

actions of the Target vessels could be experienced. Hence,

higher capabilities must be formulated into the DM system

to overcome such situations.

Acknowledgments The research work of the first author has been

supported by the Doctoral Fellowship of the Portuguese Foundation

for Science and Technology (Fundacao para a Ciencia e a Tecnologia)

under contract SFRH/BD/46270/2008. Furthermore, this work con-

tributes to the project ‘‘Methodology for ship manoeuvrability tests

with self-propelled models’’, which is being funded by the Portuguese

Foundation for Science and Technology (Fundacao para a Ciencia e

Tecnologia) under contract PTDC/TRA/74332/2006.

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