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This paper focuses on a fuzzy logic based intelligent decision making system that aims to improve thesafety of marine vessels by avoiding collision situations. Itcan be implemented in a decision support system of anoceangoing vessel or included in the process of autonomousocean navigation. Although Autonomous Guidanceand Navigation (AGN) is meant to be an important part offuture ocean navigation due to the associated cost reductionand improved maritime safety, intelligent decision makingcapabilities should be an integrated part of the future AGNsystem in order to improve autonomous ocean navigationalfacilities. In this study, the collision avoidance of theTarget vessel with respect to the vessel domain of the Ownvessel has been analyzed and input, and output fuzzymembership functions have been derived. The if–then rulebased decision making process and the integrated novelfuzzy inference system are formulated and implemented onthe MATLAB software platform. Simulation results arepresented regarding several critical collision conditionswhere the Target vessel fails to take appropriate actions, asthe ‘‘Give way’’ vessel to avoid collision situations. Inthese situations, the Own vessel is able to take criticalactions to avoid collisions, even when being the ‘‘Standon’’ vessel. Furthermore, all decision rules are formulatedin accordance with the International Maritime OrganizationConvention on the International Regulations for PreventingCollisions at Sea (COLREGs), 1972, to avoid conflicts thatmight occur during ocean navigation.
Citation preview
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
J Mar Sci Technol (2011) 16:84–99 85
123
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.
86 J Mar Sci Technol (2011) 16:84–99
123
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’’)
Fig. 5 Crossing (Own vessel ‘‘Give Way’’)
J Mar Sci Technol (2011) 16:84–99 87
123
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. 7 Crossing (Own vessel ‘‘Give Way’’)
Fig. 8 Crossing (Own vessel ‘‘Stand On’’)
Fig. 9 Parallel-crossing (Own vessel ‘‘Stand On’’)
Fig. 10 Crossing (Own vessel ‘‘Stand On’’)
Fig. 11 Crossing (Own vessel ‘‘Stand On’’)
88 J Mar Sci Technol (2011) 16:84–99
123
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
J Mar Sci Technol (2011) 16:84–99 89
123
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
90 J Mar Sci Technol (2011) 16:84–99
123
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
J Mar Sci Technol (2011) 16:84–99 91
123
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
Va,o/Vo & 0 NA Va,o/Vo & 0 NA
Va,o/Vo � 0 NA 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
Va,o/Vo & 0 dVo [ 0 Va,o/Vo & 0 dVo [ 0
Va,o/Vo � 0 dVo [ 0 Va,o/Vo � 0 dVo [ 0
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
Va,o/Vo & 0 dVo \ 0 Va,o/Vo & 0 dVo \ 0
Va,o/Vo � 0 dVo \ 0 Va,o/Vo � 0 dVo \ 0
IV a 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
g 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
h 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
NA not applicable
92 J Mar Sci Technol (2011) 16:84–99
123
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
Va,o/Vo & 0 NA Va,o/Vo & 0 NA
Va,o/Vo � 0 NA Va,o/Vo � 0 NA
h 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
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
Va,o/Vo & 0 dVo [ 0 Va,o/Vo & 0 NA
Va,o/Vo � 0 dVo [ 0 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
Va,o/Vo & 0 dVo [ 0 Va,o/Vo & 0 NA
Va,o/Vo � 0 dVo [ 0 Va,o/Vo � 0 NA
NA not applicable
J Mar Sci Technol (2011) 16:84–99 93
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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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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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