In Proceedings of the 8th IFAC Conference on Control Applications in Marine Systems, Rostock, Germany, September, 2010,

pp. 295-300.

Fuzzy-logic based parallel collisions avoidance decision formulation for an Ocean

Navigational System

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

*Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon, Instituto Superior Tecnico,

Portugal (email:prasad.perera@mar.ist.utl.pt).

**INESC-ID, Technical University of Lisbon, Instituto Superior Tecnico, Portugal (email: joao.carvalho@inesc-id.pt).

*** Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon, Instituto Superior Tecnico,

Portugal (Tel: +351 21 841 7468; email: guedess@mar.ist.utl.pt).

Abstract: This paper focuses on a Fuzzy-logic based parallel decision formulation that aims to improve

the safety of marine vessels by avoiding collision situations in ocean navigation. 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 are derived in this study. The If-Then rule based decision making

process and the integrated novel Fuzzy Inference System are formulated and implemented on MATLAB

software platform. Simulations are presented regarding several collision avoidance situations.

Furthermore, the decision rules are formulated in accordance with the International Maritime Organization

Convention on the International Regulations for Preventing Collisions at Sea (COLREGs) and expert

knowledge in navigation, to avoid conflict that might occur during the ocean navigation.

Keywords: Ocean navigation, Collision avoidance, Fuzzy logic, Decisions support system, Decision

making, Parallel decisions, COLREGs.

1. INTRODUCTION

Fuzzy-logic based systems, which are formulated to approach

the human type of thinking, facilitate a human friendly

environment during the decision making process. Hence,

several Fuzzy-logic based decision making systems have

been recently developed in research as well as commercial

applications (Hardy (1995)).

Autonomous navigation systems in ocean navigation are one

of the industrial applications of the human type of decision

making process. The functionalities and recent developments

of autonomous ocean navigational systems are summarized

by Fossen (1999) and Ohtsu (1999) and ocean applications

have been further studied theoretically as well as

experimentally by Healey and Lienard (1993), Do and Pan

(2006) and Moreira et al. (2007, 2008).

The decision making process and strategies in interaction

situations in ocean navigation, including collision avoidance

situations, are presented by Chauvin and Lardjane (2008).

Benjamin and Curcio (2004) present the decision making

process of ocean navigation based on the interval

programming model for multi-objective decision making

algorithms.

The initial work on Fuzzy-logic based collision avoidance

systems was presented in Perera et al. (2009). However, it

was observed that the Fuzzy rule failures could occur in the

navigational systems due to the boundary intersection of the

contradictory decisions, and a solution was proposed in

Perera et al. (2010a). Hence an approach to overcome the

Fuzzy rules failure is facilitated in this study. An expanded

collision avoidance system that mainly consists of two

divisions of parallel decisions making and sequential action

execution processes to avoid complex collision situations

involving multiple vessels in ocean navigation is proposed in

the overall study.

However, this paper focuses on the Fuzzy-logic based

parallel decision making process to be implemented in ocean

navigation to improve safety of a vessel by avoiding the

single vessel collision situations. In addition, Fuzzy rules are

formulated in accordance with the rules and regulations

expressed in the Convention on the International Regulations

for Preventing Collisions at Sea (COLREGs), (IMO, 1972),

extended by expert knowledge on navigation to facilitate the

regulated prevention of collision and to eliminate

navigational conflicts.

The two vessel decision making process of collision

avoidance is used in this study as the basis of a sequential

action execution process to deal with multi-vessel collision

situations. A further extension of this study, the multi-vessel

collision situations involving complicated Target vessel

collision conditions are presented in Perera et al. (2010 b).

2. COLLISION AVOIDANCE IN OCEAN NAVIGATION

2.1 Two vessel collision Space

A two-vessel collision situation is presented in Figure 1. The

"Own vessel", the vessel equipped with the collision

avoidance system (see Figure 2) is located in the point O(k)

(xo(k), yo(k)), at the kth time instant. The ith "Target vessels"

that needs to be avoided are located at the points Pi(k) (xi(k),

yi(k)), where i={1, …, n}.

As presented in the Figure, the Own vessel navigational

space is divided into three circular regions with radius Rvd, Rb

and Ra. The radius Ra represents the approximate range to the

Target vessel detection when the Own vessel is in a ”Give

way” situation, i.e., where the vessel has low priority for

navigation and should take appropriate actions to avoid

collision situations.

Fig. 1. Two Vessel Collision Situation

The radius Rb represents the approximate distance to the

Target vessel when the Own vessel is in a ”Stand on”

situation with high priority for navigation but should take

appropriate actions to avoid collision due to absence of the

appropriate actions from the Target vessel. In general, vessel

coming from the starboard side has higher priority for the

navigation. The radius Rvd represents the vessel domain

where the area is bounded for the dynamics of the ocean

vessel navigation. These regions are separated by the dotted

circles and coincide with the Range Fuzzy Membership

Functions (FMF) (see Figure 3). Finally Ri(k) represents the

Range of the ith Target vessel at the kth time instant.

The Own and Target vessels’ speed and course conditions are

presented as Vo(k), Vi(k) ,ψo(k), and ψi(k) respectively in the

same Figure. All angles are measured with respect to the

positive Yo/Yi axis. The speed ratio between the Target vessel

and the Own vessel of Vi(k)/Vo(k) is also estimated in this

analysis and coincides with the Speed Ratio FMF (see Figure

4).

The Own vessel collision regions are divided into 10 Bearing

regions, θo, from I, to X. These regions are separated by

dotted straight lines that are coincident with the regions of the

Bearing FMF (see Figure 5). It is assumed that the Target

vessel should be located within these 10 regions and the

collision avoidance decisions are formulated in accordance to

each region. Further discussion on the selection of collisions

regions with respect to the FMFs can be found in (Perera et

al., 2010a).

Further, as presented in the Figure 1, the Target vessel

position (II) has been divided into 8 divisions (from II−a to

II−h) of relative course ψi,o(k). These divisions are separated

by dotted lines that coincide with the Relative Course FMF

(see Figure 6).

2.2 Collision Avoidance System

A block diagram for complete Collision Avoidance System

(CAS) is presented in Figure 2. The complete CAS consists

of four modules: Vessel Tracking & Trajectory Prediction

(VTTP) Module, Collision Risk Assessment (CRA) Module,

Parallel Decision Making (PDM) Module, and Sequential

Action Formulation (SAF) Module.

Fig. 2. Block diagram for Collision Avoidance System

The inputs to the VTTP module are the real-time position of

the Own vessel (xo(k), yo(k)) that is measured/estimated by

the GPS/Inertial navigational systems and the Range (Ri(k))

and Bearing (θi(k)) values of the ith Target vessel that could

be measured by the Rader/Laser measurement systems on the

kth

time instant.

The VTTP module consists of four units: Scan Unit, Data

Classification Unit, Clustered Data Tracking Unit and

Trajectory Prediction Unit. The Scan Unit uses the

Radar/Laser measurement system to collect the real-time

position data of each Target vessel. Then the Target vessels’

position data will be used in the Data Classification Unit to

identify each vessel and the Clustered Data Tracking Unit

will track each vessel separately. Finally, the collected

tracking data will be used to predict each vessel’s trajectory

in the Trajectory Prediction Unit. However, one must note

that constant speed and course conditions have been assumed

for the Target vessels in this study.

The main objective of the CRA module is to evaluate the

collision risk of each Target vessel with respect to the Own

vessel conditions. This is achieved by the Relative Trajectory

Formation Unit and Collision Time and Point Estimation

Unit. The inputs into the CRA module are the position data of

the Own vessel and the Target vessels. The outputs of the

CRA module are Range (Ri(k)), Bearing (θi(k)), Relative

course (ψi,o(k)) and Relative speed (Vi,o(k)) of ith

Target

vessel. These outputs of CRA module will input into the

PDM module at kth

time instant. The Time until collision

Ti(k) of ith

Target vessel will also input into the SAF module

as shown in Figure 2. The PDM module consists of a Fuzzy-

logic based decision making process that generates parallel

collision avoidance decisions with respect to each Target

vessel and the formulation of the PDM module is the main

objective in this study.

Finally the ith parallel decision of collision avoidance Di(k)

will be forwarded from the PDM module to the SAF module.

The main objective in the SAF module is to organize the

parallel decision made by the PDM module into sequential

actions, course, Aδψi(k), and speed, Aδψi(k), control actions,

that will be executed on the Own vessel navigational system.

These collision avoidance decisions/actions, course and speed

control actions will be implemented on rudder and propeller

control systems respectively.

3. PARALLEL DECISION MAKING MODULE

An overview of the PDM module is presented in Figure 2.

The module mainly consists of 3 units: Fuzzification Unit,

Fuzzy Rules Unit and Defuzzification Unit. Further, the

Collisions Risk Warning and the Knowledge Base are

considered as the outcome and the input to the Fuzzy Rules

Unit respectively.

3.1. Fuzzification Unit

The Fuzzification Unit consists of 4 input Fuzzy Membership

Functions (FMF) (see Figure 2): Range FMF (Ri(k)) (see

Figure 3), Speed Ratio FMF (Vi(k)/Vo(k)) (see Figure 4),

Bearing FMF (θi(k)) (see Figure 5), and Relative Course

FMF (ψi,o(k)) (see Figure 6). The parameters of the respective

FMFs are presented in Figure 1.

In this unit the inputs from the CRA module, Range Ri(k),

Bearing θi(k), Relative course ψi,o(k) and Relative speed

Vi,o(k) of the ith

Target vessel at the kth

time instant will be

fuzzified using the respective input FMFs.

3.2 Fuzzy Inference and Fuzzy Rules

A Mamdani type IF <Antecedent> THEN <Consequent> rule

based system (see Table 1 & 2) has been developed and

inference via Min-Max norm has been considered in the

Fuzzy Rules Unit. The IF-THEN Fuzzy rules are developed

in accordance with the COLREGs rules and regulations and

expert knowledge in navigation.

There are three recognized distinct situations involving risk

of collision with respect to ocean navigation (Smeaton and

Fig. 3. Range FMF

Fig. 4. Speed Ratio FMF

Fig. 5. Bearing FMF.

Fig. 6. Relative Course FMF.

Fig. 7. Course Change FMF

Fig. 8. Speed Change FMF

Coenen, 1990): Overtaking, Head-on and Crossing. The

decision space of collision avoidance can be categorized into

three stages for each vessel in open ocean environment.

When none of the vessels is in the collision risk range, both

vessels have the options to take appropriate actions to avoid

collision situation.

However, 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 rules

and regulations, and the ”Stand on” vessel should maintain

course and speed. Further, 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 has the option to take appropriate actions to avoid the

collision (Cockcroft and Lameijer, 2001).

These concepts are considered for the development of the

Fuzzy rules. However, for near collision conditions in ocean

navigation, the COLREGs do not facilitate clear rules and

regulations. Therefore, expert knowledge in navigation has

been considered for the formation of the Fuzzy rules in some

regions.

Tables 1 & 2 present the summarized Collision Assessments,

Fuzzy Rules & Decisions. The first column represents the

Bearing region (θo(k)) (Be.) that is divided into 10 regions(I

to X) of the Target vessel. The second column represents the

Relative Course (ψi,o(k)) (Cou.) that has been divided into 8

regions (a to h) of the Target vessel orientations, and the

Collision Risk (Risk) assessments with respect to Relative

Course that is divided into three sections of Low Risk (Low),

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

vessel Range (Ri(k)) from Rvd to Ra is presented in the third

column, and from Ra to Rb is presented in the forth column.

The third and forth columns are further divided into two sub-

columns. The Relative Speed Ratio of (Vi(k)/Vo(k)) is

presented in the first sub-column of the third and forth main

columns. The vessel speed conditions of Vi/Vo <, ≈ and > 1

are represented by the Target vessel speed approximately less

than, equal, and greater to the Own vessel speed.

Finally the Decisions that need to be taken to avoid collision

situations are in the second sub-columns of the third and

fourth main columns. These decisions are: Course to

starboard δψo>0, course to port δψo<0 , no course change,

increase speed (δVo>0), decrease speed (δVo<0), no speed

change and not applicable (NA). Table 2 presents a similar

organization.

3.3 Defuzzification

Finally in the Defuzzification unit, the Fuzzy decisions are

defuzzified by the output FMFs of Course Change FMF (see

Figure 7) and Speed Change FMF(see Figure 8) to obtain

Course change decision (Dδψi(k)) and Speed change decisions

(DδVi(k)) that will be executed in the Own vessel navigation

where Di≡(Dδψi(k)), DδVi(k))) (see Figure 2). The

defuzzification was made using the centre of gravity method.

In this method, one calculates the centroid of the resulting

FMF and uses its abscissa as the final result of the inference.

4. COMPUTATIONAL IMPLEMENTATION

The Fuzzy logic based DM system has been implemented on

the software platform of MATLAB using the Mamdani based

Fuzzy Inference System (FIS) (Sivanandam et al., 2007)

Fig. 9. Heading

Fig. 10. Starboard Crossing

Fig. 11. Overtake

Fig. 12. Port Crossing

Table 1 : Collision Assessments, Fuzzy Rules & Decisions

Table 2 : Collision Assessments, Fuzzy Rules & Decisions

Be. Cou./Risk Range (Rvd Ra) Range (Ra Rb)

Vi

Vo

Decisions Vi

Vo

Decisions

I d / Mid. < 1 NA < 1 NA

≈ 1 NA ≈ 1 NA

> 1 NA > 1 NA

e / High < 1 δψo>0 < 1 δψo>0

≈ 1 δψo>0 ≈ 1 δψo>0

> 1 δψo>0 > 1 δψo>0

f / Mid. < 1 NA < 1 NA

≈ 1 NA ≈ 1 NA

> 1 NA > 1 NA

II e / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 δVo>0

> 1 δVo>0 > 1 δVo>0

f / High < 1 NA < 1 NA

≈ 1 δψo>0,δVo<0 ≈ 1 δψo>0,δVo<0

> 1 δψo>0,δVo<0 > 1 δψo>0,δVo<0

g / Mid. < 1 NA < 1 NA

≈ 1 δψo>0 ≈ 1 δψo>0

> 1 δψo>0 > 1 δψo>0

III f / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 δVo>0

> 1 δVo>0 > 1 δVo>0

g / High < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 δVo<0

> 1 δVo<0 > 1 δVo<0

h / Mid. < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 δVo<0

> 1 δVo<0 > 1 δVo<0

IV g / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 δVo>0

> 1 δVo>0 > 1 δVo>0

h / High < 1 NA < 1 NA

≈ 1 δψo<0,δVo<0 ≈ 1 δψo<0,δVo<0

> 1 δψo<0,δVo<0 > 1 δψo<0,δVo<0

a / Mid. < 1 NA < 1 NA

≈ 1 δψo<0,δVo<0 ≈ 1 δψo<0,δVo<0

> 1 δψo<0,δVo<0 > 1 δψo<0,δVo<0

V h / Mid. < 1 NA < 1 NA

≈ 1 NA ≈ 1 NA

> 1 NA > 1 NA

a / High < 1 δψo<0 < 1 NA

≈ 1 δψo<0 ≈ 1 NA

> 1 δψo<0 > 1 NA

b / Mid. < 1 NA < 1 NA

≈ 1 NA ≈ 1 NA

> 1 NA > 1 NA

Be. Cou./Risk Range (Rvd Ra) Range (Ra Rb)

Vi

Vo

Decisions Vi

Vo

Decisions

VI a / Mid. < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

b / High < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

c / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 NA

> 1 δVo>0 > 1 NA

VII a / Mid. < 1 NA < 1 NA

≈ 1 δψo>0 ≈ 1 NA

> 1 δψo>0 > 1 NA

b / High < 1 NA < 1 NA

≈ 1 δψo>0,δVo<0 ≈ 1 NA

> 1 δψo>0,δVo<0 > 1 NA

c / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 NA

> 1 δVo>0 > 1 NA

VIII b / Mid. < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

c / High < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

d / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 NA

> 1 δVo>0 > 1 NA

IX c / Mid. < 1 NA < 1 NA

≈ 1 δψo<0 ≈ 1 NA

> 1 δψo<0 > 1 NA

d / High < 1 NA < 1 NA

≈ 1 δψo<0,δVo<0 ≈ 1 NA

> 1 δψo<0,δVo<0 > 1 NA

e / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 NA

> 1 δVo>0 > 1 NA

X c / Mid. < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

d / High < 1 NA < 1 NA

≈ 1 δVo<0 ≈ 1 NA

> 1 δVo<0 > 1 NA

e / Mid. < 1 NA < 1 NA

≈ 1 δVo>0 ≈ 1 NA

> 1 δVo>0 > 1 NA

The assigned distance values for Range FMF are (see Figure

3): Rvd ≈ 1000 m, Rb ≈ 6000 m and Ra ≈ 10000 m. For the

Speed Ratio FMF (see Figure 4) were assigned the values χ1

≈ 0.8, χ2 ≈ 1.2 and χ3 ≈ 5. For the Bearing FMF (see Figure

5) one has: κ1 ≈ 100, κ2 ≈ 80

0, κ3 ≈ 10

0, κ4 ≈ 80

0, κ5 ≈ 26

0 and

κ6 ≈ 260 . Relative Course FMF (see Figure 6) variables were

assigned as ν1 ≈ 50, ν2 ≈ 5

0, and ν3 ≈ 5

0. The output FMF of

Course Change (see Figure 7) was formulated by the

variables of ι1 ≈ 100, and ι2 ≈ 40

0. Finally, the output FMF of

Speed Change (see Figure 8) was derived with the variables

ϑ1 ≈ 2 and ϑ2 ≈ 10.

Figures from 9 to 12 exemplify the MATLAB simulations for

two vessels collision situations with respect to the three

different collision situations: Heading (see Figure 9),

Starboard-side Crossing (see Figure 10), Overtake (see

Figure 11) and Port-side Crossing (see Figure 12),. These

figures contain the start and end positions of the Own and the

Target vessels with respect to navigational trajectories. The

Own vessel initial speed and course conditions are Vo = 12

Knots and ψo = 00

respectively. The initial position of the

Own vessel is (0 (m), 0 (m)).

As per the simulations, the successful speed and course

change decisions for collision avoidance of ocean navigation

are formulated by the Own vessel to avoid different Target

vessel collisions conditions.

5. CONCLUSIONS

In this study, a Fuzzy logic based decision making process

for the ocean navigation formulated by the COLREGs rules

and regulations and human expert knowledge in navigation is

introduced. As observed, the Fuzzy logic based decision

making process is able to overcome collision conditions in

two vessel situations. Furthermore the decision making

process has taken proper manoeuvres to avoid close-quarter

situations during ocean navigation where the collision risk is

high. The proposed system avoids the need for humans to

take sudden decisions based on inadequate information and in

short time.

ACKNOWLEDGEMENTS

This work has been made within the project ”Methodology

for ships maneuverability tests with self-propelled models”,

which is being funded by the Portuguese Foundation for

Science and Technology (Fundação para a Ciência e

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

research work of the first author has been supported by a

Doctoral Fellowship of the Portuguese Foundation for

Science and Technology (Fundação para a Ciência e

Tecnologia) under contract SFRH/BD/46270/2008.

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