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This paper focuses on a Fuzzy-logic based parallel decision formulation that aims to improvethe safety of marine vessels by avoiding collision situations in ocean navigation. The collision avoidanceof the Target vessel with respect to the vessel domain of the Own vessel has been analyzed and input andoutput Fuzzy Membership Functions are derived in this study. The If-Then rule based decision makingprocess and the integrated novel Fuzzy Inference System are formulated and implemented on MATLABsoftware platform. Simulations are presented regarding several collision avoidance situations.Furthermore, the decision rules are formulated in accordance with the International Maritime OrganizationConvention on the International Regulations for Preventing Collisions at Sea (COLREGs) and expertknowledge in navigation, to avoid conflict that might occur during the ocean navigation.
Citation preview
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:[email protected]).
**INESC-ID, Technical University of Lisbon, Instituto Superior Tecnico, Portugal (email: [email protected]).
*** Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon, Instituto Superior Tecnico,
Portugal (Tel: +351 21 841 7468; email: [email protected]).
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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