Smooth Transition Between Fuzzy Regions to Overcome Failures in Fuzzy Membership Functions of...

8/9/2019 Smooth Transition Between Fuzzy Regions to Overcome Failures in Fuzzy Membership Functions of Decisions in Coll

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25th Mini-EURO Conference on Uncertainty and Robustness in Planning and Decision Making (URPDM2010)

Coimbra, Portugal, 15 - 17 April, 2010.

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lead to unavoidable collision situations. Therefore, to overcome decision failures, a method of smooth

transition between contradictory decisions of the fuzzy regions is proposed in this work.

2. FORMATION OF COLLISION SPACE

Figure 1 presents two vessels in a collision situation with the decisions in high collision risk situation.

The Own vessel, the vessel with the AGN system, is initially located at the point O ( x o, yo), and the

Target vessel, the vessel that must be avoided, is located at point A (x a, ya). The Own and Target vessels

speeds and course could be written as Vo, Va and o, a respectively. The speed Va, relative speed Va,o,

course a, and relative course a,o values of the Target vessel with respect to the Own vessel can beestimated using the range and bearing values within a given time interval. All angles are measured with

respect to the positive Y-axis.

Figure 1. Relative Collision Situation with the Decisions in High Collision Risk Situation

The Own vessel ocean domain is divided into three circular sections with radius R vd, Rb and Ra as

presented in Figure 1. The radius Ra represents the approximate range to the Target vessel and when the

Own vessel in a Give way situation, where the vessel has low priority for navigation and should take

appropriate actions to avoid collision situations. The radius Rb represents the approximate distance where

the Own vessel is in a Stand on situation, where the vessel has high priority for navigation but should

take appropriate actions to avoid collisions due to absence of the appropriate actions from the Target

vessel. The radius Rvd represents the vessel domain where the area is bounded for the dynamics of themarine vessel. The distances of Rvd, Rb and Ra are formulated in the Range Fuzzy Membership Function

(FMF) (see Figure 2). The Own vessel collision regions were divided into ten regions, from I to X, as

presented in Figure 1. Even though eight regions (Perera et al. (2009)) are generally enough to implement

the COLREGs (IMO (1972)) rules and regulations of ocean navigation, ten regions have been proposed

to overcome the fuzzy decision failures as further discussed in the section 3.1. The Own vessel collision

regions are separated by dotted lines that are coincident with the Bearing FMF (see Figure 3). It is

assumed that the Target vessel is located within these ten regions and the collision avoidance decisions

are formulated in accordance to each region. As represented in Figure 1 the Target vessel position II has

been divided into eight divisions (from II a to II h) of vessel orientations, considering the relative


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course. These divisions are separated by dotted lines that are coincident with the Relative course

FMF(see Figure 5).

3. FORMATION OF DECISION SPACE

Three distinct situations that are involving risk of collision with respect to ocean navigation have been

recognized (Smeaton and 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 at 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 Stand on vessel

has the option to take appropriate actions to avoid the collision.

The collisions avoidance decisions of navigation with respect to the High risk collision situation with the

Range from Rvd to Ra for the respective regions are presented in the Figure 1. The decisions on region I

were formulated as course to starboard (o>0) and no speed change (Vo = 0); In region II, the proposed

decisions were course to starboard (o>0) and decrease speed (Vo


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Table 1:Collision risk assessments, Fuzzy rules and Collisions avoidance decisions

Re. Div./Risk Range (Rvd Ra) Range (Ra Rb) Re. Div./Risk Range (Rvd Ra) Range (Ra Rb)

Va

Vo

Decision Va

Vo

Decision Va

Vo

Decision Va

Vo

Decision

I d / Mid. < 1 NA < 1 NA VI* a / Mid. < 1 NA < 1 NA

1 NA 1 NA 1 Vo 1 NA > 1 NA > 1 Vo 1 NA

e / High < 1 o>0 < 1 o>0 b / High < 1 NA < 1 NA

1 o>0 1 o>0 1 Vo 1 o>0 > 1 o>0 > 1 Vo 1 NA

f / Mid. < 1 NA < 1 NA c / Mid. < 1 NA < 1 NA

1 NA 1 NA 1 Vo>0 1 NA

> 1 NA > 1 NA > 1 Vo>0 > 1 NA

II e / Mid. < 1 NA < 1 NA VII a / Mid. < 1 NA < 1 NA

1 Vo>0 1 Vo>0 1 o>0 1 NA

> 1 Vo>0 > 1 Vo>0 > 1 o>0 > 1 NA

f / High < 1 NA < 1 NA b / High < 1 NA < 1 NA

1 o>0,Vo0,Vo0,Vo 1 o>0,Vo 1 o>0,Vo 1 o>0,Vo 1 NA

g / Mid. < 1 NA < 1 NA c / Mid. < 1 NA < 1 NA

1 o>0 1 o>0 1 Vo>0 1 NA

> 1 o>0 > 1 o>0 > 1 Vo>0 > NA

III f / Mid. < 1 NA < 1 NA VIII b / Mid. < 1 NA < 1 NA

1 Vo>0 1 Vo>0 1 Vo 1 Vo>0 > 1 Vo>0 > 1 Vo 1 NAg / High < 1 NA < 1 NA c / High < 1 NA < 1 NA

1 Vo 1 NA

IV g / Mid. < 1 NA < 1 NA IX c / Mid. < 1 NA < 1 NA

1 Vo>0 1 Vo>0 1 o 1 Vo>0 > 1 Vo>0 > 1 o 1 NA

h / High < 1 NA < 1 NA d / High < 1 NA < 1 NA

1 o


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4. FUZZIFICATION AND DEFUZZIFICATION

The FMFs for inputs, Range (R), Bearing (o), Speed ratio (Va/Vo), and Relative course (a,o) arepresented in Figures 2 to 5, respectively. Figures 6 and 7 are formulated for the output FMFs of Speed

(Vo) and Course (o) change of the Own vessel. The Core and Supp variables are listed on the same

Figures of inputs and outputs FMFs. A Mamdani type IF THEN rule (see

Table 1) 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.

The block diagram for Fuzzy Inference System (FIS) with integration of navigational instruments is

presented in Figure 8. The initial step of the fuzzy inference system consists of data collection of the

Target vessel position, speed and course. Then, the data is fuzzified with respect to the input FMFs of

Range (see Figure 2), Bearing (see Figure 3), Speed Ratio (see Figure 4) and Relative course (see Figure

5). The If-Then fuzzy rules (see Table 1) are developed in accordance with the COLREGs rules and

regulations and navigational knowledge. However near collision conditions in ocean navigation the

COLREGs does not provide clear rules and regulations. Therefore navigational knowledge (Expert

knowledge) on crash-stopping maneuvers has been considered for the formation of the fuzzy rules in

some regions. The outputs of the rule based system are the Collision Risk Warning and the Fuzzy

Decisions. Finally the fuzzy decisions are defuzzified by output FMFs of Course change (see Figure 6)

and Speed change (see Figure 7) to obtain the control actions that will be executed in the Own vessel

navigation.

5. COMPUTATIONAL IMPLEMENTATION

The fuzzy logic based Decision Making (DM) process has been implemented using the Mamdani based

(Sivanandam et al. (2007)) Fuzzy Inference System (FIS) in MATLAB software platform.

Figure 2. Range FMF Figure 3. Bearing FMF

Figure 4.Speed ratio FMF Figure 5.Relative course FMF

Figure 6.Course change FMF Figure 7.Speed change FMF


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Figure 8.Block diagram for Fuzzy Inference System

Considering the Range FMF (see Figure 2), the assigned distance values are R vd 1NM, Rb 6NM and

Ra 10NM. The variables of1 100, 2 80

0, 3 10

0, 4 80

0, 5 26

0 and 6 26

0 have been

considered for the Bearing FMF (see Figure 3). For the Speed Ratio FMF (see Figure 4) were assigned

the values 1 0.8, 2 1.2 and 3 5.0 . The Relative course FMF (see Figure 5) variables were assigned

as 1 50, 2 5

0, and 3 5

0. The output FMF of Course change (see Figure 6) was formulated by the

variables of1 100, and 2 40

0. Finally the output FMF of Speed change (see Figure 7) was derived

with the variables 1

2 and 2

10.Figures 9 and 10 present the simulations of relative trajectories of the Target vessel with respect to the

Own vessel in two vessels collision situations with the zoomed view around the origin. The vessel initial

speed condition is Vo/Va = 0.5 and initial course of the Own vessel is o = 00. The Own vessel is

initially located in the initial position of (0 NM,0 NM). The Target vessel startup points around the

around the collision point (0 NM, 5 NM) with the startup distance of 10 NM have been considered for

the analysis. Further constant speed and course towards the collision point from the initial point is

assumed. It is observed that the decision failures occur in-between relative bearing range of 1800

to 2700

and from 2700

to 3600

previously and when the decision failures occur the relative trajectory of the

Target vessel intercept the Own vessel initial position. The Target vessel relative trajectories with respect

to the relative bearing from 1800

to 2700

and from 2700

to 3600

are presented in Figures 9 and 10

respectively.

As presented in the figures, the relative trajectory of the Target vessel has not intercepted the initiallocation of the Own vessel. It has instead shifted its trajectory from one side of the origin to the other

side smoothly as a result of the new fuzzy regions. The minimum distance between vessels are always

more then 0.05 NM even in critical collision situations where the Target vessel as a Give way vessel

didnt take appropriate actions to avoid collisions. Therefore the relative trajectories of the Target vessel

could be used to observe the behavior of the fuzzy rules in decision making process.


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Figure 9.Relative Trajectory of the Target vessel

from course 1800

to 2700

with zoomed view.

Figure 10.Relative Trajectory of the Target vessel

from course 2700

to 3600

with zoomed view.

6. CONCLUSION

This paper introduces further analysis of the decisions making process (Perera et al. (2009)) based on the

fuzzy logic, COLREGs rules and human expert knowledge in ocean navigation. The decision failures of

the fuzzy logic based systems with respect to the ocean navigation were further illustrated, and a proper

method to overcome decision failures was also presented in this study. As presented in Figures 9 and 10,

smooth transitions of change of course and/or speed could overcome the decision failures in collisionconditions as proposed. Further results on and the true trajectories of collisions avoidance could be found

on Perera et al. (2009). Although successful computational results were obtained by the proposed

method, it is assumed that more complex collision situations combination with multi vessel situations can

possibly occur and unexpected actions of the Target vessels could be experienced. Hence higher

capabilities should be formulated into the decision making process to overcome such situations.


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ACKNOWLEDGEMENTS

The research work of the first author has been supported by a Doctoral Fellowship of the Portuguese

Foundation for Science and Technology under contract SFRH/BD/46270/2008. Further this work

contributes to the project of "Methodology for ships maneuverability tests with self-propelled models",

which is being funded by the Portuguese Foundation for Science and Technology under contract

PTDC/TRA/74332/2006

REFERENCES

Benjamin, M. R., Curcio, J. A., COLREGS - based navigation of autonomous marine vehicles.

IEEE/OES Autonomous Underwater Vehicles, 3239, 2004.

Chauvin, C., Lardjane, S.,. Decision making and strategies in an interaction situation: Collision

avoidance at sea, Transportation Research Part F (11), 259262, 2008.

Cockcroft, A. N., Lameijer, J. N. F., A Guide to The Collision Avoidance Rules. Elsevier Butterworth-

Heinemann, Burlington, MA. USA. 2001.

Do, K. D., Pan, J., Robust path-following of underactuated ships: Theory and experiments on a model

ship. Ocean Engineering 33 (3), 13541372, 2006.

Fossen, T. I. (Ed.), Recent developments in Ship Control Systems Design. World Superyacht Review.

Sterling Publication Limited, London, 1999.

Hardy, T. L., Multi-objective decision-making under uncertainty : Fuzzy logic method. NASA Technical

Memorandum 106796 - Computing in Aerospace 10 Meeting,1995.

Healey, A. J., Lienard, D., Multivariable sliding mode control for autonomous diving and steering of

unmanned underwater vehicle,IEEE Journal of Oceanic Engineering 18 (3), 327339, 1993.

IMO, Convention on the international regulations for preventing collisions at sea (COLREGs). URL :

http://www.imo.org/conventions/, 1972.

Moreira, L., Fossen, T. I., Guedes Soares, C., Path following control system for a tanker ship model.

Ocean Engineering, 34, 20742085, 2007.

Ohtsu, K., Recent development on analysis and control of ships motions. Proceedings of the 1999 IEEE

International Conference on Control Applications, 10961103, 1999.

Ozen, T., Garibaldi, J. M., Musikasuwan, S., Modeling the variation in human decision making. IEEE

Annual Meeting of the Fuzzy Information Processing - NAFIPS 04 2, 617622, 2004.

Perera, L. P., Carvalho, J. P., Guedes Soares, C., Decision making system for collision avoidance of

marine vessel navigation based on COLREGs rules and regulations, Proc.13th Congress of International

Maritime Association of Mediterranean, Istanbul, Turkey, 1121-1128, 2009.

Perera L. P., Carvalho, J. P. and Guedes Soares, C., Autonomous guidance and navigation based on the

COLREGs rules and regulations of collision avoidance.,Advanced Ship Design for Pollution Prevention,

C. Guedes Soares and J. Parunov (Eds.), Taylor & Francis Group, London, UK, 2010.

Rommelfanger, H. J., Multicriteria decision making using fuzzy logic. Conference of the North American

Fuzzy Information Processing Society, 360364,1998.

Sivanandam, S. N., Sumathi, S., Deepa, S. N., Introduction to Fuzzy Logic using MATLAB. Springer

Berlin Heidelberg, New York, 2007.

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