Bayesian Network based sequential collision avoidance action execution for an Ocean Navigational...

8/8/2019 Bayesian Network based sequential collision avoidance action execution for an Ocean Navigational System

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In Proceedings of the 8th IFAC Conference on Control Applications in Marine Systems, Rostock, Germany, September, 2010,pp. 301-306.

Bayesian Network based sequential collision avoidance action execution for anOcean 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 study of the sequential action execution module for a collisionavoidance system in ocean navigation. The overall decision-action process of collision avoidance consistson a Fuzzy logic based parallel decision making module and those decisions are formulated into collisionavoidance actions by a Bayesian network based sequential action execution module. The presentedcollision avoidance system is capable of making multiple sequential actions to avoid complicated collisionsituations involving multiple vessels in ocean navigation while still respecting the COLREGs rules andregulations.

Keywords: Ocean navigation, Collisions avoidance, Fuzzy logic, Bayesian Network, Decisions supportsystem, Decisions making, Parallel decisions, Sequential actions, COLREGs.

1. INTRODUCTION

An intelligent decision-action making capability is animportant facility in navigation and it has been one of themajor challenges in autonomous navigational systems. Arobust intelligent decision-action making process is whatultimately influences the success of the autonomousnavigational systems in collision situations. Severalintelligent collision avoidance facilities have been developedand implemented in land and air navigational systems, but thefacilities for ocean navigational systems are stillunderdeveloped and far away from facilitating collisionavoidance capabilities even though 75-96% of marineaccidents and causalities are caused by some types of humanerrors (Rothblum et al. 2002; Anto et al. 2008a,b). Theimplementation of intelligent decision-action makingcapabilities in navigation could reduce maritime accidentsand its respective causalities and represent long-termeconomical benefits.

The vessel domain determination and safe navigationaltrajectory formation are important aspects of the safe oceannavigation. The vessel domain is defined as the area boundedfor dynamics of ocean vessel navigation. The vessel domaindetermination methods, based on, neural-classifiers isproposed by Lisowski et al. (2000) and fuzzy logic isproposed by Pietrzykowski and Uriasz (2009) in respectiveliterature. The safe navigational trajectory formation based onmathematical models of manoeuvring theory by Sutulo et al.(2002), neural networks by Moreira and Guedes Soares(2003), evolutionary algorithm by Smierzchalski andMichalewicz (2000), genetic algorithms by Ito et al. (1999),analytical geometry and convex set theory by Hong et al.

(1999), probabilistic approach based on ARPA system databy Zeng et al. (2001), repulsive force based optimizationalgorithm by Xue et al. (2009), virtual force field by Lee etal. (2004) have been presented in the literature.

The problem of collision avoidance in ocean navigation hasbeen previously approached by several authors using severalalternative techniques: Case Based Reasoning (CBR) by Liuand Liu (2006); Self learning neuro-fuzzy network by Zhuo

and Hearn (2008); Anti-collision algorithm by Yang et al.(2007); Interval programming by Benjamin et al. (2006); If-Then logic by Smeaton and Coenen (1990) and Fuzzy logicby Hasegawa, (1987). The collision avoidance analysis hasalso been approached for several particular cases: in twovessel collision situations by Kwik (1989); in narrow zig-zagchannel by Yavin et al. (1995); strategies in interactionsituations in ocean navigation by Chauvin and Lardjane(2008).

Even though the problem of collision avoidance in oceannavigation is not new, three major weaknesses have beenidentified in the previous approaches: the studies are limitedto two vessel collision situations; the Target vessel speed

conditions are neglected; the Convention on the InternationalRegulations for Preventing Collisions at Sea (COLREGs)rules and regulations IMO (1972) is simply ignored.Thisstudy focuses on the formulation of a Bayesian network based sequential action execution process that could beimplemented for ocean navigation to avoid multi-vesselcollision situations. Furthermore, the collision avoidancedecisions have been associated with a Fuzzy logic basedparallel decision making process that follows the COLREGsrules and regulations of collision avoidance (Perera et al.,2010b).


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2. COLLISION AVOIDANCE IN OCEAN NAVIGATION

2.1 Multi-vessel collision situation

A multi-vessel collision situation is presented in Figure 1.The "Own vessel", i.e., the vessel equipped with the collisionavoidance system, is located in point O(k). The "Target

vessels" that should be avoided are located at points P 1(k),P2(k), , P n(k) with the navigational trajectories of S 1(k),S2(k), , S n(k) at the k

th time instant. The Own vesseltrajectory S 0(k) intersects the trajectories S 1(k), S 2(k), ,Sn(k) at points C 1(k), C 2(k), , C n(k) at instants T 1(k), T 2(k),, T n(k) respectively. When considering the COLREGs rulesand regulations, the vessel coming from the starboard sidehas higher priority for the navigation and is called the "Standon" vessel, and the vessel coming from the port side haslower priority and is called the "Give way" vessel. Thesevessel conditions are considered in the formulation of thecollision avoidance system.

Fig. 1. Multi-vessel Collision Situations

2.2 Collision Avoidance System

A block diagram for complete Collision Avoidance System(CAS) is presented in Figure 2. The complete CAS consistsof four modules: Vessel Tracking & Trajectory Prediction(VTTP) Module, Collision Risk Assessment (CRA) Module,Parallel Decision Making (PDM) Module, and SequentialAction Formulation (SAF) Module. The inputs to the VTTPmodule are the real-time position of the Own vessel (x o(k),yo(k)) that is measured/estimated by the GPS/Inertialnavigational systems and the Range (R i(k)) and Bearing( i(k)) values of the i th Target vessel that could be measuredby the Rader/Laser measurement systems on the k th timeinstant.

The VTTP module consists of four units: Scan Unit, DataClassification Unit, Clustered Data Tracking Unit andTrajectory Prediction Unit. The Scan Unit uses theRadar/Laser measurement system to collect the real-timeposition data of each Target vessel. Then the Target vesselsposition data will be used in the Data Classification Unit toidentify each vessel and the Clustered Data Tracking Unit

will track each vessel separately. Finally, the collectedtracking data will be used to predict each vessels trajectoryin the Trajectory Prediction Unit. However, one must notethat constant speed and course conditions are assumed for theTarget vessels in this study.

Fig. 2. Block diagram for Collision Avoidance System

The main objective of the CRA module is to evaluate thecollision risk of each Target vessel with respect to the Ownvessel conditions. This is achieved by the Relative TrajectoryFormation Unit and Collision Time and Point EstimationUnit. The inputs into the CRA module are the position data of the Own vessel and the Target vessels. The outputs of theCRA module are the Range (R i(k)), Bearing ( i(k)), Relativecourse ( i,o(k)) and Relative speed (V i,o(k)) of i th Targetvessel. These outputs of CRA module will input into thePDM module at k th time instant. The Time until collisionT i(k) of the i

th Target vessel will also input into the SAFmodule as shown in Figure 2. The PDM module consists of aFuzzy-logic based decision making process that generatesparallel collision avoidance decisions D i(k) with respect toeach Target vessel.

Finally the i th parallel decision of collision avoidance D i(k)will be forwarded from the PDM module to the SAF module.The main objective in the SAF module is to organize the


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parallel decision made by the PDM module into sequentialactions, course control A i(k) and speed control A vi(k),actions (see Figure 2), that will be executed on the Ownvessel navigation system. The formulation of the SAFmodule is the main objective in this study.

3. SEQUENTIAL ACTION FORMULATION MODULE

3.1 Navigational Decisions

The collision avoidance decision space of the oceannavigation can be categorized into course and speed controldecisions. Considering the Range (R i(k)), Bearing ( i(k)),Relative course ( i,o(k)) and Relative speed (V i,o(k)) of the i th Target vessel, the PDM module makes collision avoidancedecisions D i(k) regarding each Target vessel. Further detailsregarding the collision avoidance decisions of the navigationand PDM module can be found in Perera et al. (2010a) andPerera et al. (2010b). Since these multiple collision avoidancedecisions are formatted in parallel with respect to each Targetvessel, they cannot be implemented simultaneously by the

Own vessel. Hence, the Sequential Action FormulationModule (SAF) has been proposed to sequence these paralleldecisions.

3.2 Sequential Action Formation

An illustration of a sequential action space, formulated by thedecisions of course and speed changes, is presented in Figure3.

Fig. 3. Course and Speed change action space

The main objective in the SAF module, formulation of theparallel collision avoidance decisions into a sequentialactions, can be achieved by collecting the PDM modulemultiple collision avoidance decisions D i(k)(D i(k),DVi(k)) from the k

th time instant in respect to each Targetvessel, and arranging a sequential formation of actions A i(k) (A i(k), A Vi(k)) with respect to the action execution Time(T i (k),T Vi(k)). When course change action is starboardturn, then o > 0; when is port turn, o < 0. Similarly,when the speed change action is speed increase, then Vo >0, and when it is speed decrease, Vo < 0 as presented inFigure 3.

3.3 Bayesian Network

Figure 4 presents the structure of the continuous BayesianNetwork proposed for formulation and update of the parallelcollision avoidance decisions into the sequential actionexecution formation. As presented in the Figure, the Bayesiannetwork consists of four nodes: Collision Time Estimation,

Collision Risk, Action Delay and Collision AvoidanceActions. The Collision Decision D i(k) and Time untilCollision T i(k) that are the inputs to the Bayesian network that are originated from the PDM and CRA modules (seeFigure 2) respectively.

Fig. 4. Bayesian Network Structure for Collision Avoidance.

3.3.1 Collision Risk Functions

The Collision Risk node mainly consists of the Collision Risk Function (CRF). The CRF, i(k), of the Own vesselnavigation due to the i th Target vessel in the k th time instant isdefined as a Gaussian distribution i(k) ~ N ( i(k), i2(k)),where mean i(k) is considered as the Time until collisionT i(k). Hence the CRF mean i(k) can be written as:

(k)V

|(k)OA|(k)(k)T

oi,

iii == (1)

where |OA i(k)| is the Range and V i,o(k) is the relative speedof the i th Target vessel at the k th time instant. However it isassumed that the CRF, i(k), could be obtained from a noisyobservation of Z i(k),

)(k (k)(k)Z ziii += (2)

where zi(k) ~ N (0, z2(k)), is a white Gaussian observationnoise. Hence the prior distribution of the CRF due to the i th Target vessel at k th time instant can be written as a Gaussiandistribution:

( )

= (k)(k)(k)

21

i1

i

2i

2ii

e(k))P( , (3)

where 1 i is the normalization constant. The transition modelof the CRF is considered as a Gaussian perturbation of constant covariance 2 to the current state of the CRF andcan be written as:

( )

=2

2ii

1)(k (k)

21

i2

ii e1))(k |(k)P( , (4)

where 2 i is the normalization constant. The conditionalobservation model for collision risk is assumed to be a


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Gaussian distribution with a constant covariance z2 and canbe written as:

( )

=2

z

2ii

(k)(k)Z

21

i3

ii e(k))|(k)P(Z , (5)

where 3 i is the normalization constant. The one steppredicted distribution of the CRF can be written as:

( )

( )

( ) ( )

( )

+

+

=

=

=

=

1)(k

1)(k (k)21

i2

i1

i1)(k

1)(k 1)(k 1)(k (k)1)(k 21

i2

i1

i1)(k

1)(k 1)(k

21

i1

1)(k (k)

21

i2

ii

iii

2i

2

2ii

2i

2

2ii

2

2ii

2i

2i

2ii

2

2ii

e

1)(k de

1)(k de

e

1)(k 1))d (k P(

1))(k |(k)P( (k))P(

(6)

Considering the Bayesian Rule, the CRF update from theobservations can be written as:

( ) ( )

( )

( )

++

+

++

++

+

=

=

=

2z

2

2i

2z

2

2i

2

2z

2

2i

2zi

2

2ii

i

2 i

2

2ii

2z

2ii

1)(k

1)(k

1)(k

1) (k .1)(k (k)Z(k)

2

1

i3

i2

i1

1)(k

1)(k (k)

21

i2

i1

(k)(k)Z

21

i3

iiiii

e

ee

(k))(k))P( |(k)P(Z(k))Z|(k)P(

(7)

Hence the updated mean and covariance for the updated CRFcan be written as:

( )

( )2z

2

2i

2z

2

2i2

i

2z

2

2i

2zi

2

2ii

i

1)(k

1)(k (k)

1)(k 1) (k .1)(k (k)Z

(k)

+++

=

++++

=(8)

3.3.2 Collision Avoidance Action Function

The Own vessel Collision Avoidance Action Function(CAAF) is modelled as a Gaussian distribution, i(k) ~ N(i(k), i2(k)). The CAAF function with respect to the CRFcan be written as:

(k)(k)(k) iii += (9)

where i(k) ~ N ( , 2), is the time delay functionapproximated by a Gaussian distribution with constant mean and covariance 2. The conditional mean and covarianceof the CRF with respect to the CAAF can be written as:

( ) ( ) (k)

(k)|(k)E(k)(k)|(k)E

i

iiiii

+=+= (10)

( ) ( )( ) i

iii

(k)V

(k)|(k)V(k)|(k)V

=== (11)

The conditional CRF with respect to the CAAF can bewritten as:

( )( )

+ =

(k)(k)21

i3

ii

2

2ii

e)(k)|(k)P( , (12)

where 3 i is the normalization constant. The prior distributionof the CAAF due to the i th Target vessel at k th time instant, asa Gaussian distribution, can be written as:

( )

= (k) (k)(k)

21

i1

i

2i

2ii

e)(k)P( , (13)

where 1 i is the normalization constant. The transition modelof the CAAF is considered as a Gaussian perturbation withconstant covariance 2 to the current state of the CAAF andcan be written as:

( )

=2

2ii

1)-(k (k)21

i2

ii e1))-(k |(k)P( (14)

where2

i is the normalization constant. The one stepprediction of the CAAF can be written as:

( ) ( )

( ) ( )

( )

+

+

=

=

=

=

1)-(k

1)-(k (k)21

i2

i1

i1)-(k

1)-(k 1)-(k 1)-(k (k)1)-(k 21

i2

i1

i1)-(k

1)-(k 1)-(k 21

i2

1)-(k (k)21

i1

i1i1iii

2i

2

2ii

2i

2

2ii

22ii

2i

2i

2ii

2

2ii

e

1)-(k de

1)-(k dee

1)-(k d(k))P((k))|(k)P((k))P(

(15)

One can reorganize (15) as:

( ) ( )( )

+++

= 1)-(k 1)-(k (k)

21

i2

i1

i

2i

2

2ii

e(k))P( (16)

Considering the Bayesian rule, the CAAF update from theCRF can be written as:

( )( ) ( ) ( )( )

( ) ( ) ( )

( )

+++

++++++

+++

+

=

=

=

222i

222i

2

222i

2i

22ii

i

2i

2

2ii

2

2ii

)1k (

)1k (

)1k ()1k (.)1k ()k (

(k)

21

i3

i2

i1

1)-(k

1)-(k (k)21

i2

i1

(k)(k)21

i3

iiiii

e

ee

(k))(k))P(|(k)P( (k))|(k)P(

(17)

Hence, the updated mean and covariance for the updatedCAAF can be written as:

( ) ( )

( )2

22i

2

22i2

i

2

22i

2i

22ii

i

1)(k 1)(k

(k)

1)(k

1)(k .1)(k (k)(k)

+++

=

++

+++=

(18)


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Fig. 5. Avoidance of the 1 st Target Vessel

Fig. 6. Avoidance of the 2 nd Target Vessel

Fig. 7. Avoidance of the 3 rd Target Vessel

3.3.3 Implementation of CAAF

The implementation of the accumulated CAAF A i(k) can bedivided into two sections of Course Control (A i(k)) andSpeed Control (A Vi(k)) actions, as presented in Figure 3.However, the CAAF states are generated with respect to thecollision avoidance decision D i(k) from PDM module, of

Course Control (D i(k)) and Speed Control (D Vi(k))decisions. Hence, the accumulated Course and Speed ControlCAAF can be written as:

( )

( )(k)|(k)P(k)D(k)A

(k)|(k)P(k)D(k)A

ViViVi

n

1iV

iii

n

1i

=

=

=

= (19)

These functions are implemented on the computationalsimulations and the simulation results are presented infollowing section.

4. COMPUTATIONAL IMPLEMENTATION

A computational simulation for 4 vessels collision situation isused as an example for the analysis of this study. Aspresented in Figure 6, the Own vessel starts navigation at theorigin (0 (m), 0 (m)) and the Target vessels 1, 2 and 3 startfrom positions (6000 (m), -6000 (m)), (8800 (m), 10000 (m)),and (-13200 (m), 12000 (m)) respectively. It is assumed thatthe Target vessels are moving in constant speed and courseconditions and dont honour any navigational laws of the sea.The Bayesian network based CRF is presented in the x =-12000 (m) axis. The CAAF of course and speed controlactions are presented in x = -9000 (m) and x = -6000 (m) axisrespectively. Furthermore the scaled time axis (Actual Time 5 (s)) with respect to the CRF and CAAFs is presented inthe y axis.

The avoidance of the 1st

Target vessel is presented in Figure5. The CRF was detected and appropriate action was taken toavoid the Target vessel that was not honouring theCOLREGs rules and regulations. The same figure, shows theOwn vessel detecting the 2 nd target vessel, and presents theCRF and course and speed control actions of CAAFs. TheCAAFs are course to the starboard and speed reduction. Theavoidance of the 2 nd Target vessel is presented in Figure 6.Further the Own vessel detected the 3 rd Target vessel andcourse to port and speed reduction of CAAFs are presented inthe respective axis. Finally the avoidance of the 3 rd Targetvessel is presented in Figure 7. After executing the controlactions proposed in the previous section, the Own vessel iscrossing the Target vessel trajectory safely at the back of the

vessel.

5. CONCLUSIONS

This paper introduces a novel method to formulate theparallel decisions made by the Fuzzy-logic based system intosequential actions execution using a Bayesian network approach in a collisions avoidance system in oceannavigation. As presented in the results, the Bayesian network based action execution process could be used for complexnavigational conditions as well as complicated collision

situations. Further, this method is capable of avoidingmultiple vessels under various collision conditions in oceannavigation.


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ACKNOWLEDGEMENTS

This work has been made within the project Methodologyfor ships maneuverability tests with self-propelled models,which is being funded by the Portuguese Foundation forScience and Technology (Fundao para a Cincia eTecnologia) under contract PTDC/TRA/74332/2006. Theresearch work of the first author has been supported by aDoctoral Fellowship of the Portuguese Foundation forScience and Technology (Fundao para a Cincia eTecnologia) under contract SFRH/BD/46270/2008.

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