Detections of potential collision situations by relative motions of vessels under parameter...

8/4/2019 Detections of potential collision situations by relative motions of vessels under parameter uncertainties

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Sustainable Maritime Transportation and Exploitation of Sea Resources Rizzuto & Guedes Soares (eds) 2012 Taylor & Francis Group, London, ISBN 978-0-415-62081-9

Detections of potential collision situations by relative motionsof vessels under parameter uncertainties

Lokukaluge P. Perera & C. Guedes SoaresCentre for Marine Technology and Engineering (CENTEC), Instituto Superior Tcnico,Technical University of Lisbon, Lisbon, Portugal

ABSTRACT: The detection of potential collision situations by relative motions of vessels under param-eter uncertainties in vessel manoeuvring is presented in this study. The detection process consists of theobservations of the relative navigation trajectory and course-speed vector between two vessels. The pro-posed detection process is developed as a part of the intelligent navigation system that makes decisionsunder multi-vessel collision situations. A two vessel collision situation is considered and the extendedKalman filter algorithm is used in this study to estimate the relative navigational trajectory as well as therelative course-speed vector. Finally, prior and posterior collision/near-collision situations are simulatedand successful simulation results on the detection of potential collision situations are also presented inthis paper.

situations in maritime transportation. The proposedmethodology (i.e. detections of collision situations)is a part of the intelligent navigation system (INS)that is presented in Figure 1 and further describedin section 2.

1 INTRODUCTION

The detections of collision situations are impor-tant facilities of transportation systems to improvethe safety and security in navigation. However, col-lision situations could be simplified by assumingthat the targets are moving in straight line motions

and states/parameters conditions are deterministic.Even though, land and air transportation systemscould satisfy these assumptions, maritime trans-portation systems are often involved with maneu-vering trajectories and stochastic state/parametersituations under varying sea conditions.

Furthermore, the navigation constraints androuting schemes in maritime transportationhave enforced vessels to execute close quarternavigation, which increases the risk of collisions(Robson, 2006). Therefore, the detections of col-lision situations under maritime transportation

will be a complicated process that needs advancedtools and technologies.

This study proposes a methodology to detectcollision and near collision situations by esti-mating the relative navigation trajectory and therelative course-speed vector between two vessels.Furthermore, the vessels navigation under maneu-vering and stochastic states/parameter conditionsis considered. Even though, this study is limited toa two vessels collision situation, this concept canbe developed for a multi-vessel collision situationby accumulating multiple two vessel collision situ-

ations as proposed by Perera et al. (2011a).The estimated relative navigation trajectory andrelative course-speed vector can use as an evaluationmechanism prior to collisions or near collision Figure 1. Intelligent navigation system.


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1.1 Collision in maritime transportation

Human errors are still one of the major causes ofmaritime accidents (Guedes Soares & Teixeira,2001) and 7595% of marine accidents and cau-salities are caused by some types of human errors

(Rothblum et al., 2002, and Anto & GuedesSoares 2008) in accordance with the reported data.Therefore, as illustrated by e-navigation (eNAV2010), the accumulation of intelligent decisionmaking capabilities into navigational systems willlimit the human subjective factors in navigation,which can increase the safety and security of mari-time transportation.

The proposed e-navigation concept can beformulated as a collaborated network of trafficinformation among vessels and shore based sta-tions to improve safety and security in maritime

transportation. Furthermore, the e-navigation candecrease navigational errors, increase awareness ofvessel situations, improve traffic monitoring facili-ties, and reduce transportation costs. (Ward andLeighton, 2010).

1.2 Safety measures and risk assessments

The safety measures of maritime transportationwere influenced by several groups (Wang et al.,2006): ship designer, ship operators and maritimesocieties. The ship designers influence by safedesign of bridge layout, navigational equipments,

engine and steering control, maneuverability, andredundancy. The ship operators influence by safeoperation of ship speed, manning levels, crew atti-tude and training, and maintenance. The maritimesocieties influence by safe aiding and monitoringof vessel traffic systems, pilots, traffic lanes, aidsto navigation (i.e. AIS, GPS) and safety inspectionprocedures.

However, the effectiveness of maritime safetymeasures are eventually evaluated under rigorousnavigation and collision conditions with respectto the vessel operators decisions. Therefore, the

best onboard navigation tools (i.e. intelligent sys-tems and sensors) should be available to influencethe ship operation to make better decisions thatimprove the safety and security conditions withinmaritime transportation.

The analysis of vessel navigation informationwill help to detect collision situations and to assesscollision risk. The collision risk should be evalu-ated in real-time by vessels and/or Vessel TrafficMonitoring and Information Systems (VTMIS) inorder to guarantee safety and security measures inmaritime transportation. As illustrated by Imazu(2006), the mathematical formulation of collisiondetection between two vessels can be divided intwo methods: Closest Point Approach method(CPA) that is a two dimensional method (2D) and

Predicted Area of Danger method (PAD) that is athree dimensional method (3D).

The CPA method consists of calculating theshortest distance between two vessels and assess-ing the collision risk that could be predicted withrespect to each vessel domain. However, the CPAmethod alone cannot be implemented in the evalu-ation process of collision risk, since it does notconsider the vessel size, course and speed varia-tions. An extensive study of the CPA method withrespect to a two vessel collision situation is pre-sented by Kwik (1989).

The PAD method consists of modeling one ves-sel possible trajectories as an inverted cone andthe other vessel trajectory as an inverted cylinder,being the region of both object intersections cat-egorized into the Predicted Area of Danger. Bothvessels size, course and speed conditions could be

integrated into the geometry of the objects of navi-gational trajectories in this study.

However, both studies are limited to constantparameter conditions (i.e. fixed vessels speed andcourse conditions) that may not always be realis-tic in maritime transportation. Therefore, a novelmethod to detect potential collision situations withthe parameter uncertainties in maritime transpor-tation (i.e. variation in vessel speed and course con-ditions) is proposed in this study.

1.3 Collision risk assessment

This study formulates a methodology to detectpotential collision situations, while vessels aremaneuvering in close proximity. The proposeddetection process consists of the derivation of rela-tive navigation trajectory and course-speed vectorbetween two vessels that could use to evaluate priorcollision/near collision conditions.

Even though, in this study, the collision detec-tion process is derived with respect to a two vesselcollision situation that can be developed for a multi-vessel collisions situation by the accumulation of

two vessel collision situations. The proposed colli-sion detection process consists of following steps;the observation of both vessels positions; theestimation of both vessels velocities, accelerationsand navigational trajectories; the calculation ofthe vessel relative navigational trajectory and rela-tive course-speed vector of a selected vessel withrespect to other vessel.

In general, the vessel navigators monitor collisionsituations by observing the relative bearing of othervessels in open sea; the unchanged relative bearing ofa vessel could lead to a collision situation. However,this requirement alone could not predict accuratecollision conditions and should not be used in thedecision making process under complex navigationalconditions; that involve multiple vessels.


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Therefore, the observation of relative navigationtrajectory and relative course-speed vector of theother vessel could use to improve the detectionof collision situations. The relative navigationtrajectory could illustrate as a conventional bear-ing observation situation. However, the relativecourse-speed vector of the other vessel can be usedas an additional tool that could improve the colli-sion detection process.

It is assumed that both vessels positions aremeasured by conventional AIS and GPS systems.However, there are many challenges faced by thesystems during its position measurements: Thefirst, the AIS and GPS position signals can beassociated with sensor noise and/or system errors,therefore the measurements accuracy would becompromised. The second, the vessels are maneu-vering under varying sea conditions; the own and

target vessel kinematics and dynamics could beassociated with time-varying parameter condi-tions. Therefore, these conditions are identified asparameter uncertainties that have been illustratedin this study.

Hence, a proper mechanism to identify the ves-sel states (i.e. position, velocity and acceleration)is considered. The extended Kalman filter, one ofthe well known estimation algorithms, to overcomeprevious challenges and to estimate accurate ves-sel states is proposed. One should note that thestate estimation based only on both vessels posi-

tion measurements is another advantage in thisapproach.

The main contribution of this study can be sum-marized as the estimation of vessels relative navi-gation trajectory and course-speed vector based onparameter uncertainties in vessel maneuvering thatcan be used to detect potential collision situationsamong vessels. The organization of this paper is asfollows. Section 2 contains an overview of the INS.Section 3 contains the mathematical formulationof detection of collision situations. Computationalsimulations are presented in Section 4. Finally, the

conclusion is presented in section 5.

2 INTELLIGENT NAVIGATION SYSTEM

The proposed INS that is designed to accumulateintelligent e-navigation facilities into maritimetransportation is presented in Figure 1. As indi-cated in the figure, the system consists of threemain sub-systems: Vessel Monitoring & Informa-tion System (VMIS), Collision Avoidance Sys-tem (CAS), and Autonomous Navigation System(ANS).

The main objective of the VMIS is to facilitatethe INS by vessel traffic information that consistsof vessels position, course, speed, acceleration

and trajectory conditions. The system consistsof a scan sensor (i.e. Radar/Laser Sensor) andthree main modules: Vessel Detection & Tracking(VDT) Module, Vessel State Estimation and Tra-

jectory Prediction (VSETP) Module and Inter Ves-sel Communication (IVC) Module.

A Radar/Laser sensor is used as a target detec-tion unit in the VMIS. The VDT module consistsof an Artificial Neural Network (ANN) basedmulti-vessel detection and tracking process. Themain objective of the VDT module is to detect andto track vessels that are represented by clusters ofdata points that have been generated by the Radar/Laser sensor.

The VSETP module consists of an ExtendedKalman filter (EKF) based vessel state estimator(i.e. position, velocity and acceleration) and navi-gational trajectory prediction process. This process

is executed by information given by the VDT mod-ule. Furthermore, each vessel state conditions (i.e.position, course, speed, etc.) will transfer from theIVC module to the respective vessel OVC modulethrough a wireless network.

The proposed CAS is presented in Figure 1. Themain objective of the CAS module is to generalcollision avoidance decisions/actions in a sequen-tial format that could be executed during vesselnavigation. As presented in the figure, the CASconsists of the following modules: Own VesselCommunication (OVC) Module, Parallel Decision

Making (PDM) Module, Sequential Action For-mation (SAF) module, and Collision Risk Assess-ment (CRS) Module.

The OVC module is the communication unitbetween the vessel and the VMIS as mentionedpreviously. The PDM module consists of a Fuzzylogic based decision making process that gener-ates parallel collision avoidance decisions withrespect to each vessel that is under collision risk.The inputs to the PDM module are the range,bearing, relative course and relative speed of theother vessel. The outputs from the PDM mod-

ule are course and speed change decisions of thevessel. The inputs and outputs are formulated asfuzzy membership functions. The Convention onthe International Regulations for Preventing Colli-sions at Sea (COLREGs) rules and regulations andexpert navigational knowledge are considered forthe devolvement of Fuzzy rules.

The main objective of the CRA module is toevaluate the collision risk and the expected timeuntil collision of each target vessel with respectto vessel navigation. The tools developed in thisstudy, the relative navigation trajectories and thecourse-speed vectors, will use in the CRA moduleto improve the system capabilities.

Furthermore, the CRA module will transfercollision risk information to the SAF module for


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collision avoidance actions. The main objective ofthe SAF module is to organize the parallel decisionsthat were formulated by the PDM module intosequential actions, considering the time until col-lisions that were formulated by the CRA module.Furthermore, these actions will be executed on ves-sel navigation.

Finally, the collision avoidance actions formu-lated by the SAF module will be transferred intothe ANS. These actions are further divided intotwo categories of course and speed controls thatwill implement on vessel navigation.

The main objective of the ANS is to control thevessel course and speed conditions with respect tocollision situations. The proposed ANS is associ-ated with a decentralized control approach wherethe two control sub-systems are introduced: Steer-ing Control Sub-system (SCS), and Speed Control

Sub-system (SPS). The main objective of the SCSis to control the vessel course conditions. The mainobjective of the SPS is to control the vessel speedconditions. Therefore, the proposed INS is capableof handling multi-vessel collision situations undercomplex collision conditions. Further details onthe INS can be found on Perera et al. (2010a,b,2011a,b).

3 DETECTIONS OF COLLISIONSITUATIONS

The mathematical formulation of detection ofcollision situations is presented in this section.Therefore, the section is divided into three sec-tions of derivation of system model, formulationof measurement model and Extended Kalmanfilter. In the system model section, a mathemati-cal model for a two vessel collision situation isderived. In the measurement model section, theobservations of available vessel states are formu-lated. In the extended Kalman filter section, theprocedure for the estimation of relative vessel

navigation trajectory and course-speed vector ispresented.

3.1 Two vessel collision situation

A two vessel collision situation is presented inFigure 2. The own vessel, the vessel that is equippedwith the INS, is located in point O (xo,yo). The tar-get vessel, the vessel that needs to be avoided, islocated at point A (xa, ya). The own vessel speedand course conditions are represented by Vo and

o

respectively. The target vessel speed and courseconditions are represented by Va and a respec-tively. The own and target vessels instantaneousradius of curvature of maneuvering are presented

by Ro and Ra. The x andy velocity components ofthe own and target vessels are presented by vxo, vyo,vxa and vya respectively. The own and target vesselsnormal and tangential acceleration componentsare presented by ano, ato, ana and ata respectively.The collision encounter angle between vessels ispresented by a.

To capture the maneuvering conditions in both

vessels a suitable mathematical model is consid-ered. The continuous-time curvilinear motionmodel that could be formulated for ocean vesselnavigation is illustrated in this study. The standardcontinuous-time curvilinear motion model for theown vessel can be written as:

(1)

The standard continuous-time curvilinear

motion model for the target vessel can bewritten as:

(2)

To avoid trigonometrical angle conditions, thefollowing functions are proposed:

fv

v v

v

v v

f

vy yo

yo

vxoo

xo

yo

vya

==;=2 2

v

v v

v

v v

ya

a ya

vxa xa

xa ya2 2 2 2

; =

Figure 2. Two vessel collision situation.


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3.2 System model

The own and target vessels continuous-timecurvilinear motion models presented in Equations(1) and (2) can be summarized into a system modeland that can be written as:

(3)

where the system states, x, and the system func-tion,f(x), can be further illustrated as:

x

o

y

vxo

vyoato

ano

x

ya

vxa

vya

ta

na

=

= f x)

vxo

vyo

ato

v o ano

fvyo

ato

vyno

vx

vxa

vya

ata

vxa ana

vy

ata

vya

0

0

anf vxa

0

0

where wx is white Gaussian process noise with 0mean and Q covariance. The covariance, Q, can befurther written as:

Q diag Q Q Q

Q Q Q

vx ato ano

vx vy

a naQata

where Qxo, Qyo, Qvxo, Qvyo, Qato, Qano, Qxa, Qya, Qvxa,

Qvya, Qata and Qana are respective system state cov-ariance values. Furthermore, the own and targetvessels tangential and normal acceleration compo-nents are presented by ato, ano, ata, and ana respec-tively. The respective acceleration derivates can bewritten as:

where wato, wano, wata and wnta are derivates oftangential and normal accelerations of the ownand target vessels that are formulated as whiteGaussian distributions with 0 mean and Qato,Qano, Qata, and Qana respective covariance values.

The Jacobian of the system function,f(x), can bewritten as:

( )( ) =x

f

a f a f a f axvxo

xvyo

yovxo

n

0 0 1 0 0

0 0 0 1 0

0 0 vxo vy

xovyo vxo v o

y

v ovyo f

a fo v fno v++ a0 0 oovxo vxof

0

0

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 00

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 a fxav axx

xvya

yavxa

yavya vya

xavya

na a v a fna fvxa

a fta v

+0 0 ann ta nav a vxf avxa f av fv a f

0 0 0 0 0 0

0 0 0 0 0 0

where the respective functions are derived as:

fv

v v

v v

v v

f

xovxo yo

yo

vxo xo

yo

=( )

= 2

2 23 2

,o

xovy xo yo

yo

vy xo

yo

v v

v v

v

v v

( )=

2 23

2

2yo2

f

v

v

v v

v v

f

xavxaya

ya

vxaxa

ya

= ( ) = 2

2 23 2 ,

xavya ya

ya

vya a

ya

v v

v v

v

v v

= ( )

=2 2

2

2ya2 3

3.3 Measurement model

The measurement model is formulated to meas-ure the own and target vessel actual positions.The position measurements in discrete-time areconsidered due to the availability of own andtarget vessels positions in discrete time instants.It is assumed that the correlations between vesselposition measurements are negligible. The own and


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target vessels position measurement model can bewritten as:

z wz)k ( )kx (4)

where the system states, z(k), and the function,h(x(k)), can be further illustrated as:

z z z z

x k

x

y k

xo yo xa ya

T)k ;

( ))

)k

(k (k (k ( )k

=))

)

)y (

where zxo(k), zyo(k), zxa(k) and zya(k) are the own

and target vessel x and y position measurementsrespectively, and wz(k) is white Gaussian measure-ment noise with 0 mean and covariance R(k). Thecovariance, R(k), can be further illustrated as:

R iag R k Ro yo)k k ) )kR k Rxa a

where Rxo(k), Ryo(k), Rxa(k), and Rya(k) are presentedby the respective system measurement covariancevalues. The Jacobian matrix of the measurementfunction, h(z(k)), can be written as:

(h

1 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 00

3.4 Extended kalman filter

The Kalman filter is a well known estimationalgorithm. However, the Kalman Filter (KF) gen-eral algorithm is limited for application of linear

systems; therefore the Extended Kalman Filter(EKF) is considered as a standard technique thatcould be used for a number of non-linear estima-tion applications. The Extended Kalman filter isproposed in this study as the estimation algorithmfor the own and target vessels states (i.e. position,velocity and acceleration). The estimated vesselstates are used to calculate the relative navigationtrajectory and course-speed vector of the targetvessels.

In general, the own and target vessel positionsare measured as noisy position values; therefore,the estimation algorithm is used to increase theposition accuracy. In some situations, the own ves-sel acceleration conditions can also be measuredand can be used to improve the state estimation.

However, this study is limited to the vessel positionsmeasurements. The EKF algorithm (Gelb et al.,2000) can be summarized as:

System Model

x w

E E

x

,

)t ( )tt= xwx t ]w ;wx x(t )t = [ ]Q )t

(5)

Measurement Model

z w , k , ..

E E

z

,

)k (k= x

wz k ]w ;wz (k )k =2

[ ]RR )k(6)

Error Conditions

(7)

where x )t is the state error vector and is theestimated states of the system. System Initial States

(8)

where P(0) is the state initial covariance, describingthe uncertainty present on the initial estimates. Other Conditions

E t,f r all kt (wz (9)

State Estimation Propagation

(10)

Error Covariance Extrapolation

(11)

where P(k) is the estimated error covariance with

P iag P P P P

P P P P

)k )k )k k )k

)k )k )k

=

ay

P P P P

( )

k )k )k )k

where Px

(k), Pvx

(k), Py

(k), Pvy

(k), Pat

(k) and Pan

(k)are respective estimated state error covariancevalues. State Estimate Update


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When the measurement data is available fromthe sensors, the system state can be estimated as:

(12)

where x(k) and x(k+) are the prior and posteriorestimated system states respectively, and K(k) is theKalman gain.

Error Covariance Update

(13)

where P(k) and P(k+) are the prior and posteriorerror covariance values of the system respectively.

Kalman Filter Gain

(14)

3.5 Relative trajectory and course-speed vector

The relative trajectory of the target vessel can becalculated by the target vessels relative x and ypositions that can be written as:

(15)

(16)

where and are estimated relative x and ypositions of the target vessel. The relative course-speed vector of target vessel is calculated by therelative x and y velocity components and can bewritten as:

(17)

(18)

where and represent the estimated x and

y relative velocity components of target vesselrespectively. Hence, the target vessels estimatedx and y relative velocity components can beused for the calculations of relative course-speedvector.

4 COMPUTATIONAL SIMULATIONS

A computational simulation of a two vessel nearcollision situation is presented in Figure 3. The topplot of Figure 3 represents the own and target ves-sels actual (Act.), measured (Mea.) and estimated(Est.) navigation trajectories. The vessel positionmeasurements are generated by adding sensornoise into the actual trajectory. As presented in the

figure, a near collision situation can be observed.A zoomed view of the same trajectories nearthe collision point is presented in the top plot ofFigure 4. The zoomed view of the relative trajec-tory of the same situation is presented in the bot-tom plot of Figure 4.

One should note that the intersection of the twotrajectories will not necessarily represent a col-lision point because each vessel can pass the col-lision point in different time intervals. However,this confusion can be clarified by the observationof the relative navigational trajectories; where therelative trajectory of target vessel propagation nearthe own vessel initial position should be in a nearcollision situation. These conditions are furtherillustrated in Figures 3 and 4.

Considering the respective zoomed view nearthe own vessel position in the bottom plot of

Figure 4, each estimated position of the targetvessel consists of the relative course-speed vector

Figure 3. Two vessels near collision situation.

Figure 4. Two vessels collision situation (zoomed view).


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that is presented by an arrow and estimated by theextended Kalman filter. This representation is animportant factor in the detection of collision con-ditions even under near collision situations.

The own and target vessels velocity and rela-tive velocity components that are estimated by theEKF are presented on Figure 5. The own and tar-get vessels acceleration components that are alsoestimated by the EKF are presented in Figure 6.These estimated states can be further used for thedecision making process of collision avoidanceamong vessels.

This detection of collision situation is furtherelaborated in Figure 7, where a prior collision situ-ation is presented. The navigational trajectoriesof both vessels are presented in the top plot ofFigure 7.

The zoomed view of the prior collision situation

is presented in the bottom plot of Figure 7.As presented in the plot, the target vessel relativetrajectory is heading towards the own vessel initialposition with course-speed vectors that are pointedtowards the own vessel. Therefore, the target vesselrelative navigational trajectory and course-speedvectors can be used for prior collision situationsin order to detect the collision risk as proposed inthis study.

5 CONCLUSION

A methodology for detection of collision situationsthat is based on uncertain parameters in vesselmaneuvering is presented in this study. As presentedin the simulations, the target vessels relative tra-

jectory as well as the relative course-speed vectorcould be used for the assessment of prior collisionsituations. The proposed collision detection proc-ess will be used on the INS that is previouslydescribed in this paper.Figure 5. Velocity estimation.

Figure 6. Acceleration estimation.

Figure 7. Two vessel prior collision situation.


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ACKNOWLEDGEMENTS

The first author has been supported by the Doc-toral Fellowship of the Portuguese Foundationfor Science and Technology (Fundao para aCincia e a Tecnologia) under contract n. SFRH/BD/46270/2008. Furthermore, this work contrib-utes to the project on the Methodology for shipsmanoeuvrability tests with self-propelled models,which is being funded by the Portuguese Founda-tion for Science and Technology under contract n.PTDC/TRA /74332/2006.

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