591
1 INTRODUCTION
The continuous increase in the density of marine
trafficmakesitnecessarytosearchfornewsolutions
improving the safety aspect of maritime
transportation. These solutions, among others,
include various methods and tools dedicated to
collision avoidance. They range from optimal ship
control (Lisowski 2013, Lisowski 2014) through ship
tra
jectory planning (Lazarowska 2015, Lazarowska
2016) to determining and visualizing safe
manoeuvres,whichisaddressedintheherebypaper.
The long‐lasting development of marine radars
andassociatedAutomaticRadarPlottingAid(ARPA)
followedbytheintroductionandmassapplicationof
AutomaticIdentificationSystems(AIS)madeiteasier
to make navigational decisions concerning evasive
manoeuvres. Integration of those two technologies
with ElectronicNavigational Cha
rts (ENC) (Weintrit
2009)resultedinanewgenerationofdisplays,which
cannow offer consolidatednavigationalinformation
on a single screen. A proposal of such a display is
presented here. It is based on a Collision Threat
ParametersArea(CTPA)techniqueofpresentingship
motion parameters and result
ing collision risk
graphically. This is supplemented with other
information, including risk of grounding and
compliancewithCOLREGS.Finally,thenewversion
of the method presented here utilizes a heuristic
manoeuvre selection algorithm to offer an explicit
manoeuvre recommendation. Owing to thi
s,
navigator’s decisions in collision situations can be
madeeasierandfaster.
Thefollowingsectionsareorganizedasfollows.In
Section 2 a brief history of the research in this field
andrelatedliteraturesummaryisprovided.Section3
presentsanoverviewoftheCTPA‐baseddisplayand
briefly recalls it
s version given in (Szlapczynski &
Szlapczynska, 2017). Then Section4 describes the
newlyproposedmethodofautomaticsafemanoeuvre
selection in the display. Section 5 presents some
examples of usage for the updated display. The last
Section 6 summarizes and concludes the presented
material.
Heuristic Method of Safe Manoeuvre Selection Based
on Collision Threat Parameters Areas
J
.Szlapczynska
GdyniaMaritimeUniversity,Gdynia,Poland
R.Szlapczynski
GdanskUniversityofTechnology,Gdansk,Poland
ABSTRACT: This paper is a continuation of papers dedicated to a radar‐based CTPA (Collision Threat
ParametersArea)displaydesignedtosupportsafemanoeuvreselection.Thedisplayvisualizesalltheshipsin
anencounterandpresentssituationaloverviewfromtheownship’spointofview.Itcalculatesanddisplays
informat
iononunsafeorunrealisticownship’scourse&speedallowingausertoselectasafemanoeuvre.So
faronlythemanualselectionwaspossible, thusthepaperaimsatpresentingaheuristicapproachtowardsthe
manoeuvreselectionwhenusingthedisplay.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 4
December 2017
DOI:10.12716/1001.11.04.03
592
2 LITERATUREOVERVIEW
The first displays designed especially for marine
radar applications were available already in 1960s
(Birtley 1965). They were restricted though to
displayingrawdataoftargets’velocityvectorsonly.
Almost a decade later two new radar display
approaches appeared, namely Potential Points of
Collision (PPC) and Predicted
Areas of Danger
(PAD).InPPCandPADdangerpointsweremarked
thatiftheownshipshouldsteertowardsanyofthese
points a collision would occur. The idea of how to
buildsuchareaswaschangingwithtime.Theywere
initiallycircles(Riggs1973),laterellipses(Fleischeret
al.1973),irregularshapes(O’Sullivan1982,Zhao‐lin
1988), polygons (Hakoyama et al. 1996) and curves
(Wood et al. 2002). Quite different approach was
presented in (Lenart 1983) where a Collision Threat
ParametersArea (CTPA) has beendefined. For each
target CTPA is as an area where the tip of the
own
velocityvectorshouldnotbeplaced,becauseitwould
cause violating the safe distance between the ships.
This approach was later continued in Qiao and
Pedersen(2004)andQiaoetal.(2006)ascone‐shaped
CollisionDangerSectors(CDS)andCollisionDanger
Lines(CDL).
An extended CTPA version presented
in (Lenart
1999)hasinspiredoneoftheauthorsofthispaperto
designing a new display focused on presenting safe
manoeuvring possibilities and introducing a ship
domain instead of the safe distance (Szlapczynski
2008).Sincethen the displayhas beensignificantly
expanded:firstin(Szlapczynski&Szlapczynska2015)
itsversion
withgoodandrestrictedvisibilitysupport,
acceleratedlook‐aheadmodeandtime‐basedfiltering
waspresented.Thenin(Szlapczynski&Szlapczynska
2017) the display was further extended by
introducing analytical support for ship domains
(which seriously accelerated its performance) and
restricted waters support (via uploading and
presenting information about shoal
waters and land
obstacles).Sincesofarthedisplayhadnomethodfor
safe manoeuvre selection, this paper aims at filling
thisgap.
3 ANOVERVIEWOFCTPA‐BASEDTARGET
INFORMATIONDISPLAY
The CTPA‐based radar display offers a situational
viewfromtheown‐ship(OS)standpoint.Itassumes
that for
all the target ships (TSs) in range of the
displaytheircurrentcourseandspeedisknown.The
OSislocatedinthecentreofthedisplaywithherbow
up (however, her true course doesn’t have to be
North‐oriented, it is merely a visualization
assumption). The Cartesian coordinate
system, with
OS located in its origin, presents points as ship
position(x, y, inNm)and ship speed(V
x,Vy, inkn)
coupledbyτvalueasgivenbelow:
,
,
x
y
xV
yV
(1)
whereτisaconstantvalueoftime(inhours),utilized
to calibrate the display. The range of available ship
speedva luesissetconstantinthedisplay,thuswhen
increasingtheτvaluethemoredistanttargetsarein
view.
Intheoriginalmethodin(Lenart1983)and
(Lenart
1999) the CTPAs were cone‐shaped areas, each area
assignedtoonetargetinanencounter,withitsshape
and location dependent on target’s relative
parameters (position & course) and the configured
safe distance. Here, in the display being described,
presentedinFigure1,theCTPAsaredeterminedby
taking
intoaccountelliptically‐shapeddomainwitha
ship position offset. It is possible by utilizationof a
Degree of Domain Violation (DDV), a risk‐related
parameter introduced in (Szlapczynski &
Szlapczynska2015)as:
min
max 1 ,0DDV f (2)
where f
min is a scale factor of the largest domain‐
shapedarea (aroundOS)that is free from the target
ships.
Figure1. The CTPA‐based target information display – a
sampleview
The display as in Fig.1 offers much more
informationthanjustCTPAs. Based on thecoloured
areaspresentedinthedisplay’sviewtheuserisable
toselectasafemanoeuvrefortheOS. Asdepictedin
the legend of Fig. 1 there are the following colour
codes:
yellow: possible
groundings, provided OS speed
and course would be kept within a fixed time
horizon(configuredbytheusere.g.for1hour),
red: OS domain violations by any TS in the
encounter, determined (for the assumed elliptic
domain with OS position offset) by the DDV
valuesin[0.0;0.5]
range(lightred)orforserious
domainpenetrationbytheTS(possiblyleadingto
acrash)withDDVin[0.5;1.0]range(darkred),
light blue: OS speed and course, when kept,
resulting in violation of one or more COLREG
rules,
white:safepairsofOSspeedandcourse.
Another colour coding (dark blue) for maximal
and minimal OS speed, previously presented in
(Szlapczynski & Szlapczynska 2017), has not been
appliedinthispaperinordertoimproveitsclarity.
Eachpointinthedisplaycanbeconsideredasin
the polar coordinate system with OS true speed
represented
by its radial coordinate and OS course,
593
relativetohertruecourse,representedbyitsangular
coordinate (measured clockwise from the North). In
ordertoinvestigatecurrentOSstatustheusershould
lookatthetipofhertruespeedvector(inblue).Here
inFig.1thetipislocatedintheborderbetweenlight
and
dark red areas indicating quite serious domain
violation, providing current OS course and speed
wouldbekept.Thus, to avoidcollision withthe TS,
manoeuvringisstronglyrecommended.Tofindasafe
OSmanoeuvreitisenoughtomovethetipofhertrue
speed (which obviously assumes some OS
manoeuvring) to any white point in the display (as
white depicts safe OS speed and course).In Fig.1
there are roughly two possibilities for OS: to turn
starboard for 15‐18° or to divert her course (turn
starboard for 165‐180°). The user would probably
selectthestarboard15°turn
withkeepingspeed,since
it’s the easiest while technically and economically
reasonablemanoeuvre,inthiscaseassuringcollision
avoidancewiththeTSintheencounter.
The display provides also an additional
“accelerated look‐ahead” mode in which the user is
able to simulate future (for a configured time)
encountersituation,
assumingthatalltheshipskeep
theircoursesandspeeds.Thiswaytheuserisableto
determineafterwhattimepastthecollisionavoidance
manoeuvreheisabletosafelygetbacktotheoriginal
track.
Uptothistimeitwasassumedthattheprocessof
safe manoeuvre selection
would be manual, as
presented in (Szlapczynski 2008), (Szlapczynski &
Szlapczynska 2015) and (Szlapczynski &
Szlapczynska 2017). However, in orderto improve
the display and increase safety level of the ships
utilizingthesolutioninfuture,theauthorsdecidedto
introduce an automatic safe manoeuvre selection
method,describedinthe
nextsection.
4 PROPOSEDSAFEMANOEUVRESELECTIONIN
THEDISPLAY
Anactionof selecting safe manoeuvreinthe CTPA‐
baseddisplay is a processof selectinga safe pairof
OSspeed and course thewaythat the tip of theOS
truespeedvectorwouldbeplacedinthewhite
(safe)
display area. In order to automate this action the
followingpoliciesareapplied:
1 selectinga“keepspeed”manoeuvre:thelengthof
the true speed vector would not change, only
rotationofthevectorispossible,
2 selectinga“keepcourse”manoeuvre:thevector’s
angular coordinate would not change,
but vector
lengthcouldincreaseordecrease,
3 selecting a mixed manoeuvre, in which
simultaneoustruespeedvectorlengthandangular
coordinate(rotation)changesarerequired.
Each of the abovementioned policies has slightly
different limitations. In the first “keep speed”
approachtherotationshouldbebigenoughtomake
the manoeuvre
apparent, thus rotations below 15°
would not be possible. Obviously, the lesser the
rotationabove15°,thebetter,thustherotationangle
would be minimized in the given range. Moreover,
due to COLREGS implications rotations to the right
(starboard)willbefavouredoverrotationstotheleft
(portboard)for
encountersotherthanovertaking.
The “keep course” approach assumes that the
vectorlengthisamendedandthefinalvectorcannot
be longer than the maximal and shorter than the
minimal possible OS speed (if applied). Similarly to
the previous case, the change should be minimized
withinpossibleOSspeedlimits.
The
last mixed approach would be applied to
situationswhenno“keepcourse”or“keepspeed”is
possible(incaseswhenwhiteareasareirregular,far
from the current OS speed circle and current OS
course direction). In such situations it is difficult to
determine which manoeuvre is better: is it
well‐
foundedtohaveabiggerrotationanda slightspeed
change or the opposite. To solve such problems
Pareto‐optimality technique has been introduced. A
similar approach has already been applied to a
differentnavigationalproblemse.g.in(Szlapczynska
2015).
Pareto‐dominanceisanunderlyingelementofthe
Pareto‐optimality
concept. It is stated that an
elementAPareto‐dominatesanotherelementBifand
only if A is no worse than B for all the considered
criteriaexceptatleastonecriterion,forwhichAhas
tobebetterthanB.Incaseofthemanoeuvreselection
in the
mixed approach one manoeuvre dominates
another if either it requires a smaller course change
and exactly the same speed change or it requires a
smaller speed change and exactly the same course
change. Thus a manoeuvre of 20° to starboard and
increasethespeedof5knwilldominateamanoeuvre
of
22° to starboard and 5kn increase, but will not
dominate another one of 18° to starboard and 6kn
increase. All the search space elements that are not
dominated by any other element of the same space
are called non‐dominated and constitute a set of
Pareto‐optimalsolutions.
The precise
rules of dominance used here for
selectingaPareto‐optimalsetareasfollows.
Forcrossingorheadonencounters:
1 Asolution, whosecourse alteration is15 degrees
and speed alterationis 0knots dominates all
solutionswhosespeedalterationsarelargerthan0
knots.
2 Asolution,whosecourse
alterationislarger than
15 degrees and speed alterationis 0 knots
dominates:
allsolutionsoflargercoursealterations,
all solutions of equal course alterations and
speedalterationslargerthan0knots.
3 A solution, whose speed alterationis larger
than 0 knots dominates all solutions where
alteration
of one parameter (course or speed) is
largerandalterationof theother oneis larger or
equal.
Forovertakingencounters:
1 Asolution, whosecourse alteration is15 degrees
and speed alterationis 0knots dominates all
solutions, whose speed alteration are larger than
0knots and course alterations are
in the same
direction.
2 Asolution,whosecoursealterationis largerthan
15 degrees and speed alterationis 0knots
dominates:
594
allsolutions of larger coursealterations inthe
samedirection,
all solutions of equal course alterations in the
same direction and speed alterations larger
than0knots.
3 A solution, whose speed alterationis larger
than0knotsdominatesallsolutionswhere:
alterationofcourseisin
thesamedirectionand
alterationofoneparameter(courseorspeed)is
largerandalteration of the other one is larger
orequal.
Following the abovementioned dominance
analysis,Paretosetinadiscretizedmanoeuvrespace
ispresentedwitharesolutionof1degreeand1knot.
Anexampleof
suchaPareto‐optimalsetisshownin
Figure2,whereallnon‐dominatedsolutions(Pareto‐
optimal) are marked as green dots. Optionally,
additionalrulesandarankingmethodmaybe used
to further estimate and compare the quality of
solutionswithinaParetoset.
Figure2. Pareto‐optimal solutions for a close quarters
overtakingencounter
5 USAGEEXAMPLES
Inthissectiontwoscenarios–overtakingatargetand
crossing encounter with a target – are described in
detail.Inbothcasestheownshipisapproachingtwo
targetsandanencounterwouldleadtoacollisionin
lack of a safe manoeuvre. Both scenarios emphasize
how
difficult it might be to choose this manoeuvre
basedonships’motionparametersonly.Fortunately
theprovideddisplayviewmakesiteasytochoosea
safe solution. Additionally the “accelerated look
ahead” mode visualizes the consequences of a
manoeuvre – future motion parameters of all ships
involvedintheencounter.
5.1 Scenario1–overtaking
InthisscenariotheOSisapproachingatarget(TS1)
navigating in roughly the same direction, but at a
muchlowerspeed.Overtaking is the solesituation
where both manoeuvres to port and starboard are
compliantwith COLREGS. Becauseof the proximity
oflandmasson
starboardandanadditionaltargeton
port (TS 2) it may be difficult at first to choose a
manoeuvrebasedontheoverviewshowninFigure3.
However the situation gets clearer when looking at
Figure 4, where the display view is shown with the
two non‐dominated Pareto‐optimal
solutions shown
as green dots. As can be seen, it is possible to
manoeuvre to port by altering own course by 15
degrees.Asformanoeuvringtostarboard,however,it
wouldrequireadditionalspeedreductionbyatleast4
knots. Also, as shown in Figure 5, 50minutes after
manoeuvring to
starboard combined with speed
reductionthe own shipshould planturning back to
port by at least 20 degrees so as to avoid running
aground.As opposed to that, in Figure 6 the
consequences of manoeuvring to port are more
convenient:theownshipcankeepthenewcoursefor
aslongasittakesbeforegettingbacktotheoldone.
Figure3.Scenario1(overtaking)–overview
Figure4.Scenario1(overtaking)–displaymainview
595
Figure5.Scenario1(overtaking)–“acceleratedlookahead”
mode – 50 minutes after manoeuvring to starboard by 15
degreesandreducingownspeedby4knots
Figure6.Scenario1(overtaking)–“acceleratedlookahead”
mode–40minutesaftermanoeuvringtoportby15degrees
5.2 Scenario2‐crossing
InthisscenariotheOSisabouttomeettwotargetson
starboard (Figure 7). The encounter with the TS 2
would lead to collision in lack of manoeuvres, so
some action of the OS is necessary. Possible
manoeuvresoftheOSarelimitedbythelandmasson
starboard, so it is not sure whether such a turn
(compliantwithCOLREGS)isindeedsafe.However,
a look at the display main view (Figure 8) indicates
thatanumberofmanoeuvrestostarboard(markedas
green dots) are possible. The OS may either simply
turn to starboard by 20
degrees or may combine a
slightly lesser course alteration with a minor speed
reduction. Of these possibilities, the manoeuvre of
coursealterationaloneisthebestsolutionintermsof
executionandeconomics.Itsconsequencesareshown
in Figure 9 as “accelerated look ahead” mode. 32
minutesaftermanoeuvringtostarboard
by20degrees
theownshipispassingasternoftheclosesttargetand
neitheroftheships’domainsisviolated.
Figure7.Scenario2(crossing)–overview
Figure8.Scenario2(crossing)–displaymainview
Figure9. Scenario 2 (crossing) – “accelerated look ahead”
mode – 32 minutes after manoeuvring to starboard by 20
degrees
6 SUMMARY
The paper describes an extended version of the
previously introduced method of visualizing safe
manoeuvres in complex encounter situations. The
new element is an algorithm, which utilizes
information on all safe manoeuvres and specified
criteriatodetermineasetofPareto‐optimalsolutions.
Once this set is determined, additional
user
preferences may be applied to limit the proposed
solutions to one or two recommended manoeuvres,
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whicharegraphicallyhighlightedinthedisplay.The
practicalusageofthepresentedversionofthemethod
is illustrated by two examples, where possible
manoeuvresandtheirconsequencesareanalysed.The
research on the method is ongoing and the future
researchwillbefocusedontakingintoaccountrough
weather
conditions, when possible manoeuvres are
seriouslylimitedduetotheriskoflosingstability.
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