625
1 INTRODUCTION
Duetotheincreaseinthenumber,size,andspeedof
ships,theproblemofcollisionavoidanceisbecoming
more complicated. Despite the measures taken,
including development of Collision Avoidance
SupportSystem(CASS),thisproblemisurgent. One
of the ways to solve this problem is to improve
information support for decisions, including the
development of recommendations for and mapping
the zones of acceptable values of manoeuvre
parameters, and a number of other elements. Such
mappingmakesiteasierfortheoperatortoevaluate
thesystemʹsrecommendationstoavoidcollisionand
tocorrectthem.
In the paper
[10], indicators of dangerous course
and velocity areas are presented to determine
effective actions in one of onboard CASS. In the
Visualization‐basedCASS[9],evasivemanoeuvresare
selected according to the diagram of own ship
velocityvectors,safefortargetspassing.Thismethod
is called Velocity Obstacle (VO) [2]. The
paper [8]
highlights an algorithm that allows, using the VO
method,tofindCOLREG‐compliantmanoeuvres.The
creationofvisualaidsisalsoenvisagedinadditionto
the definition of recommendations by the methods
‘ArtificialPotentialField’[5],‘DynamicWindow’[1],
‘ModelPredictiveControl’[7],andothers[3,6,12,
13].
In the paper [13], the search for the optimalevasive
manoeuvre in terms of sailing time loss is based on
theenumerationmethod,andtablesareproposedthat
makeiteasierfortheoperatortoevaluateandcorrect
thefoundoption.Thecomplexesofgraphicelements
to facilitate the adoption
of anti‐collision decisions
developed still have drawbacks,and the questionof
theirimprovementisurgent.
Theobjectiveofthepaperistodevelopgraphical
tools to facilitate the selection, evaluation and
Graphical Tools to Facilitate the Selection of
Manoeuvres to Avoid Collision
L.L.Vagushchenko
1
&A.A.Vagushchenko
2
1
NationalUniversity“OdessaMaritimeAcademy”,Odessa,Ukraine
2
BSMCrewServiceCentre,Odessa,Ukraine
ABSTRACT:Graphicaltoolshavebeenproposedtofacilitatetheselection,evaluation,andcorrectionofanti‐
collision actions in situations with moving and stationary obstacles, assuming that such situations are not
extreme or ordinary with sailing vessels and that the target movement parameters are constant
or their
upcomingchangeisknown.ThechoiceofevasivecombinedZ‐manoeuvre(bothcourseandspeedchangeat
onepointandreturntotheoriginalvaluesoftheseparametersatanotherpoint)andonecombinedaction(both
course and speed alteration at the selected point) were considered. The graphical tools
developed contain
diagrams,showingeightzonesofactions,andspecialmarksoftargetsatthemomentoftheirclosestapproach
to the own ship. In view of the COLREG and good seamanship, these zones were arranged in order of
application priority. The results of the enumeration of a representative discrete
set of possible manoeuvre
variantswereusedtoconstructthediagrams.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 17
Number 3
September 2023
DOI:10.12716/1001.17.03.14
626
correctionofcombinedZ‐manoeuvre(CZM)andone
combinedaction(OCA)insituationwithmovingand
stationary obstacles, assuming that such situation is
not extreme, the target movement parameters are
constantortheirupcomingchangeisknown.
The following abbreviations are used: OS‐own
ship;TS‐targetship;CPA‐closest
pointofapproach;
DCPA‐distanceatCPA;TCPA‐timetoCPA;GWV–
give‐way vessel;SOV–stand‐onvessel;XTD‐cross
track distance. For DCPA, TCPA and XTD the
symbolsδ,τandηarealsousedinthetext.Ownship
was given the number ‘0’, and the targets
were
numbered from 1 to n. The number of the most
dangerous (main) target was denoted byμ, and the
targetswithnumbersjandμweremarkedbyTS
Jand
TS
μ.Thesameindiceswereusedforthecharacteristics
of these ships.Theinitialcourse, speed of own ship
and TS
J were respectively marked K0, V0 and KJ, VJ.
Theownshipcourseandspeedontheevasionsection
weredenotedbyK
U,VU.TheRulesreferencedinthe
textarepartofCOLREG.
2 CONSIDARATIONOFREQUIREMENTSFOR
EVASIVEACTIONS
Collision avoidance actions include course or/and
speed changes. The anti‐collision manoeuvre was
defined as a sequence of actions with sections of
movement between them with the constant course
andspeed. This manoeuvre
contains evasion actions
(evasive manoeuvre) and actions to back to the
passage plan (comeback manoeuvre). According to
Rule 8, the first actions must be substantial, i.e.,
sufficiently large andshort in time. The use of slow
course and/or speed changes, even by a sufficient
amount, to avoid collision is not
reasonable. Such
actions may be interpreted as successive small
alterationswhichshouldbeavoided(Rule8).
When solving problems of collision avoidance, a
situational approach is used, in which the choice of
measures is determined depending on the current
situation. The used classification of the situations,
influencing the conduct of two
vessels (with the
exception of sailing ones) in normal and restricted
visibility,ispresentedinFig.1.
Figure1.Situationsoftwoshipsnearing
Normalsituationsrefertothevesselapproaching
phase, inwhichactionsare carriedoutattheample
time.Instrenuousandinextraordinarysituations,the
vessel, respectively,may or must refuse the conduct
prescribed for her. Strenuous situations are those in
which give‐way vessel is late in evading actions.
Situations
areextremewhentheownshipissoclose
to thetarget that a collision can be avoidedonly by
maximumstrongmanoeuvreofoneshiporactionsof
both vessels. Extreme situations, as well as ordinary
situationswithtwosailingvessels,arenotconsidered
below.
Inapairof
shipsnearingwithriskofcollisionthe
give‐wayvesselwasdefined:
underRules14and15,forpower‐drivenvesselsin
sight of each other in meeting situations (see
Figure1);
under Rule 18, for ships of different navigational
statusinsightofeachotherinmeetingsituations;
underRule13,forpower‐drivenvesselsandships
of different navigational status in sight of each
otherinovertakingsituations;
under Rule 19, in restricted visibility where both
shipstakeevasiveactions.
It is preferable,if circumstances ofcase admit,to
avoidacollisionbyemployingmanoeuvres
involving
a few actions. These manoeuvres include the
proposedheremanoeuvrecontaining:
evading a collision with combined Z‐manoeuvre
byshiftingtoparalleloriginaltrackline,onwhich
movementissafe;
passing along this line by the target that was
dangerous;
typicalcomebackmanoeuvres.
The typical comeback manoeuvres
were
considered(Fig.2):
4. incomingattheactiveroutelegundertheselected
angle(Q
C);
5. goingtotheactivewaypoint(WP);
6. Followingtotheintersectionofcourselinewiththe
nextlegoftheroute.
Figure2. Typical comeback manoeuvres: B, E‐the
beginning and the end points of the second action in the
evasion manoeuvre;η‐lateral deviation from the active
routeleg;S
i‐distancefromtheevasivemanoeuvreendto
thecomebackmanoeuvrestart;H
1,F1andH2,F2‐thestart
and end points of the first and second actions in the first
typecomebackmanoeuvre
When the direction to turn on the next route leg
coincides with the side of evasion, the third type of
comebackispreferable.Ifsuchsidesareopposite,the
second manoeuvre is best. If necessary the first
manoeuvreapplies.
CombinedZ‐manoeuvreincludestwoaсtions[14]:
thefirstisboth
courseandspeedchangeataselected
point,thesecond‐returningtotheoriginalvaluesof
theseparametersatanotherpoint.Particularcasesof
combinedZ‐manoeuvreareZ‐manoeuvre,includinga
course alteration at one point and a return to its
original value at a second point, and a
manoeuvre
627
containingaspeedchangeatonepointandareturnto
itspreviousvalueatanotherpoint.Additionally,the
paper consideredthe choice of one combined action
(both course and speed alteration at the selected
point). Partial cases of one combined action are the
alteration in course or velocity only.
Combined Z‐
manoeuvre and one combined action together with
their parameters below are denoted by
CZM(S,W,Q,U),OCA(S,W,Q),whereSisthedistance
fromownshiptothebeginningofthemanoeuvreat
the time of its calculation; W is speed change; Q is
angleof turn;U is
lengthof thestraight segmentof
theevasion.
TheRules13‐19regulatetheconductoftwoships
approachingatriskofcollisioninwatersfreeoffixed
andmovingobstacles.Theseconditionsanddecisions
prescribedforthem(turnside, actions,manoeuvres)
arecalledstandardbelow.Understandardconditions,
in normal
visibility, a give‐way vessel usually tries
without changing speed to minimize the loss of
sailingtimeandavoidcrossingthecourseofstand‐on
vessel on the bow. The action that stand‐on vessel
maytakeinstrenuoussituationsisselectedtoensure
safetybothwhentheothership
performstheactions
directedbytheRules,andintheirabsence.Inviewof
theabove, forstandardconditions,normal visibility,
for power‐driven vessels and vessels with different
navigational status, standard side of turn to avoid
collisionwasdetermined:
insituationsofmeetingonreciprocalcourses,the
standard action
of give‐way vessel is the turn to
starboard;
in both meeting and overtaking situations with
ships on crossing courses, the standard action of
give‐wayvesselisturntowardthestand‐onvessel;
in overtaking situations of ships on coinciding
courses,thestandardactionofgive‐way
vesselis
change course to port, if she is to the left of the
overtaken vesselʹs track, and to starboard, when
sheistotherightoforonthatline;
in strenuous meeting situations with ships on
crossing courses, when stand‐on vessel may
perform evading manoeuvre, the
standard action
of thatvessel is turn totheside thatcoincides in
namewiththestandardsideofturnforthegive‐
wayvessel;
in strenuous overtaking situations with ships on
crossing courses, when stand‐on vessel may
perform evading manoeuvre, the standard action
ofthatvesselis
turntotheside,oppositenameto
thestandardsideofturnforthegive‐wayvessel.
Itwasconsideredthattheturnindex(σ)isequalto
one(σ=1)whenchangingcoursetothestandardside,
σ=‐1whenturningtotheoppositedirection,andσ=0
if
alteringspeedonly.
For waters constricted by ships, the action is
determinedinrelationtothemost dangerousofthem,
and is selected as safe with respect to all stationary
and moving obstacles. In normal visibility, the
statements for actions in standard conditions apply
for constricted waters also, when circumstances
permit.
For other cases, alternatives to the standard
optionsareused.Whenthemainengineofownship
isreadyformanoeuvre,turningtothestandardside,
alteringspeed,andturningtothestandardsidewith
speedchangearethepreferredactionsoverturningto
the opposite side without or with
speed change. In
most cases, the second actions are used when there
arenooptionsofpreferredactions.Evadingactionsin
constricted waters are generally accompanied by
crossingthecourse of oneorthe othertargetonthe
bow.Suchvariantismoredangerousthanpassingon
thestern.Therefore,the
acceptedbyGWVdistanceof
crossing the target course on the bow should be
greaterthanonthestern.
Forrestrictedvisibility,thestandardsideofturnto
keepclearisestablishedbyRule19.Thebasisofsuch
prescriptionistherequirement,thatshipsmustassist
each other to
avoid collision. Fulfilling this
requirement helps to quickly increase the distance
betweenships.Rule19doesnotestablishthestandard
evasiveturnsideinasituationsuchaswhentheother
vessel,innormalvisibility,isbeingovertaken.Based
onthe ‘assistance’ requirement,in thiscase, a vessel
thatisabaft
thebeamofanothershipshouldchange
coursetotheoppositesideofanothershiplocation.
Itisnowrequired(MSC.192(79),IEC62388)inon‐
board collision avoidance systems to detect ships at
risk and select evasive manoeuvres using pre‐
determinedDCPAandTCPAlimits(denoted
ˆ
and
ˆ
),whichmustbeconsistentwithsailingconditions.
Inadditionto
ˆ
,theminimumacceptable(
)under
the given conditions DCPA was used. The main
factorsinfluencingsuchrestrictionsarethefollowing
[11,14]:
typeofnavigationareaandthedensityoftrafficin
it(theconstrictionofthewaterareabyfixedand
movingobstacles);
features (size, manoeuvreability, speed) of own
shipand
target;
errors in determining the parameters of target
positionandmovement.
Here are the main types of navigation areas
usuallydistinguisheddependingonthedistance(ρ)in
nauticalmilestonavigationalobstacles:
opensea(ρ≥50);
coastalwaters(50>ρ≥5);
constrictedwaters(ρ<5).
Whenconsideringlimitsoftargetdanger,wecan
distinguish:
generalized limits (
ˆ
δ
G
,
ˆ
τ
G
), which did not take
into account own ship and targets features and
refertoordinarymediumtonnagevessels;
limits (
ˆ
δ
O
,
ˆ
τ
O
) specified with regard to the own
ship characteristics for ordinary medium‐tonnage
targets;
limits(
ˆ
δ
j
,
ˆ
τ
j
)calculatedconsideringthefeatures
ofownshipandtarget.
Todeterminegeneralizedlimits,theirdependence
on the degree of tightness of the water area can be
used. These limits for the main types of navigation
areas are usually recommended for use on seagoing
vessels. One such recommendation is:
ˆ
δ
G
=20 cb,
ˆ
τ
G
=30 min for open sea;
ˆ
δ
G
=15 cb,
ˆ
τ
G
=25 min for
coastal waters;
ˆ
δ
G
=10 cb,
ˆ
τ
G
=20min for constricted
waters.TheminimumacceptableDCPAvalueforthe
open sea is usually considered to be 10 cb, and for
constrictedwaters‐5cb[11].Itshouldbenotedthat
the above limits for coastal and constricted waters
correspondtotheaverageofdistancestonavigational
obstaclesin
theseareas.
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Whenstudyingtheproblemofcollisionavoidance,
ˆ
δ
is often used in a broader sensethanthe limit of
targets DCPA. This threshold is considered an
argumentforcalculatingtheboundariesofoneshape
or another of target domain of danger. The variant
where
ˆ
δ
isthelimitofDCPAisaparticularcaseof
this interpretation. Circular domain of danger with
thecentreinthetargetmasscentreandradiusequal
to
ˆ
δ
corresponds to this particular variant. In
navigation practice such domains are used in the
predominant majority of cases. A circular domain
shifted relative to the target in the direction of its
motioncanbeappliedsothattheacceptablecrossing
distance of target course would be greater fore than
aft.
More complex domains shapes are proposed to
take into account factors not considered by circular
domains.Thedomainformisusuallytakenthesame
for all targets. When the features of the targets are
taken into account, their domain sizes will be
different.
TCPA limit defines when Rules 13‐19 come
into
force. The distance between own ship and main
target,whichcorrespondstosuchstart,waslimitedto
D
=1,1∙
ˆ
δ
from below and
ˆ
D
=8∙
ˆ
δ
from above. If
appropriate
ˆ
τ
this distance was smaller than
D
or
greaterthan
ˆ
D
the
ˆ
τ
valuewascorrected:
IF(
ˆ
τ
∙vμ0<
D
)THEN
ˆ
τ
=
ˇ
D /vμ0; (1)
IF(
ˆ
τ
∙vμ0>
D
)THEN
ˆ
τ
=
ˆ
D
/vμ0; (2)
wherev
μ0isthemaintargetspeedrelativetotheown
ship.
Takingintoaccount
ˆ
τ
andthelength(LOS)ofthe
ownship,thepoints(B
τ,Eτ)ofthestartandendofthe
Rules13‐19actionweredeterminedontheownship
pathline.Thedistancesfromtheownshipʹsposition,
atthemomentoftheclosestapproachwiththemain
target,tothepoints B
τandEτwerecalculated using
thefollowingexpressions
0
τ
ˆ
B
V ; 5
EOS
L . (3)
The parameter S of manoeuvre was obtained as
S=Y
S‐Y,whereYSandYarethedistancesfrompoint
E
τ to the own ship position at the moment of task
solutionandtothemanoeuvrestartpoint.IntheB
τEτ
interval two stages were distinguished: of give‐way
vesselinampletimeaction,andofpossiblestand‐on
vessel action. The boundary of these stages was
considered by default to be the middle of the B
τEτ
interval.
Intheprocessofcollisionavoidance,theownship
should remain controllable and be able to accelerate
thecourseandspeedalteration.Inorderfortheaction
to be fast enough and not impair the shipʹs
controllability,itwasassumedthat:
turnsaremadewitharadius
(RZ)averageforthe
ownship;
thespeedisreducedbyapplyingthemode‘slow
astern’ or ‘dead slow astern’, and should not be
lessthanthedeadslowahead;
enginepowertoincreasespeedtoagivenvalueV
Z
is greater, if possible, than the powerto move at
thisspeed,soactiontimewillnotbetoolong.
To define large enough changes in courseand/or
speed,theβindexwasused
/
ˆˆ
/
Qq W w
(4)
where
ˆ
w
,
ˆ
q
are the limits of sufficiently large
changesinspeedandcourse.
Usuallyit was recommended that
ˆ
q
be takenas
30°. The minimum acceptable value of Q is most
commonly considered to be
q
=15° [15]. One of the
recommendations for the lower limits of sufficiently
large and acceptable values of W when avoiding
collisionbyspeedreductionis
ˆ
w
=V0/3and
ˇ
w
=0,2V0.
Theboundary
ˆ
β
ofsufficientvaluesofβisequalto
one,i.e.theactionislargeenoughwhenβ≥1.Tofind
the minimum acceptable value ofβ, the expression
ˇ
β =
//2
ˆˆ
/
qq ww
wasused:
Topreventcollisionswithnavigationalobstacles,a
safetylanewasdefinedbylimits(
η
,
ˆ
η
)ofownship
safelateraldeviationsfromtracklinetotheportand
starboard.Theboundariesoflanecutoffwaterareas
dangerousindepthsfortheownshipandprohibited
fornavigationregions
.
3 OFFEREDGRAPHICALTOOLS
Below for simplicity, the domains of danger are
assumedtobeunbiased,circular,andequalinsizefor
all targets. Proposed graphical aids to facilitate the
selection of anti‐collision manoeuvres include
diagrams, showing the zones of acceptable actions,
and special marks of targets at the
moment of their
closest approach to the own ship. When developing
these tools, in the area of the acceptable manoeuvre
variants, the basic and alternative sets were
distinguished. The first set contains the manoeuvres
satisfying the requirements for evasive actions. The
alternative sets included acceptable manoeuvres not
meeting this requirements for
magnitude (
ββ
ˆ
β
)
and/or evasion side (σ=‐1) and/or safety (
ˆ
δδ δ
m
),
whereδ
m is the minimum value among DCPA of
targetsintheownshippath.When(β<
β
)or(
δδ
m
)
or (η<
η
) or (η>
ˆ
η
), the manoeuvre was considered
unacceptable. The basic variants of the combined
Z‐manoeuvreandonecombinedactionweredenoted
as CZM{0} and OCA{0}. In the designation of the
alternativemanoeuvreoption,theparameters,whose
values do not meet the requirements, are given in
curly brackets, e.g., CZM{δ,β}. For
own ship with
enginesreadyformanoeuvre,table1showsinorder
of application’s priority the combined Z‐manoeuvre
zonesZ
h,wherehisthepriorityindex(h=1,2,…,9),
andthecolorswehavechosentorepresentthem.The
samecolorsareusedforonecombinedactionsets.In
general,themanoeuvremustbeselectedinthezone
withthehighestpriority.
629
Table1.Setsofacceptablemanoeuvres
________________________________________________
Zone Manoeuvretype Areacolor
________________________________________________
Z1 CZM{0}lightgreen
Z
2 CZM{β}green
Z
3 CZM{δ}darkyellow
Z
4 CZM{δ,β} yellow
Z
5 CZM{Ϭ}lightgray
Z
6 CZM{Ϭ,β} gray
Z
7 CZM{Ϭ,δ} lightviolet
Z
8 CZM{Ϭ,δ,β} lightblue
Z
9 Unacceptable darkred
________________________________________________
Thebasis of obtaining data for the diagrams was
the method of enumerating a representative discrete
set of possible manoeuvre variants. A finite discrete
setisconsideredrepresentative,whenitreplacesthe
infinite continuous set with sufficient completeness
for the task at hand. Before obtaining data for the
diagrams, the lower
,,,
SWQU
and upper
,
ˆˆ
ˆˆ
,,SW QU boundaries of the possible values of the
manoeuvreparameters, andthe limits (
η
,
ˆ
η
) of OS
safedeviationsfromtheroutelinetotheportandto
the starboard, are set. When enumerating for each
manoeuvre option the valuesδ
m,β, η, h, dT for
combinedZ‐manoeuvre,W
Sforonecombinedaction
aredetermined,wheredTisthelossofsailingtime,
W
S=V0‐VU∙cosQ.Theenumerationmethodisinferior
in time to the accelerated search procedures for
optimal anti‐collision manoeuvres [8, 10]. But
enumeration allows obtaining the necessary
characteristics of each of the possible manoeuvre
variants, andto define in the form of representative
subsets the areas of sufficient, acceptable and
unacceptable such options, taking into account
variousfactors.In thisrespect,theapproachapplied
has an advantage over finding such areas by
calculating their borders using analytical geometry
methods [2]. The dynamics of own ship when
enumerating was taken into account in a simplified
manner.Thetrajectoryoftheturnswith
theaverage
forownshipradius(R
Z)wasrepresentedbyasetofa
straight‐linesegment andanarcofacirclewiththis
radius. The length of the straight‐line segment was
equal to l=κ∙L
OS, whereκ– is the coefficient
considering the shipʹs initial turning ability. The
change in V during braking and acceleration was
representedbytheexpressions
2
12
Watat
,
2
12
Wbtbt
; (5)
wheretistheprocesstime.
The coefficients of these expressions were found
usingthestoppingandaccelerationdata,giveninthe
own ship manoeuvreing booklet, and the
mathematicalmodeloftheshipdynamicsintheform
of an interconnected systemof nonlinear differential
equations. If to use speed change with a given
acceleration,thenexpressionsforpredictingWwillbe
thesimplest.Whencalculatingthetrajectoriesofturn
with speed change, these processes were considered
independent.
Figure3.Exampleofvirtualtargetsformation
With the help of AIS, ships are able to transmit
elementsoftheirroutes.The changeinmotion data,
provided by the targets can be accounted for in a
numberofways.Wereducedthisproblemtothetask
with unchanged parameters of targets motion by
entering additional virtual targets. Fig.
3 shows an
example of input virtual targets 2a, 2b for target 2,
withaknowntrajectoryofmovement.Thepositions
oftargets2a,2b,aswellasrealtarget,correspondto
the moment of the problem‐solving start. By setting
TCPAlimits,thetrajectorysection‘I)’wasassignedto
target 2, and the trajectory sections ‘II)’ and ‘III)’ –
wereassignedtotargets2a,2b,respectively.
Diagrams with one and two coordinates (for
example,SandQ, W)arepresentedasS‐diagramand
QW‐diagram.Whenworkingwithdiagramstoobtain
combinedZ‐manoeuvreandonecombinedaction,
the
cursorinthe toppriorityareais placed to the point
that determines the preferred, in the operatorʹs
opinion, values of the manoeuvre parameters.
Symbolsofthevaluesselectedbythecursoraregiven
below with the index Z. Diagrams for choosing
combinedZ‐manoeuvrearethefollowing:
WS‐andQU‐diagrams,whenthemainengineisin
manoeuvreingmode;
S‐ and QU‐diagrams, when main engine is not
readytomanoeuvre(W
Z=0).
The WS‐diagram cell has the colour of the zone
(see Table 1) of the top priority combined Z‐
manoeuvrevariantamongitspossiblevariants,values
of S and W parameters of which are this cell
coordinates. The colour of S‐diagram cell is
determined similarly. WS‐diagram, or S
‐diagram, is
usedbytheoperatortosetsuitableS
Z,WZvalues,or
only S
Z (WZ=0), to obtain the QU‐diagram
corresponding to these values, and to determine
amongpossiblemanoeuvrevariants,withtheS
Zand
W
ZvaluesofSandWparameters,oronlySZvalueof
parameter S, the values of Q, U parameters of the
optimalvariant:
forZ
1,Z5‐withminimumlossofsailingtime;
forZ
2,Z6‐withthemaximumofβvalue;
forZ
3,Z4,Z7,Z8‐withthemaximumvalueofthe
minimum distance between the own ship and
targetsontheownshiptrajectory.
TheQU‐diagramcellhasthecolourofthezoneof
the combined Z‐manoeuvre variant, the values of S,
W, Q, U parameters of which are S
Z, WZ and
630
coordinates of this cell. By selecting a point on the
QU‐diagramwiththecursor, it ispossibletocorrect
the combined Z‐manoeuvre variant obtained by the
computerusingtheWS‐orS‐diagram.
If one combined action is found when the main
engineisinmanoeuvreingmode,the
S‐diagramand
the QW‐diagramare used. If themain engine is not
readytomanoeuvre,theQS‐diagramisapplied.The
S‐diagramcellhasthe colourofthezoneofthetop‐
priority one combined action variant among its
possible variants, the value of the S parameter
of
which is the coordinate of this cell. This diagram
serves to set S
Z with the cursor, to receive the QW‐
diagram corresponding to this value, and to
determineamong possible manoeuvrevariants, with
valueS
ZofparameterS,valuesofQ,Wparametersof
optimumvariant.ForzonesZ
1,Z5theonecombined
actionvariantwiththeminimumvalueW
Sissearched
for.Forotherzonestheoptimalitycriteriaaresimilar
to those used in the selection of combined Z‐
manoeuvre.ThecellofQW‐diagramhasthecolourof
thezoneofonecombinedactionvariant,thevaluesof
S,Q,UparametersofwhichareS
Zandcoordinatesof
thiscell.TheonecombinedactionvariantfoundbyS‐
diagramcanbecorrectedbyQW‐diagram,settingon
it with the cursor a point with suitable coordinates.
Note that usage in maritime navigation the QW‐
diagram in polar coordinates was proposed by E.
Pedersen,andis
coveredinhisworks,inparticular,in
[2].
QS‐diagram cell has the color of the zone of the
one combined action variant, the S, Q parameters
values of which are the coordinates of this cell. The
selectionofanti‐collisionmanoeuvreswiththehelpof
diagramsispresentedin
Section4.
When finding diagrams to select the comeback
manoeuvre,theenumerationmethodisalsoapplied.
Themanoeuvreofthefirsttype(seeFig.2)issearched
bytheS
С‐diagramfortheset angleofapproachtothe
route, and by the S
СQС‐diagram when the range of
thisanglevaluesisgiven.Toselectthemanoeuvreof
thesecondtypetheS
C‐diagramisused.Inthenameof
thediagramsQ
Сistheangleofapproachtotheactive
segmentoftheroute,andS
Cis
the distance from the end of combined Z‐
manoeuvre to the beginning of the comeback
manoeuvre, if this manoeuvre is searched before
theendofcombinedZ‐manoeuvre,
thedistancefromtheownshiplocationatthetime
ofthecomebackmanoeuvrecalculationtoitsstart,
if
thismanoeuvreisselected afterthe completion
ofcombinedZ‐manoeuvre.
In order to assess the quality of selected
manoeuvres visually, it is proposed, along the own
ship trajectory, planned to keep clear, to use special
CPAmarksoftargets at the moment of theirclosest
approachtotheownship.
Thismarkcontains:
the predicted positions of own ship andtargetat
thetimeoftheirclosestapproach;
the base segment of
ˆ
δ
length, beginning at the
predicted target location and pointing to the
predictedownshipplace;
the short segment pointing to the current target
location.
FromCPAmarkitiseasytoestimatethevalueof
theshortestdistancebetweentheownshipandtarget,
foreorafttheown
shipwill cross thetargetcourse.
CPAmarksweredeterminedbynumericalprediction
in accelerated time of future ship positions in 1 s
increments. Rule 8 requires that the effectiveness of
theactiontakentoavoidcollisionwithanothervessel
shall be carefully checked until this vessel is finally
past and
clear. Therefore, in the process of the anti‐
collision manoeuvre execution, it is expedient at a
shorttimeinterval(2min,forexample)tofind,taking
into account the information obtained, the future
minimumdistancesbetweenownshipandtargetson
the own ship path for timely detection of adverse
changesinthesituation.
4 VALIDATIONOFPROPOSEDMETHOD
The proposed method of manoeuvre selection was
validated with the help of a program developed in
Delphi programming language. In this program, the
quantity of targets was limited to 20. Various
simulated encountered situations were resolved in
this program, confirming that the
research goal was
achieved. In the solved tasks, the computer time to
obtainallthediagramsdatadidnotexceed4seconds.
Onesuch task isdescribedbelow,inwhichtheown
shipand9targetsarepower‐drivenvessels.Ownship
andtargetsdataareshowninTables2
and3,whereB
andDarethetargetbearinganddistance.TargetTS
1
is the most dangerous vessel, which the own ship
mustgiveway.
Table2.Ownshipdata
________________________________________________
L K V RZ κ a1 a2 b1 b2
m dg kn cb ‐ cb/min
2
cb/min
3
cb/min2 cb/min
3
________________________________________________
220 345 17,1 3,5 1,0 ‐ 0,93 0,073 0,89 ‐0,78
________________________________________________
Table3.Targetsdata
________________________________________________
TS 1 2 3 4 5 6 7 8 9
________________________________________________
B,dg 36 51 69 326 325 101 27 332 331
D,cb 71,0 73,1 39,3 30,0 43,3 38,8105,7 83,7 144,7
K,dg 258 260 267 88 197 346 194 132 133
V,kn 19,1 16,9 17,3 21,2 8,6 9,7 7,2 9,0 7,2
________________________________________________
The used constraints are presented in Table 4, in
which p is the general notation of the parameter,
regardlessofitstype.
Table4.Parameterlimits
________________________________________________
Para‐ S W Q U η δ τ w q
meter cb kn dg cb cb cb min kn dg
________________________________________________
p
0 ‐12‐90 0 ‐30 5 ‐ 2,0 16
ˆ
p
50 0 90 70 30 7 15 4,0 30
________________________________________________
TheenumerationstepforSandUwas1cb,forW‐
1kn,andforQ‐2dg.Theinformationpresentation
formisshowninFig.4,where:
chartfield;
indicator of distances between waypoints of the
combinedZ‐manoeuvre;
buttontomemorizethemarkedsupposedchange
ofthetargetmotionparameters;
indicator of the basic data of the selected
manoeuvre(CZMorOCA);
631
indicatorofthebasicdataofmanoeuvre(CZMor
OCA),correspondingtothecursorcoordinateson
theQU‐diagramorQW‐diagram;
QU‐diagramorQW‐diagram;
indicatorofthebasicdataofmanoeuvre(CZMor
OCA),correspondingtothecursorpositiononthe
WS‐diagramor
S‐diagram;
WSdiagramorS‐diagram;
switch for the type of manoeuvre to be defined
(CZMorOCA);
ON/OFF switch of the information presentation
mode, when moving the cursor in the diagram
field.
IfthecomponentON/OFFisinOFFposition,the
indicator5(or7)
showsthemanoeuvredatarelevant
to the cursor coordinates on diagram. In the ON
position, in addition to the data in indicator 7, the
followingelements,correspondingcursorcoordinates
onWS‐diagramorS‐diagram,aredisplayed:
QU‐diagramorQW‐diagram;
own ship evasive path and CPA target
marks on
thenavigationchart.
IfthecursormovesalongthefieldofQU‐diagram
or QW‐diagram, in addition to the data on the
indicator 5, the own ship evasive path and CPA
marks, responding to the cursor position, are
displayedonthenavigationchart.
Figure4.Informationpresentationform
ThediagramsshowallZhzonesofmanoeuvres.It
is possible to represent from one to eight of these
zones,aswellasonlythezonewiththetoppriority.
The selection of combined Z‐manoeuvre by the
cursor on the WS‐diagram is explained in Fig. 5,
which shows with a change of proportions
the
componentsofthepresentationform:dataindicators,
partofthechartfield,WS‐diagramwiththeposition
ofthecursoronit,QU‐diagram,switchesforthetype
ofmanoeuvrestobedefinedandtheoverlaymode.In
thisfigure:
1. indicatoroftheselectedcombinedZ‐manoeuvre;
2. manoeuvre
laneboundaries;
3. trajectoryoftheselectedmanoeuvre;
4. CPAmarks;
5. point on the QU‐diagram, marking coordinatesof
the optimal manoeuvre corresponding to the
positionofthecursorontheWS‐diagram.
6. indicatorofcombinedZ‐manoeuvredataselectable
onWS‐diagram;
7. edge of give‐way
vessel manoeuvres started at
ampletime;
8. the beginning of COLREG requirements
accounting;
9. line,correspondingtoownshipcurrentposition;
10. lowerboundofthediagram,respondingtotheOS
positionatthetimeofthediagramsreceiving;
11. ownshippositionatthattimeonchart.
Figure5.TothecombinedZ‐manoeuvrechoiceontheWS‐
diagram
Asthecursormovesalong theWS‐diagramfield,
thevaluesofitsparametersSandWcorrespondingto
the chosen combined Z‐manoeuvre variant, the
designationofthehighest‐priorityzone,thevalueof
the optimality criterion for this zone, and the
parameters Q and U of the optimal manoeuvre
are
displayedaboveWS‐diagram.Whenclickingonacell,
itis coloured black. The coordinatesof such cell are
labelledasS
Z,WZ.TheappearanceoftheQU‐diagram
correspondstoS
Z,WZ.Theblackdotonthisdiagram
marksthecoordinatesoftheoptimalmanoeuvre.The
basic data of the selected combined Z‐manoeuvre is
given on the indicator. Own ship on the electronic
chart is supplemented by trajectory of the chosen
manoeuvreandbyCPAmarksoftargetsifnecessary
(Fig.
5).Theindicatorshows:thevaluesof
ˆ
δ
and
δ
(Dcz, Dcp), optimal Q and U of combined Z‐
manoeuvreparameters (S=S
Z,W=WZ),thecross‐track
distance, the loss of sailing time (dT), the minimum
valueofDCPAandthetargetnumberwiththisvalue.
TheCPAmarkisshownwhenδ
jislessthanspecified
value(20cbintheexample).TheQandUparameters
ofthecombinedZ‐manoeuvreobtainedfromtheWS‐
diagram can be corrected by pointing their new
valuesontheQU‐diagramwiththecursor(Fig.6).
Figure6.TotheselectionofcombinedZ‐manoeuvreonthe
QU‐diagram
632
The operation with S‐diagram and QW‐diagram
foronecombinedaction choice (Fig.7 and Fig. 8) is
similarto the work with the diagrams for combined
Z‐manoeuvreselection.
Figure7. To the one combined action choice on the S‐
diagram
Figure8.TotheonecombinedactionselectionontheQW‐
diagram
When main engine is not ready to manoeuvre,
findingcombinedZ‐manoeuvreissimilartochoiceon
theWS‐diagramandQU‐diagram,butinthiscasethe
firstdiagramhasonecolumn(W=0).Todeterminethe
one combined action in this case, the QS‐diagram is
applied(Fig.9).
Figure9. Selecting the one combined action using the QS‐
diagram
Itispossibletocheckhowthesafetyofownship
manoeuvre can be affected by a potential change in
thetargetmotionparameters.Todothis,theneeded
targetishighlightedinthechartfieldwiththecursor,
and its trajectory is supplemented with one or two
segments. After that
the computer, in 1‐second
increments,determines the future distances between
the own ship and that target. The closest of these
distancesis definedandthe CPA mark is shown on
thechart.Bythismarktheimpactofthetargetaction
onthesafetyoftheselectedownship
manoeuvrecan
be evaluated. Digitally, shortest distance between
own ship and target is displayed in the upper left
cornerofthechart.Ifitisgreaterthan
ˆ
,thecolour
ofthesymbolsisblack,ifitislessthan
,thecolour
is red, if the distance value is between these
boundaries,thecolorislightbrown.Theparameters
of the created target paths can be memorized by
pressingthe‘SaveTSroutes’button.Toillustratethe
presented procedure, Fig. 10 shows the effect of
possible changes in the target
TS2 and target TS5
motion parameters on the selected combined Z‐
manoeuvre. The assumed paths of these targets
movement are indicated on the chart. The figure
showsthatchangesinthepathofTS
2willresultinthe
collisionthreatimmediatelyaftertheendofcombined
Z‐manoeuvre. The possible action of TS
5 is not
accompaniedbyacollisionrisk.
Figure10.Effectofpossiblechangesinthetargetmotionon
themanoeuvre
The developed program also provides the ability
to display diagrams for the choice of comeback
manoeuvres after combined Z‐manoeuvre. As an
example, Fig. 11a shows a Q
CSC‐diagram for the
selectionofthefirstkindofthatmanoeuvreinthe10°‐
60°rangeofarrivalanglestotherouteactivesegment.
The situation at the time of diagram calculation is
showninFig.11b.Inthisexample,ownshipis16.0cb
tothestarboardofthe
route.Thevaluesof
ˆ
and
intheexample are5 cband 3 cb, respectively.Own
ship and targets data at the time of the diagram
calculationareshownintables5and6.Thecomeback
trajectory and CPA target marks shown in Fig. 11b
corresponds to the cursor position on the diagram
(Q
C=30°,SC=15cb).
Table5.Ownshipdata
________________________________________________
L K V RZ κ
m dg kn cb ‐
________________________________________________
220 345 17,1 3,5 1,0
________________________________________________
633
Table6.Targetsdata
________________________________________________
TS 1 2 3 4 5
________________________________________________
B,dg 53 65 287 12 358
D,cb 19,2 34,9 18,5 55,4 62,2
K,dg 293 302 116 217 122
V,kn 19,1 16,9 14,8 10,1 9,4
________________________________________________
Figure11. To the comeback manoeuvre choice by QCSC‐
diagram
5 CONCLUSION
To achieve the researchobjective, the following was
carriedout:
theclassificationofsituationsintheprocessoftwo
vessels approaching was specified, and general
provisions for determining actions in free waters
undernormalvisibilitywereestablished;
theareasofpossibleevasionactionsweresingled
outand
orderedbypriority;
the possibility of using enumeration of
representative discrete set of evasion manoeuvre
variants to solve collision avoidance tasks in
situationswithseveraltargets,wasconfirmed;
diagramswereobtainedforselecting,insituations
with stationary and moving obstacles,an evasive
andatypicalcomebackmanoeuvres;
theprocedurehasbeendefinedtoassesstheeffect
on the manoeuvre safety of known or probable
futurechangesintargetmovement;
special CPA marks for visual evaluation of the
manoeuvrequalityareproposed.
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