guidance and control of ocean vehicles

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Professor Thor I. FossenDepartment of Engineering CyberneticsNTNU Centre for Autonomous Marine Operations and SystemsNorwegian University of Science and Technology (NTNU)

Lecture Notes: TTK 4190 Guidance and Control of Vehicles

Home page: http://www.fossen.biz/

Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)

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Textbook and Notation

Fossen,T.I.(2011)HandbookofMarineCraftHydrodynamicsandMotionControl.JohnWiley&SonsLtd.

MSSToolbox:www.marinecontrol.org

xb

yb

zb

u ( )surge

r ( )yaw

v ( )sway

( )heavew

( )rollp

( )pitchq

ü SNAME(1950). NomenclatureforTreatingtheMotionofaSubmergedBodyThroughaFluid.TheSocietyofNavalArchitectsandMarineEngineers,TechnicalandResearchBulletinNo.1-5,April1950,pp.1-15.

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Useful Reference Book

ü Fossen,T.I.(1994). “GuidanceandControlofOceanVehicles”, JohnWiley&SonsLtd.ISBN0-471-94113-1

xb

yb

zb

u ( )surge

r ( )yaw

v ( )sway

( )heavew

( )rollp

( )pitchq


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Goals for the Course:1. Mathematicalmodeling

ofvehicles.Thisincludes:§ Kinematics§ Kinetics§ Equationsofmotion

formarinecraftandaircraft

§ Wind,waveandoceancurrentmodels

§ Hydrodynamics:maneuveringandseakeepingtheory

Copyright © Bjarne Stenberg/NTNU


2. Designofguidance,navigation andmotioncontrolsystemsforalargenumberofapplications

3. Simulate themotionsofmarinecraftandaircraftinthetime-domainusinghydrodynamic/aerodynamicmodels

5 TTK 4190 Guidance and Control (T. I. Fossen)

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Marine Craft in Operation

Copyright © Bjarne Stenberg/NTNULecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)

7 TTK 4190 Guidance and Control (T. I. Fossen) Lecture Notes 2005Pipe-laying vessel

Geologicalsurvey

Heavy lift operations

Positionmooring

Pipe and cable laying

Marine Craft in Operation

ROV operations

Vibrationcontrolof marinerisers

Cable-layingvessel

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Italian supply ship Vesuviorefueling two ships at sea.

Courtesy: Hepburn Eng. Inc.

Path Following and Trajectory Tracking

Underactuated container ship in transit. Fully actuated supply ship cruising at low speed.


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Formation Control/Underway Replenishment


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Interdisciplinary: Rocket Launch / DP system / THCS

SMMarine Segment

Courtesy: SeaLaunchhttp://www.sea-launch.com

Courtesy: SeaLaunch LLC


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Trim & Heel Correction System (THCS)

Process andMarine Control


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NTNU Infrastructure

Copyright © Bjarne Stenberg/NTNU


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ROV Minerva

Applied Underwater Robotics Laboratory

Hugin AUV

Remus 100 AUVLight AUV (LAUV)

ThefleetoftheAUR-LabatNTNUTrondheimhttps://www.ntnu.no/aur-lab


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Marine Cybernetics Laboratory (MCLab)

MCLab Dimensions:

üThesoftwareisdevelopedbyusingrapidprototypingtechniquesandautomaticcodegenerationunderMatlab/Simulink™andRT-Lab™.

üThetargetPConboardthemodelscalevesselsrunstheQNX™real-timeoperatingsystem,whileexperimentalresultsarepresentedinreal-timeonahostPCusingLabview™.

L ! B ! D " 40 m! 6.5 m! 1. 5 m

Cybership II


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NTNU Research Vessel Gunnerus31meterslongTopspeed13knots http://www.ntnu.edu/marine/gunnerus


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UAV Factory Penguin B w/ Piccolo SL• 28 m/s cruise speed• Gasoline, 8 hr

endurance• MTOW 21 kg• 2-5 kg payload capacity• Large payload bay• 80W generator• Avionics system

integration made with Maritime Robotics based on Cloudcap technology

• Telemetry on 2.4 GHz radio, GPRS (and VHF)

• Catapult launch• Custom payload system

integration with avionics interface


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Penguin equipped with Camera, INS and GPS Sensor Suite for Data Logging

Penguinnavigationpayload:TwoIMUs,opticalcamera,infraredcamera,RTKGPSandembeddedcontrollerfordatalogging

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Skywalker X8 w/Ardupilot• 18 m/s cruise speed• Catapult launch• Belly or net landing• Electric, 1hr

endurance• Large payload bay• >1 kg payload

capacity• Inexpensive• Flexible avionics and

payload system integration with ArduPilot open source autopilot and mission planning SW

• Currently telemetry on 433 MHz or 5.8 GHz radio for VLOS

• Can be set up for BLOS with GPRS and VHF radio links


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3DRobotics hexa-copter w/Ardupilot• Electric, 5-10 min

endurance• 1 kg payload capacity• Inexpensive• Flexible system

integration with Ardupilot open source autopilot and mission planning SW

• Telemetry on 433 MHz og 5.8 GHz radio


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Microdrone Quad-copter

• Turn-key solution• Various camera, video

and radio systems• Electric, 45 min

endurance• 2-3 kg payload

capacity


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NTNU Airfield at AgdenesWealsousetheairportsatEggemoen andØrland

Located94kmNorth-WestofTrondheim

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Offshore UAV Launch and Recovery Systems

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Launching – The Easy Part“Human-Inspired Approach”

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Automatic Launch of the Penguin UAV

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Net Landing onboard a Research Vessel outside the Azores in 2016

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Coordinated Control: Master-Slave Principle: The fixed-wing aircraft acts like an master, while the cooperative multicopters is the slave following the master.

Virtually-Moving Airfield: The airfield/net is moved in an optimal manner vertically and horizontally to improve landing accuracy and reduce impact speed.

K. Klausen, J. B. Moe, J. C. van den Hoorn, A. Gomola, T. I. Fossen and T. A. Johansen. Coordinated Control Concept for Recovery of a Fixed-Wing UAV on a Ship using a Net Carried by Multirotor UAVs. Proc. of the 2016 International Conference on Unmanned Aircraft Systems (ICUAS'16), Arlington, VA, 7-10 June, 2016.

Cooperative Control: A suspended net is transported away from the ship to a safe distance by using two or more multicopters, which cooperates. They UAVSs are intelligent and share positions in order to control the tension of the net.

The NTNU AMOS Ship-Landing Concept

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The NTNU AMOS Ship-Landing ConceptTwo or more Multicopters Catches the UAV

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Marinecraft:ships,high-speedcraft,semi-submersibles,floatingrigs,submarines,remotelyoperatedandautonomousunderwatervehicles,torpedoesandotherpropelled/poweredstructuresforinstanceafloatingairfield.

Vehicles thatdonottravelonland(oceanandflightvehicles)areusuallycalledcraft.

Vessel: "hollowstructuremadetofloatuponthewaterforpurposesoftransportationandnavigation;especially,onethatislargerthanarowboat".

Thewordsvessel,shipandboatareoftenusedinterchangeably.InEncyclopediaBritannica,ashipandaboataredistinguishedbytheirsizethroughthefollowingdefinition:

Ship:"anylargefloatingvesselcapableofcrossingopenwaters,asopposedtoaboat,whichisgenerallyasmallercraft.Thetermformerlywasappliedtosailingvesselshavingthreeormoremasts;inmoderntimesitusuallydenotesavesselofmorethan500tonsofdisplacement.

Submarine: "anynavalvesselthatiscapableofpropellingitselfbeneaththewateraswellasonthewater'ssurface.

UnderwaterVehicle: "smallvehiclethatiscapableofpropellingitselfbeneaththewatersurfaceaswellasonthewater'ssurface.Thisincludesunmannedunderwatervehicles(UUV),remotelyoperatedvehicles(ROV)andautonomousunderwatervehicles(AUV).

Marine Craft Ref.EncyclopediaBritannica


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Marinevesselsarealsoclassifiedaccordingtotheirmaximumoperatingspeed.ForthispurposeitiscommontousetheFroudenumber

Marine Craft

Fn ! UgL

Thepressurecarryingthevesselcanbedividedintohydrostatic and hydrodynamicpressure.Thecorrespondingforcesare:

• Buoyancyforceduetothehydrostaticpressures(proportionaltothedisplacementoftheship)

• Hydrodynamicforceduetothehydrodynamicpressure(approximatelyproportionaltothesquareofthespeed)

Thenwecanclassifythevesselsaccordingto(Faltinsen 2005):

• Displacementvessels(Fn<0.4):Thebuoyancyforcedominates.• Semi-displacementvessel(0.4-0.5<Fn>1.0-1.2):Thebuoyancyforceisnotdominantatthemaximumoperatingspeed.

• Planningvessels(Fn>1.0-1.2):Thehydrodynamicforcemainlycarriestheweight.

U:shipspeedL:overall(submergedlengthoftheship)G:accelerationofgravity

Inthiscourse,onlydisplacementvesselsarecovered


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Classification of ModelsSimulation Model: Thismodelisthemostaccuratedescriptionofasystem,forinstancea6-DOFhigh-fidelitymodelforsimulationofcoupledmotionsinthetimedomain.Itincludesthemarinecraftdynamics,propulsionsystem,measurementsystemandtheenvironmentalforcesduetowind,wavesandoceancurrents.

Themodelshouldbeabletoreconstructthetimeresponsesoftherealsystemanditshouldalsobepossibletotriggerfailuremodessoyoucansimulateaccidentsanderroneoussignalsetc.Simulationmodelswherethefluidmemoryeffectsareincluded(frequency-dependentmodels)typicallyconsistof50-200ODEswhileafrequency-independentmodelcanberepresentedin6DOFwith12ODEsforgeneralizedpositionandvelocity.

Inadditionyouneedsomestatestodescribetheenvironmentalloadsandactuatorsbutstillthenumberofstateswillbelessthan50forafrequency-independentvesselmodel


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Classification of ModelsControl Design Model: Thecontrollermodelisareduced-orderorsimplifiedsimulationmodelthatisusedtodesignthemotioncontrolsystem.Initssimplestform,thismodelisusedtocomputeasetofconstantgainsforaPIDcontroller.Moresophisticatedcontrolsystemsuseadynamicmodeltogeneratefeedforward andfeedbacksignals.Thisisreferredtoasmodel-basedcontrol.

ThenumberofODEsusedinconventionalmodel-basedshipcontrolsystemsisusuallylessthan20.APIDcontrollertypicallyrequirestwostates:onefortheintegratorandoneforthelow-passfilterusedtolimitnoiseamplification.Consequently,setpoint regulationin6DOFcanbeimplementedbyusing12ODEs.However,trajectory-trackingcontrollersrequireadditionalstatesforfeedforwardaswellasfilteringsohigher-ordercontrollawsarenotuncommon.

Observer Design Model: Theobservermodelwillingeneralbedifferentfromthemodelusedinthecontrollersincethepurposeistocapturetheadditionaldynamicsassociatedwiththesensorsandnavigationsystemsaswellasdisturbances.Itisasimplifiedversionofthesimulationmodelwhereattentionisgiventoaccuratemodelingofmeasurementnoise,failuresituationsincludingdead-reckoningcapabilities,filteringandmotionprediction.

Formarinecraft,themodel-basedobserveroftenincludesadisturbancemodelwherethegoalistoestimatewave,windandoceancurrentforcesbytreatingtheseascolorednoise.FormarinecraftthenumberofODEsinthestateestimatorwilltypicallybe20foraDPsystemwhileabasicheadingautopilotisimplementedwithlessthan5states.


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The Classical Models in Naval Architecture

m!u! ! vr " wq ! xg"q2 " r2# " yg"pq ! r!# " zg"pr " q! #$ # Xm!v! ! wp " ur ! yg"r2 " p2# " zg"qr ! p! # " xg"qp " r!#$ # Ym!w! ! uq " vp ! zg"p2 " q2# " xg"rp ! q! # " yg"rq " p! #$ # ZIxp! " "Iz ! Iy#qr ! "r! " pq#Ixz " "r2 ! q2#Iyz " "pr ! q! #Ixy

" m!yg"w! ! uq " vp# ! zg"v! ! wp " ur#$ # KIyq! " "Ix ! Iz#rp ! "p! " qr#Ixy " "p2 ! r2#Izx " "qp ! r!#Iyz

" m!zg"u! ! vr " wq# ! xg"w! ! uq " vp#$ # MIzr! " "Iy ! Ix#pq ! "q! " rp#Iyz " "q2 ! p2#Ixy " "rq ! p! #Izx

" m!xg"v! ! wp " ur# ! yg"u! ! vr " wq#$ # N

Themotionsofamarinecraftexposedtowind,wavesandoceancurrentsareusuallymodeledin6DOFbyapplyingNewton's2ndlaw:


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The Classical Models in Naval ArchitectureTheexternalforcesandmomentsX,Y,Z,K,M andN actingonamarinecraftareusuallymodeledbyusing:

ManeuveringTheory: ThestudyofashipmovingatconstantpositivespeedUincalmwater withintheframeworkofmaneuveringtheoryisbasedontheassumptionthatthehydrodynamiccoefficientsarefrequencyindependent(nowaveexcitation).Themaneuveringmodelwillinitssimplestrepresentationbelinearwhilenonlinearrepresentationscanbederivedusingmethodslikecross-flowdrag,quadraticdampingorTaylor-seriesexpansions.

SeakeepingTheory:Themotionsofshipsatzeroorconstantspeed inwavescanbeanalyzedusingseakeepingtheorywherethehydrodynamiccoefficientsandwaveforcesarecomputedasafunctionofthewaveexcitationfrequencyusingthehullgeometry.Thefrequency-dependentmodelsareusuallyderivedwithinalinearframeworkwhileextensionstononlineartheoryisanimportantfieldofresearch.


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Maneuvering TheoryAssumesthattheshipismovinginrestrictedcalmwater.Hence,themaneuveringmodelisderivedforashipmovingatpositivespeedUunderazero-frequencywaveexcitationassumptionsuchthataddedmassanddampingcanberepresentedbyusinghydrodynamicderivatives(constantparameters).

Thezero-frequencyassumptionisonlyvalidfor surge,sway andyaw sincethenaturalperiodofaPDcontrolledshipwillbeintherangeof100-150s.For150s thisresultin:

!n ! 2"T

! 0.04 rad/s #

Thenaturalfrequenciesinheave,rollandpitcharemuchhighersoitisnotstraightforwardtoremovethefrequencydependenceinthesechannels.


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Maneuvering TheoryItiscommontoformulatetheshipmaneuveringmodelasacoupledsurge-sway-yawmodelandthusneglectheave,rollandpitchmotions:

• Hydrodynamicaddedmasspotentialdampingduetowaveradiationandviscousdamping• Hydrostaticforces(springstiffness)• Windforces• Waveforces(1st- and2nd-order)• Controlandpropulsionforces

m!u! ! vr ! xgr2 ! ygr! " " Xm!v! # ur ! ygr2 # xgr! " " YIzr! # m!xg#v! # ur$ ! yg#u! ! vr$" " N

#

MRB!" ! CRB!!"! " #RB #

!RB ! !hyd " !hs hydrodynamic andhydrostatic forces

" !wind " !waveenvironmental forces

" !control #

!i ! !Xi,Yi,Zi,Ki,Mi,Ni"!, i ! #hyd, hs, wind, wave, control$ #


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Linearized Maneuvering ModelsInthelinear6-DOF casetherewillbeatotalof36massand36dampingelements proportionaltovelocityandacceleration.Inadditiontothis,therewillberestoringforces,propulsionforcesandenvironmentalloads.Ifthegeneralizedforce iswrittenincomponent,thelinearaddedmassanddampingforcesbecome:

where Xu,Xv , . . . ,Nr are the linear damping coefficientsand Xu! ,Xv! , . . . ,Nr! represent hydrodynamic added mass.

!hyd

X1 ! Xuu " Xvv " Xww " Xpp " Xqq " Xrr" Xu# u# " Xv# v# " Xw# w# " Xp# p# " Xq# q# " Xr#r#!

N1 ! Nuu " Nvv " Nww " Npp " Nqq " Nrr" Nu# u# " Nv# v# " Nw# w# " Np# p# " Nq# q# " Nr#r#

#

#


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Nonlinear Maneuvering ModelsApplicationofnonlineartheoryimpliesthatmanyelementsmustbeincludedinadditiontothe36linearelements.

TruncatedTaylor-seriesexpansionsusingoddterms(1st- and3rd-order)whicharefittedtoexperimentaldata(Abkowitch 1964)or2nd-ordermodulusterms(Fedyaevsky 1963)

Theequationsbecomerelativelycomplicatedduetothelargenumberofhydrodynamiccoefficientsontheright-handsideneededtorepresentthehydrodynamicforces.

Taylor-seriesexpansionsarefrequentlyusedincommercialplanarmotionmechanism(PMM)testswherethepurposeistoderivethemaneuveringcoeffs.experimentally.

X1 ! Xu" u" # Xuu # Xuuuu3 # Xv" v" # Xvv # Xvvvv3 # !

"

N1 ! Nu" u" # Nuu # Nuuuu3 # Nv" v" # Nvv # Nvvvv3 # !

#

#

X1 ! Xu" u" # Xuu # X |u|u|u|u # Xv" v" # Xvv # X |v|v |v|v # !

"

N1 ! Nu" u" # Nuu # N |u|u|u|u # Nv" v" # Nvv # N |v|v |v|v # !

#

#


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Seakeeping,isthestudyofmotionwhenthereiswaveexcitationandthecraftkeepsitscourseanditsspeedconstant(whichincludesthecaseofzerospeed).Thisintroducesadissipativeforceknownasfluidmemoryeffects(Cummins1962).

Thegoverningmodelisformulatedinthetimedomain(Cumminsequation):

Seakeeping Theory

!MRB ! A"!#$!" ! B total"!#!# ! "0

tK"t # !#!#"!#d! ! C! " $wind ! $wave ! "$ #


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- body-fixedvelocities:- positionandEulerangles:-M,CandDdenotethesysteminertia,Coriolisanddampingmatrices- gisavectorofgravitationalandbuoyancyforcesandmoments

- q isavectorofjointangels- isavectoroftorque-M andC arethesysteminertiaandCoriolismatrices

InFossen(1991)therobotmodel:

M!q"q! " C!q,q# "q $ %

wasusedasfoundationtowritethe6-DOFmarinecraftequationsofmotioninacompactvectorial setting.

Matrix-VectorRepresentation

Therobotmodelwasmodifiedtodescribemarinecraftaccordingto:

!

! ! !u,v,w,p, q, r"T! ! !x,y, z,!, ",#"T

Fossen's Robot-Like Vectorial Model for Marine Craft

M!" ! C!!"! ! D!!"! ! g!#" ! g0 " $ ! $wind ! $wave


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Itisadvantageoustoexpresstheequationsofmotioninmatrix-vectorform:

sincenonlinearsystempropertiessuchas:

§ symmetry ofmatrices§ skew-symmetryofmatrices§ positiveness ofmatrices

canbeexploitedinthepassivity/stabilityanalysis.Thesepropertiesrelatestopassivity ofthemodel.NoticethThese propertiesaredestroyedbylinearization.

Thesepropertiesalsorepresentsphysicalpropertiesofthesystemwhichshouldbeexploitedwhendesigningnonlinearcontrollersandobservers formarinecraft.

Thematrix-vectornotationmakesitveryeasytosimulatethemodel(inMatlab andC++)

Why use Matrix-Vector Form?

M!" ! C!!"! ! D!!"! ! g!#" ! g0 " $ ! $wind ! $wave


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forces and linear and positions and

DOF moments angular velocities Euler angles

1 motions in the x-direction (surge) X u x2 motions in the y-direction (sway) Y v y3 motions in the z-direction (heave) Z w z4 rotation about the x-axis (roll, heel) K p !

5 rotation about the y-axis (pitch, trim) M q "

6 rotation about the z-axis (yaw) N r #

xb

yb

zb

u ( )surge

r ( )yaw

v ( )sway

( )heavew

( )rollp

( )pitchq

ThenotationisadoptedfromSNAME(1950).

Foramarinecraft,DOFisthesetofindependentdisplacementsandrotationsthatcompletelyspecifythedisplacedpositionandorientationofthecraft.Acraftthatcanmovefreelyinthe3-Dspacehasmaximum6DOFs—threetranslationalandthreerotationalcomponents.

Consequently,afullyactuatedmarinecraftoperatingin6DOFmustbeequippedwithactuatorsthatcanproduceindependentforcesandmomentsinalldirections.

Degrees of Freedom (DOF)

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Whendesigningfeedbackcontrolsystemsformarinecraft,reduced-ordermodelsareoftenusedsincemostvehiclesdonothaveactuationinallDOF.Thisisusuallydonebydecouplingthemotionsofthevesselaccordingto:

1-DOFmodelscanbeusedtodesignforwardspeedcontrollers(surge),headingautopilots(yaw)androlldampingsystems(roll).

3-DOFmodelsareusuallyhorizontal-planemodels(surge,swayandyaw)forships,semi-submersiblesandunderwatervehiclesthatareusedinDPsystems,trajectory-trackingcontrolsystemsandpath-followingsystems.Forslenderbodiessuchastorpedo-shapedAUVsandsubmarines,itisalsocommontoassumethatthemotionscanbedecoupledintolongitudinalandlateralmotions.

·Longitudinalmodels(surge,heaveandpitch)forforwardspeed,divingandpitchcontrol.·Lateralmodel(sway,rollandyaw)forturningandheadingcontrol.

4-DOFmodels (surge,sway,rollandyaw)areusuallyformedbyaddingtherollequationtothe3-DOFhorizontal-planemodel.Thesemodelsareusedinmaneuveringsituationswherethepurposeistoreducerollbyactivecontroloffins,ruddersorstabilizingliquidtanks.

6-DOFmodels (surge,sway,heave,roll,pitchandyaw)arefullycoupledequationsofmotionusedforsimulationandpredictionofcoupledvesselmotions.Thesemodelscanalsobeusedinadvancedcontrolsystemsforunderwatervehicles,whichareactuatedinallDOF.

Degrees of Freedom (DOF)

guidance and control of ocean vehicles

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