Stabilization, Tracking and Formation Control of Autonomous Marine Vessels

244 Pages·2021·9.498 MB·English

by  Ge Guo, Zhenyu Gao, Pengfei Zhang

Ge Guo
Zhenyu Gao
Pengfei Zhang
Stabilization,
Tracking and
Formation Control
of Autonomous
Marine Vessels
Stabilization, Tracking and Formation Control
of Autonomous Marine Vessels
· ·
Ge Guo Zhenyu Gao Pengfei Zhang
Stabilization, Tracking
and Formation Control
of Autonomous Marine
Vessels
GeGuo ZhenyuGao
StateKeyLaboratoryofSynthetical SchoolofControlEngineering
AutomationforProcessIndustries NortheasternUniversityQinhuangdao
NortheasternUniversity Qinhuangdao,Hebei,China
Shenyang,Liaoning,China
PengfeiZhang
SchoolofEngineering
HuzhouUniversity
Huzhou,Zhejiang,China
ISBN978-981-16-8108-0 ISBN978-981-16-8109-7 (eBook)
https://doi.org/10.1007/978-981-16-8109-7
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Preface
Recentyearshavewitnessedrapiddevelopmentandwideapplicationsofintelligent
vehiclesofvarioustypes,especiallyautonomousmarinevessels(AMVs).However,it
isinterestingtoseethatdespitetheequalimportanceofalltypesofvehicles,technolo-
giesdevelopedforAMVsarelessmature.Thisisinpartduetothecomplexityofthe
nonlineardynamicsofvessels,theenvironmenttheyoperate,andinevitabledistur-
bances and uncertainties. Hence, it is very challenging and worthwhile to develop
advancedtechnologiesforbetteroperationandcollaborationofAMVs.Thisbook
coversdifferentaspectsofrecentresearchadvancesonthemodeling,analysis,and
designofAMVcontrolsystems.
This book contains all the information that is needed to formulate and conduct
detaileddesignanalysisofmarinevesselsystems,focusingonthedevelopmentof
mathematical models and methodologies for stabilization, tracking, and formation
controlofAMVswithvariousconcernsandfromdifferentperspectives.Thisbook
is composed of three parts, with Chaps. 1–3 as Part I, Chaps. 4–5 as Part II, and
Chaps.6–9asPartIII,dealingwiththeissuesofstabilization,tracking,andformation
controlofAMVs,respectively.
Chapter1providesaninsightintoglobalexponentialstabilizationofAMVswith
actuatordead-zones.Byutilizinginputandstatetransformations,thedynamicmodel
ofAMVisconvertedintoanequivalentsystemconsistingoftwocascadeconnected
subsystems. For the transformed system, a switching scheme based on fixed-time
control theory is presented. For one of the subsystems with actuator dead-zones,
a fixed-time control method is proposed, which addresses the dead-zone problem
whileguaranteeingglobalexponentialstabilization.
Chapter2dealswithasymptoticstabilizationofautonomousmarinevesselswith
actuatordead-zonesandyawconstraintsbasedonfixed-timedisturbanceobserver.
By transforming the system model into two subsystems, a backstepping control
methodbasedonaBarrierLyapunovFunction(BLF)isintroducedtostabilizethe
transformedsystemandpreventtheAMVfromreachingtheboundariesofyawangle
andvelocityconstraints.Afixed-timedisturbanceobserverisinvolvedintheAMV
controllertodealwithactuatordead-zonesanddisturbances.Themethodisextended
v
vi Preface
tocoverthecaseinwhichtheyawconstraintsaretime-varyingandtheinitialstates
exceedtheconstraintregions.
Stabilization of AMVs under mismatched condition is discussed in Chap. 3.
Withintheframeworkofbacksteppingcontrolandbyintroducingaperiodictermin
thecontrollawsofvirtualyawangleandsurgevelocity,acontroldesignmethodis
developedtostabilizetheAMVsintoaboundedregion.Bytheinductionmethod,a
novelfixed-timedisturbanceobserverbasedonhigher-orderslidingmodedifferen-
tiatorsisintroduced.Thenacontrollawbasedontheproposedobserversisproposed,
bywhichtheerrorsbetweenthevirtualandactualyawangleandsurgevelocitycan
convergetozero,andthestatesoftheAMVsconvergetoaboundedregion.
Chapter4addressescommandfilteredpath-trackingcontrolofsaturatedAMVs
based on time-varying disturbance observer. A robust nonlinear control law is
proposedbasedonadisturbanceobserverandanauxiliarysysteminthecontextof
commandfilteredcontrol.Here,thedisturbanceobserverisconstructedtoestimate
theunknowntime-varyingdisturbances,theauxiliarydynamicsystemisemployed
tohandleinputsaturation,andthecompensator-basedcommandfilteredcontroltech-
niquemakesthedesignedpath-trackingcontrollawsimpleandeasytoimplement
inpractice.Itisprovedthatthenonlinearcontrollawcantrackthedesiredvessel’s
position and heading, while guaranteeing the uniform ultimate boundedness of all
signalsinthepath-trackingcontrolsystem.
In Chap. 5, trajectory tracking control of AMVs with model parameter uncer-
taintiesandexternaldisturbancesisinvestigated.Thedisturbancesduetothewind,
waves,andoceancurrentsarecombinedwiththemodelparameteruncertaintiesasa
compounddisturbance.Thenadisturbanceobserver(DO)isintroducedtoestimate
thecompounddisturbancewithinafinite-timeindependentoftheinitialestimation
error.BasedontheDOandinthecontextofcommandfilteredcontrol,anovelfixed-
time backstepping control scheme is developed, by which the vessel can track the
desiredtrajectorywithallthestatesgloballystabilizedinagivenfixedtime.
Chapter6presentsareal-timeformationcontrolmethodforAMVswithunknown
control directions. By employing the Nussbaum gain technique to deal with the
unknowncontroldirections,afinite-timeformationcontrolapproachisproposed.To
dealwiththeexplosionofcomplexityissueinbacksteppingcontrol,acompensator-
based command filter technique is introduced to realize the derivative of virtual
controlsignals.Withtheproposedmethod,theformationcanbeachievedwithina
finitesettlingtimeandallsignalsintheclosed-loopsystemareuniformlybounded.
Chapter7investigatesvelocityfreeleader-followerformationcontrolforAMVs
withlosrangeandangleconstraints.Anobserverisinvolvedtoestimatetheleader
velocityinfinitetimewithzeroerror,alleviatingtheneedofcommunicationsbetween
theAMVs.Basedonthefinite-timeobserver,theformationcontrollersoftheAMVs
aredesignedusingtime-varyingln-typebarrierLyapunovfunction(ln-BLF)method,
whichcanguaranteethattheAMVsformationcontrolsystemisuniformlyultimately
bounded.Todealwiththeproblemofexplosionofdifferentiationtermsinbackstep-
pingcontrol,weintroduceacommandfiltertorealizethederivativeofvirtualvari-
ables.Atthesametime,acompensatingsignalisconstructed(basedontheauxiliary
systemtechnique)tocompensatefortheerrorsofthecommandfilter.
Preface vii
Chapter8studiesprescribed-timeformationcontrolofautonomousmarinevessels
with asymmetric constraints on los range and bearing angles. To cope with the
time-varying constraints, this chapter presents a control method based on Asym-
metricBarrierLyapunovFunctions(ABLFs).Ascalingfunctionisintroducedinthe
control law with which the settling time can be prescribed in advance as needed.
Thecontrollersaredevelopedunderthebacksteppingmethodframework,withthe
environmentaldisturbancebeingestimatedbyanovelprescribed-timeobserver,to
ensure the global prescribed-time convergence of the AMV formation. We prove
that under the proposed control method, despite the interference of environmental
disturbance,theformationtrackingerrorscanconvergetozerointheprescribedtime
withoutviolatingtheconstraintsonthetrackingerrors.
Chapter 9 presents results on adaptive fixed-time formation control of AMVs
without velocity measurement, focusing on improving system convergence speed
and overcoming velocity measurement limitation. By employing the fixed-time
controltheoryandcommandfilteringtechnique,afullstatefeedbackformationalgo-
rithmisproposed,whichmakesthefollowerAMVtracktheleaderinagiventime
withallsignalsinthesystemgloballypracticallystabilizedinfixedtime.Toavoid
degradedcontrolperformanceduetoinaccuratevelocitymeasurement,afixed-time
convergentobserverisdesignedtoestimatethevelocityofAMVs.Wethengivean
observer-basedfixed-timecontrolmethod,withwhichacceptableformationtracking
performancecanbeachievedinfixedtimewithoutvelocitymeasurement.
Inthisbook,specialattentionisgiventoaclearpresentationoftheformulations,
algorithms, and their numerical implementation. Related references to guide the
readers further in this field are given at the end of each chapter. The book can be
usedincoursesforgraduatestudentsinmodelingandcooperativecontrolofmarine
vehicles. Researchers and engineers can also draw upon the book in developing
mathematicalmodelsforanalyticalanddesignpurposes.
Shenyang,China GeGuo
Qinhuangdao,China ZhenyuGao
Huzhou,China PengfeiZhang
September2021
Acknowledgements
The following financial supports are greatly appreciated: the National Natural
Science Foundation of China under Grant 62173079 and U1808205, the Funda-
mental Research Funds for the Central Universities under Grant N2023011, the
NaturalScienceFoundationofHebeiProvinceunderGrantF2020501018,andthe
YouthFoundationofHebeiEducationalCommitteeunderGrantQN2020522.
ix
Contents
PartI StabilizationControl
1 Fixed-Time Stabilization Control of AMVs with Actuator
Dead-Zones .................................................... 3
1.1 Introduction ............................................... 3
1.2 SystemModelingandPreliminaries ........................... 5
1.2.1 DynamicandKinematicModel ........................ 5
1.2.2 TheObjective ....................................... 6
1.2.3 Preliminaries ........................................ 7
1.3 ModelTransformation ...................................... 11
1.4 Fixed-TimeControllerDesign ................................ 14
1.4.1 SwitchingScheme ................................... 14
1.4.2 Fixed-TimeControlLaw .............................. 18
1.4.3 ControlAlgorithm ................................... 21
1.5 NumericalSimulations ...................................... 21
1.5.1 StabilityAnalysis .................................... 22
1.5.2 Comparisons ........................................ 24
1.6 ConclusionandFutureWork ................................. 26
Appendix:ProofofLemma1.3 .................................... 27
References ..................................................... 28
2 StabilizationControlofAMVsUnderMismatchedDisturbance .... 31
2.1 Introduction ............................................... 31
2.2 ProblemStatementsandPreliminaries ......................... 33
2.2.1 Modeling ........................................... 33
2.2.2 TheObjective ....................................... 34
2.3 Fixed-TimeDisturbanceObservers ............................ 35
2.4 StabilizationofAMVs ...................................... 38
2.4.1 StabilizationofHorizontalSubsystem ................... 38
2.4.2 ControlLawDesign .................................. 42
2.4.3 StabilityAnalysis .................................... 44
2.4.4 ControlAlgorithm ................................... 45
xi
xii Contents
2.5 NumericalSimulations ...................................... 46
2.5.1 StabilityAnalysis .................................... 46
2.5.2 EstimationError ..................................... 47
2.5.3 Comparisons ........................................ 48
2.6 ConclusionandFutureWork ................................. 49
References ..................................................... 50
3 AsymptoticStabilizationofAMVswithActuatorDead-Zones
andYawConstraints ........................................... 53
3.1 Introduction ............................................... 53
3.2 SystemModelingandObjective .............................. 54
3.2.1 KinematicModel .................................... 54
3.2.2 TheObjective ....................................... 56
3.3 ModelTransformations ...................................... 57
3.4 StabilizationofAMVswithYawConstraints ................... 58
3.4.1 StabilizationwithConstantYawConstraints ............. 58
3.5 StabilizationofAMVswithDisturbances ...................... 65
3.5.1 Fixed-TimeObserver ................................. 65
3.5.2 InitialStatesOutsideConstraintRegions ................ 69
3.5.3 ControlAlgorithm ................................... 70
3.6 FurtherDiscussions ......................................... 71
3.6.1 InfluenceofDisturbanceontheSway ................... 71
3.6.2 StabilizationwithTime-VaryingYawConstraints ......... 73
3.7 NumericalSimulations ...................................... 75
3.7.1 StabilityAnalysis .................................... 75
3.7.2 Comparisons ........................................ 76
3.7.3 SwayDisturbance .................................... 78
3.8 ConclusionandFutureWork ................................. 78
Appendix:ProofofLemma3.4 .................................... 78
References ..................................................... 80
PartII TrackingControl
4 CommandFilteredTrackingControlofAMVs .................... 85
4.1 Introduction ............................................... 85
4.2 ProblemFormulationandPreliminaries ........................ 88
4.2.1 ProblemFormulation ................................. 88
4.2.2 Preliminaries ........................................ 90
4.3 MainResult ............................................... 92
4.3.1 Fixed-TimeBasedDisturbanceObserverDesign ......... 92
4.3.2 Line-of-sightBasedGuidanceSystemforMarine
Vessels ............................................. 94
4.3.3 DesignofPath-TrackingController ..................... 95
4.3.4 StabilityAnalysis .................................... 97
4.4 NumericalSimulations ...................................... 101
4.5 ConclusionandFutureWork ................................. 105
References ..................................................... 106