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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 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SingaporePteLtd.2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore 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