Research on Intelligent Manufacturing Jian Huang · Mengshi Zhang · Toshio Fukuda Robust and Intelligent Control of a Typical Underactuated Robot Mobile Wheeled Inverted Pendulum Research on Intelligent Manufacturing Editors-in-Chief HanDing,HuazhongUniversityofScienceandTechnology,Wuhan,Hubei,China RongleiSun,HuazhongUniversityofScienceandTechnology,Wuhan,Hubei, China SeriesEditors Kok-MengLee,GeorgiaInstituteofTechnology,Atlanta,GA,USA Cheng’enWang,SchoolofMechanicalEngineering,ShanghaiJiaoTong University,Shanghai,China YongchunFang,CollegeofComputerandControlEngineering,NankaiUniversity, Tianjin,China YushengShi,SchoolofMaterialsScienceandEngineering,HuazhongUniversity ofScienceandTechnology,Wuhan,Hubei,China HongQiao,InstituteofAutomation,ChineseAcademyofSciences,Beijing,China ShudongSun,SchoolofMechanicalEngineering,NorthwesternPolytechnical University,Xi’an,Shaanxi,China ZhijiangDu,StateKeyLaboratoryofRoboticsandSystem,HarbinInstituteof Technology,Harbin,Heilongjiang,China DinghuaZhang,SchoolofMechanicalEngineering,NorthwesternPolytechnical University,Xi’an,Shaanxi,China XianmingZhang,SchoolofMechanicalandAutomotiveEngineering,SouthChina UniversityofTechnology,Guangzhou,Guangdong,China DapengFan,CollegeofMechatronicEngineeringandAutomation,National UniversityofDefenseTechnology,Changsha,Hunan,China XinjianGu,SchoolofMechanicalEngineering,ZhejiangUniversity,Hangzhou, Zhejiang,China BoTao,SchoolofMechanicalScienceandEngineering,HuazhongUniversityof ScienceandTechnology,Wuhan,Hubei,China JiandaHan,CollegeofArtificialIntelligence,NankaiUniversity,Tianjin,China YongchengLin,CollegeofMechanicalandElectricalEngineering,CentralSouth University,Changsha,Hunan,China ZhenhuaXiong,SchoolofMechanicalEngineering,ShanghaiJiaoTong University,Shanghai,China ResearchonIntelligentManufacturing(RIM)publishesthelatestdevelopments and applications of research in intelligent manufacturing—rapidly, informally and in high quality. 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The series’ scope includes monographs, professional books and graduate text- books,editedvolumes,andreferenceworksintendedtosupporteducationinrelated areasatthegraduateandpost-graduatelevels. · · Jian Huang Mengshi Zhang Toshio Fukuda Robust and Intelligent Control of a Typical Underactuated Robot Mobile Wheeled Inverted Pendulum JianHuang MengshiZhang HuazhongUniversityofScience HuazhongUniversityofScience andTechnology andTechnology Wuhan,Hubei,China Wuhan,Hubei,China ToshioFukuda NagoyaUniversity Nagoya,Aichi,Japan ISSN 2523-3386 ISSN 2523-3394 (electronic) ResearchonIntelligentManufacturing ISBN 978-981-19-7156-3 ISBN 978-981-19-7157-0 (eBook) https://doi.org/10.1007/978-981-19-7157-0 JointlypublishedwithHuazhongUniversityofScienceandTechnologyPress TheprinteditionisnotforsaleinChina(Mainland).CustomersfromChina(Mainland)pleaseorderthe printbookfrom:HuazhongUniversityofScienceandTechnologyPress. ©HuazhongUniversityofScienceandTechnologyPress2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsofreprinting,reuseofillustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface Citiesallovertheworldaregraduallyimplementingplanstobangasolineanddiesel- poweredvehicleswithinthenextdecadeorso.Toachievethisgoal,theconceptoflast mileisoneofthekeyproblemsthatshouldbeaddressedinvariousmeasurestaken byadministrators.Thelastmileisthatdistancetraveledbetweentheterminationof public transport and one’s destination. For example, your office might be as far as amileawayfromthenearestbusstop.Eventakingthebustoandfromwork,you havetoconquerthefinalmilewithportableurbantransportationifyoudon’twant towalk. Themobilewheeledinvertedpendulum(MWIP)isatypicalunderactuatedrobotic system, which is widely used in modern urban transportation vehicles aiming at solvingthelastmileproblem.Thiskindofurbantransportationvehicleincludesthe SegwayPT,ToyotaWinglet,HondaU3-X,andsoon.Inthereal-worldapplication scenarios,theMWIPsuffersfrommanyinternal/externaluncertainties,e.g.,different roadconditions,therandomuser,orwindload.Besides,thesystemidentificationof MWIPparametersisalsodifficultduetothecomplexstructureandmultipledegrees- of-freedom(DOFs).Theconventional model-basedcontrolmethodisthushardto fulfillthehigh-performancecontroltasksofMWIP.Therefore,theadvancedrobust and intelligentcontrolofMWIPisvital,andthismotivates us towritethecurrent monograph. SincethedynamicmodelofMWIPistheprerequisiteforitscontroldesign,this bookfirstlyintroducesthemodelingprocedureofMWIP,inbothtwo-dimensional andthree-dimensionalcases.Second,todealwiththeinternal/externaluncertainties, welumpedtheuncertaintiesintoasingledisturbancetermanddesignedanovelhigh- orderdisturbanceobserver(HODO)toonlineestimatethisdisturbanceterm.Withthe compensationofdisturbance,anewhigh-orderdisturbanceobserver-basedsliding modecontrol(HODOSMC)strategyisproposed.Third,consideringthechattering problem in sliding mode control (SMC), this book introduces two approaches for the MWIP. One is the adaptive super-twisting algorithm, which is a second-order SMCstrategyandabletoefficientlyalleviatethechatteringphenomenon.Theother is the terminal sliding mode control (TSMC), which can ensure that all variables converge to the expected value in a limited time. Next, to better model and cope v vi Preface withuncertainties,theintervaltype-2fuzzysets(IT2FSs)areintroducedtodesign a new fuzzy controller for the MWIP system. The proposed controller can control itsbalance,position,anddirectionsimultaneously.Finally,alltheproposedcontrol approachesareimplementedinaphysicalMWIPplatform.Variousexperimentsare conducted,andtheresultsdemonstratethattheseapproachesareeffectivetosolve theuncertaintyproblemsincontrollingMWIP. ThisbookmainlypresentstheoreticalexplorationsforcontrollingMWIPsystems. Readers can systematically study the MWIP system, including its modeling, controller design, stability analysis, numerical simulation, and experimental plat- formconstruction.Thebookisprimarilyintendedforresearchersandengineersin the robotics and control community. It can also serve as complementary reading for nonlinear system theory and underactuated robotic control techniques at the postgraduatelevel. Wuhan,China JianHuang Wuhan,China MengshiZhang Nagoya,Japan ToshioFukuda Contents 1 Introduction ................................................... 1 1.1 AnOverviewofMWIPRobots ............................... 1 1.2 ControlMethodsoftheMWIPSystem ........................ 7 1.3 OutlineofBook ............................................ 9 References ..................................................... 10 2 ModelingofMobileWheeledInvertedPendulums ................. 13 2.1 Introduction ............................................... 13 2.2 Two-DimensionalDynamicModel ............................ 13 2.3 Three-DimensionalDynamicModel .......................... 15 2.4 DynamicModelwithUncertainties ........................... 20 2.5 PhysicalDesignoftheMWIPRobot .......................... 23 2.5.1 SensingSystemoftheMWIP .......................... 23 2.5.2 ServoMotorControlSystemoftheMWIP ............... 26 2.6 Conclusion ................................................ 28 3 DisturbanceObserver-BasedSlidingModeControlforMobile WheeledInvertedPendulumSystems ............................ 31 3.1 Introduction ............................................... 31 3.2 First-OrderDisturbanceObserver ............................. 32 3.3 Second-OrderDisturbanceObserver .......................... 33 3.4 High-OrderDisturbanceObserver ............................ 36 3.5 High-Order Disturbance Observer-Based Sliding Mode ControlforMobileWheeledInvertedPendulumSystems ......... 41 3.6 SimulationStudies .......................................... 45 3.6.1 DisturbanceObservers ................................ 45 3.6.2 High-Order Disturbance Observer-Based Sliding ModeControl ....................................... 48 3.7 Conclusion ................................................ 49 References ..................................................... 50 vii viii Contents 4 SlidingModeVariableStructure-BasedChatteringAvoidance ControlforMobileWheeledInvertedPendulums .................. 53 4.1 Introduction ............................................... 53 4.2 Adaptive Super-Twisting Control for Mobile Wheeled InvertedPendulumSystems .................................. 55 4.3 TerminalSlidingModeControlforMobileWheeledInverted PendulumSystems ......................................... 61 4.3.1 TSMCControllerDesign .............................. 61 4.3.2 AnalysisofVelocityConvergence ...................... 63 4.4 SimulationStudies .......................................... 65 4.4.1 AdaptiveSuper-TwistingControl ....................... 65 4.4.2 TerminalSlidingModeControl ........................ 67 4.5 Conclusion ................................................ 76 References ..................................................... 77 5 Interval Type-2 Fuzzy Logic Control of Mobile Wheeled InvertedPendulums ............................................ 79 5.1 Introduction ............................................... 79 5.2 Interval Type-2 Fuzzy Logic Modeling and Control ofaMobileTwo-WheeledInvertedPendulum .................. 80 5.3 IT2FLSsforControllingtheBalance,Position,andDirection oftheMWIP ............................................... 84 5.3.1 BalanceControl ..................................... 84 5.3.2 PositionandDirectionControl ......................... 88 5.4 SimulationStudies .......................................... 90 5.5 Discussions ................................................ 91 5.5.1 RobustnessoftheIT2FLS ............................ 91 5.5.2 StabilityoftheIT2FLS ............................... 92 5.6 Conclusion ................................................ 92 References ..................................................... 93 6 ExperimentsofControllingRealMobileWheeledInverted Pendulums .................................................... 97 6.1 ExperimentalSetup ......................................... 97 6.2 ExperimentalResults ....................................... 99 6.2.1 ExperimentalResultsofHigh-OrderDisturbance Observer-BasedSlidingModeControl .................. 99 6.2.2 ExperimentalResultsofAdaptiveSuper-Twisting Control ............................................. 105 6.2.3 ExperimentalResultsofIntervalType-2FuzzyLogic Control ............................................. 112 6.3 Conclusion ................................................ 115 7 Conclusion .................................................... 117 Symbols ψ Rotationangleoftheleftwheel l ψ Rotationangleoftherightwheel r α YawangleoftheMWIPsystem θ Inclinationangleofthebody m Massofthebody b mw Massofawheel I MomentofinertiaofthebodyaboutY-axis by I MomentofinertiaofthebodyaboutZ-axis bz Iwa MomentofinertiaofawheelaboutY-axis Iwd MomentofinertiaofawheelaboutZ-axis l Lengthbetweenthewheelaxleandthecenterofgravityofthebody r Radiusofthewheel 2b Distancebetweentwowheels D Viscousresistanceinthedrivingsystem b Dw Viscousresistanceoftheground u Rotationtorqueoftheleftmotor r u Rotationtorqueoftherightmotor l τ Externaldisturbances ext τ∗ Lumpedmodeluncertaintiesandexternaldisturbances d (x ,y ) PositionoftheMWIPbodyintwo-dimensionalmodel b b (xw,yw) PositionoftheMWIPwheelintwo-dimensionalmodel q Configurationalvectoroftwo-dimensionalmodel 2D (x ,y ,z ) PositionoftheMWIPbodyinthree-dimensionalmodel 1 1 1 q Fullstatevectorofthree-dimensionalmodel f q Configurationalvectorofthree-dimensionalmodel 3D T TranslationalkineticenergyoftheMWIPbody b Tw TranslationalkineticenergyoftheMWIPwheels R RotationalkineticenergyoftheMWIPbody b Rw RotationalkineticenergyoftheMWIPwheels U PotentialenergyoftheMWIPsystem D DissipatedenergyoftheMWIPsystem ix