Robust and Intelligent Control of a Typical Underactuated Robot: Mobile Wheeled Inverted Pendulum

123 Pages·2023·4.256 MB·English

by  Jian Huang, Mengshi Zhang, Toshio Fukuda

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
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· ·
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
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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