Table Of ContentAdvances in Industrial Control
Forfurthervolumes:
www.springer.com/series/1412
Pål Liljebäck (cid:2) Kristin Y. Pettersen (cid:2)
Øyvind Stavdahl (cid:2) Jan Tommy Gravdahl
Snake Robots
Modelling, Mechatronics, and Control
PålLiljebäck ØyvindStavdahl
AppliedCybernetics DepartmentofEngineeringCybernetics
SINTEFICT NorwegianUniversityofScience&
Trondheim,Norway Technology
and Trondheim,Norway
DepartmentofEngineeringCybernetics
NorwegianUniversityofScience& JanTommyGravdahl
Technology DepartmentofEngineeringCybernetics
Trondheim,Norway NorwegianUniversityofScience&
Technology
KristinY.Pettersen Trondheim,Norway
DepartmentofEngineeringCybernetics
NorwegianUniversityofScience&
Technology
Trondheim,Norway
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ISSN1430-9491 ISSN2193-1577(electronic)
AdvancesinIndustrialControl
ISBN978-1-4471-2995-0 ISBN978-1-4471-2996-7(eBook)
DOI10.1007/978-1-4471-2996-7
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To ourfamilies
Series Editors’ Foreword
The series Advances in Industrial Control aims to report and encourage technol-
ogy transfer in control engineering. The rapid development of control technology
has an impact on all areas of the control discipline. New theory, new controllers,
actuators, sensors, new industrial processes, computer methods, new applications,
new philosophies,..., new challenges. Much of this development work resides in
industrialreports,feasibilitystudypapersandthereportsofadvancedcollaborative
projects.Theseriesoffersanopportunityforresearcherstopresentanextendedex-
position of such new work in all aspects of industrial control for wider and rapid
dissemination.
OvertheyearstheAdvancesinIndustrialControlserieshasbeenveryfortunate
in publishing monographs that were often seminal for the developmentof new ar-
eas in control systems theory and industrial technology. These monographs were
oftenwrittenbyyoungresearchersmakingtheirwayintheindustrialcontrolfield
or were a report of a substantial research project that was now ready for holistic
presentationanddissemination.Foramonographseriesthatspanstwodecades,itis
actuallyquiteeasytofindexamplesofthistypeofmotivationaltext.Fromtheearly
yearsoftheseries, IterativeLearningControl for DeterministicSystemsby Kevin
L.Moore(ISBN978-3-540-19707-2,1992)andAutotuningofPIDControllersby
Cheng-ChingYu(ISBN978-3-540-76250-8,1999)aregoodexamples.Inmorere-
cent years we can cite Control of Fuel Cell Power Systems by Jay T. Pukrushpan,
AnnaG.Stefanopoulou,andHueiPeng(ISBN978-1-85233-816-9,2004),Predic-
tive Functional Control by Jacques Richalet and Donal O’Donovan (ISBN 978-
1-84882-492-8, 2009) and finally Internet-Based Control Systems by Shuang-Hua
Yang (ISBN 978-1-84996-358-9, 2011) as typical Advances in Industrial Control
monographsthatarestudiedaskeytextsfortheirrespectivetopics.
Clearly Snake Robots by Pål Liljebäck, Kristin Y. Pettersen, Øyvind Stavdahl,
andJanTommyGravdahlisgoingtobeamuchread,studied,andcitedmonograph
in this particular field of robot development. After a truly fascinating introductory
chapterthatexaminesamongothertopics,biologicalsnakemotion,themonograph
isstructuredintotwoparts.PartIinvestigatesandreportsonmodelling,technology,
andcontrolforsnakerobotlocomotioninaplanar(flat)environment(Chaps.2–8).
vii
viii SeriesEditors’Foreword
Part II moves on to snake locomotion in a cluttered environment with stationary
objects(Chaps.9–13).Thisgroupofchaptersintroducesandexplorestheconcept
of“obstacle-aided”locomotion.Somuchofmobilerobottechnologyisconcerned
withobstacleavoidance,soitisinterestingtoseearobotapplicationthatexploitsthe
contact with objects (obstacles) in the environment to aid locomotion. The mono-
graph closes with a concluding chapter, three short technical appendices, a useful
Glossaryoftechnicalterms,andanexhaustiveIndex.
Theauthorshavesucceededinwritingawell-structuredtextthatisbothascien-
tific and an engineering monograph. The structure and contents of the monograph
can be accessed in several different ways. For example, the monograph presents
mathematical models that elucidate snake motion per se; this describes important
fundamental scientific principles in the field. Alternatively, the monograph can be
used as a source for up-to-date survey and review material on snake-robotic engi-
neeringandtechnology;apartfromthethoroughhistoricalreviewinChap.1,each
subsequent chapter opens with a section that creates the context and reviews the
past literature relating to the work to be presented by the authors. One of the at-
tractivefeaturesofthemonographisthewayinwhichtheauthorsusethechapter
sequencetoworkthroughincreasinglycomplexissuesintheunderstanding,control
andtechnologyofsnakerobots.Suchcarefulattentiontostructureallowstheexpert
researcher and the researcher new to the field rapidly to assess the importance of
thematerialpresentedanditsrelationtopastdevelopments.Finally,themonograph
presentstheauthors’ownresearchanddevelopmentinthefield.Thisresearchcov-
ersthefullspectrumofmathematicalmodelling,controldesign,simulationstudies
andfascinatingexperimentaldemonstratorprototypes.Closingthemonographisa
chapteronthefutureresearchandtechnologicalchallengesforsnakerobotlocomo-
tion(Chap.14).
The series Editors have no doubt that the control and robotics community will
find much of interest in this monograph. The monograph’s progress through the
historicalrecordforthefield,theproofsanddescriptionsoffundamentalsnakerobot
principlesandthepracticaldemonstrationsusingrobotprototypeswillensurethis
newentrytotheAdvancesinIndustrialControlseriesbecomesakeyreferenceand
sourcetextforsnake-robotlocomotionresearchanddevelopment.
IndustrialControlCentre M.J.Grimble
Glasgow M.A.Johnson
Scotland,UK
Preface
The purpose of this book is to present theoretical and practical topics related to
snakerobots.Snakerobotsareroboticmechanismsdesignedtomovelikebiologi-
calsnakes.Theadvantageofsuchmechanismsistheirabilitytomoveandoperate
inchallengingenvironmentswherehumanpresenceisunwantedorimpossible.Fu-
tureapplicationsofthesemechanismsincludesearchandrescueoperations,inspec-
tionandmaintenanceinindustrialprocessplants,andsubseaoperations.Research
on snake robots has been conducted for several decades. For instance, the world’s
firstsnakerobotwasdevelopedinJapanalreadyin1972.Thereare,however,still
many theoretical and practical aspects of snake robot locomotion which have not
yet been addressed in the snake robot literature. Current literature is characterised
bynumerousdifferentapproachestomodelling,development,andcontrolofthese
mechanisms, but a unified theoretical foundation of snake robots has not yet been
established.
Inthisbook,weattempttotargettheselimitationsofcurrentliteratureonsnake
robots.Themaingoalofthebookistocontributetothemathematicalfoundationof
thecontroltheoryofsnakerobots,andalsostimulateandsupportfutureresearchon
thesefascinatingmechanisms.Tothisend,thebookisacompletetreatmentofsnake
robotics,withtopicsrangingfrommathematicalmodellingtechniques,mechatronic
designandimplementation,andcontroldesignstrategies.Inparticular,severalnew
approachesto modellingsnake robot locomotionare presented. Moreover, numer-
ouspropertiesofsnakerobotdynamicsarederivedusingnonlinearsystemanalysis
tools, and several new control strategies for snake robots are proposed. The book
also describes the development of two snake robots that are employed to exper-
imentally validate many of the theoretical results. Whereas previous literature has
mainlyfocusedonflatsurfacelocomotion,adistinctfeatureofthebookisthestrong
focusonlocomotioninunevenandclutteredenvironments.Theorganisationofthe
bookisdetailedinSect.1.5.
Althoughtheresultspresentedinthisbookarenewandbasedonrecentconfer-
enceandjournalpublications,theyarepresentedataninitiallevelwhichisacces-
sible to audiences with a standard undergraduate background in control theory or
mechatronics.Thebookiswritteninaclearandeasilyunderstandablemannerwith
numerousfiguresandpictureswhichhelpillustrateandvisualisethematerial.The
target audience of this book includes academic researchers and graduate students
withaninterestinsnakerobotsorunderactuatedsystemsingeneral.Thebookmay
ix
x Preface
also be used for self-study or as a reference by engineers and applied mathemati-
cians, and by anyone who would like to find out more about the exciting field of
snake robotics. We believe the book will be particularly useful to new researchers
taking on a topic related to snake robotics since the book provides an extensive
overview of the snake robot literature and also represents a suitable starting point
forresearchinthisarea.
Weareindebtedtoanumberofpeoplewhohavebeenintegraltothecompletion
ofthisbook.WeexpressoursinceregratitudetoProfessorScottDavidKelly(Uni-
versity of North Carolina at Charlotte), Professor Shugen Ma (Ritsumeikan Uni-
versity),andProfessorOleMortenAamo(DepartmentofEngineeringCybernetics
at NTNU) for their feedbackto the materialin this book in conjunctionwiththeir
participationinthedoctoraldissertationofPålLiljebäck.
Furthermore,wegratefullyacknowledgeallthesupportwehavereceivedfrom
ourfriendsandcolleaguesattheDepartmentofEngineeringCyberneticsatNTNU.
Inparticular,wethankIdarHaugstuenforourcooperationinconjunctionwithhis
M.Sc.projectonsnakerobotsin2009/2010.Moreover,wethankChristianHolden
for providing useful feedback to the material in this book, and we thank Alexey
Pavlov for our talks and his many useful suggestions regarding our research. For
theiruntiringhelpandeffortswiththeexperimentalsystemsconsideredinthisbook,
wethankTerjeHaugen,PerIngeSnildal,andGlennAngelatthemechanicalwork-
shopofthedepartment.WealsothankStefanoBertelliforhispositivespiritandfor
hishelpwithdocumentingtheexperimentalresults.
We owe many thanks to our friends and colleagues at SINTEF Applied Cyber-
neticsfortheirsupportandforcontributingtoapositiveandstimulatingworken-
vironment.Inparticular,wethanktheResearchDirector,StureHolmstrøm,forhis
enthusiasmandhiswillingnesstofinanciallysupportresearchonsnakerobots.We
are thankful to Aksel A. Transeth, Sigurd Fjerdingen, and Erik Kyrkjebø for their
positivityandforourmanyinterestingdiscussionsrelatedtosnakerobotsoverthe
last years. A special recognition goes to Aksel A. Transeth for contributing to the
researchunderlyingthisbookwithhisknowledgeandexpertiseofsnakerobots.We
thank Geir Mathisen, Espen Helle, and Knut Vidar Skjersli for their work on cir-
cuitboardsandsoftwarefor theexperimentalsystemsconsideredinthebook.We
aregratefultoAndersBeitnesforconceivingtheideaofaself-propelledfirehose,
which initiated research on snake robots at SINTEF and NTNU. We also thank
WheekoandKulkofor theiroutstandingandobedientperformanceduringexperi-
ments,andfornevercomplainingaboutlateworkhours.
Finally,weexpressourdeepestgratitudetotheNorwegianUniversityofScience
andTechnology(NTNU)andSINTEFforprovidingtheresourcesandenvironment
thatmadeitpossibletowritethisbook,andtotheResearchCouncilofNorwayfor
supportingourresearchonsnakerobots.
Trondheim,Norway PålLiljebäck
KristinY.Pettersen
ØyvindStavdahl
JanTommyGravdahl
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 BackgroundandMotivation . . . . . . . . . . . . . . . . . . . . . 1
1.2 BiologicalSnakes . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 TheAnatomyofSnakes . . . . . . . . . . . . . . . . . . . 5
1.2.2 TheLocomotionofSnakes . . . . . . . . . . . . . . . . . 7
1.3 PreviousWorkonModelling,Mechatronics,andControlofSnake
Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 PreviousWorkonModellingandAnalysisofSnakeRobots 10
1.3.2 Previous Work onImplementationof PhysicalSnake
Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.3 PreviousWorkonControlofSnakeRobots . . . . . . . . . 22
1.4 TheScopeofThisBook . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.1 AnAnalyticalApproach . . . . . . . . . . . . . . . . . . . 27
1.4.2 SnakeRobotsWithoutaFixedBase. . . . . . . . . . . . . 27
1.4.3 APlanarPerspective . . . . . . . . . . . . . . . . . . . . . 27
1.4.4 LocomotionWithoutSideslipConstraints. . . . . . . . . . 28
1.4.5 MotionBasedonLateralUndulation . . . . . . . . . . . . 28
1.5 AnOutlineofThisBook . . . . . . . . . . . . . . . . . . . . . . 28
1.5.1 Outline of Part I—Snake Robot Locomotion on Flat
Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.2 OutlineofPartII—SnakeRobotLocomotioninCluttered
Environments . . . . . . . . . . . . . . . . . . . . . . . . 32
1.6 PublicationsUnderlyingThisBook . . . . . . . . . . . . . . . . . 34
PartI SnakeRobotLocomotiononFlatSurfaces
2 AComplexModelofSnakeRobotLocomotiononPlanarSurfaces . 39
2.1 TheRelationBetweenThisChapterandPreviousLiterature . . . . 40
2.2 BasicNotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 TheParametersoftheSnakeRobot . . . . . . . . . . . . . . . . . 40
2.4 TheKinematicsoftheSnakeRobot . . . . . . . . . . . . . . . . . 42
xi
xii Contents
2.5 TheGroundFrictionModels . . . . . . . . . . . . . . . . . . . . 45
2.5.1 TheFrictionModelsandTheirRoleinThisBook . . . . . 45
2.5.2 ACoulombFrictionModel . . . . . . . . . . . . . . . . . 46
2.5.3 AViscousFrictionModel . . . . . . . . . . . . . . . . . . 47
2.6 TheDynamicsoftheSnakeRobot . . . . . . . . . . . . . . . . . 48
2.7 SeparatingActuatedandUnactuatedDynamics . . . . . . . . . . . 50
2.8 PartialFeedbackLinearisationoftheModel . . . . . . . . . . . . 52
2.9 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Developmentof a MechanicalSnake Robotfor Motion Across
PlanarSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 TheRelationBetweenThisChapterandPreviousLiterature . . . . 55
3.2 TheJointActuationMechanism . . . . . . . . . . . . . . . . . . . 56
3.3 ThePassiveWheels . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 ThePowerandControlSystem . . . . . . . . . . . . . . . . . . . 59
3.5 TheExperimentalSetupoftheSnakeRobot . . . . . . . . . . . . 59
3.6 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 AnalysisandSynthesisofSnakeRobotLocomotion . . . . . . . . . . 63
4.1 TheRelationBetweenThisChapterandPreviousLiterature . . . . 64
4.2 IntroductiontoNonlinearControllabilityAnalysis . . . . . . . . . 65
4.3 StabilisabilityPropertiesofPlanarSnakeRobots . . . . . . . . . . 67
4.4 ControllabilityAnalysisofPlanarSnakeRobots . . . . . . . . . . 68
4.4.1 ControllabilitywithIsotropicViscousFriction . . . . . . . 69
4.4.2 ControllabilitywithAnisotropicViscousFriction . . . . . 69
4.5 AnalysisofPropulsiveForcesDuringSnakeLocomotion . . . . . 74
4.6 SynthesisofPropulsiveMotionfortheSnakeRobot . . . . . . . . 76
4.7 TheGaitPatternLateralUndulation . . . . . . . . . . . . . . . . . 80
4.8 TheControlSystemoftheJoints . . . . . . . . . . . . . . . . . . 81
4.8.1 ASimpleJointController . . . . . . . . . . . . . . . . . . 81
4.8.2 AnExponentiallyStableJointController . . . . . . . . . . 82
4.9 AnalysisofTurningMotionDuringLateralUndulation . . . . . . 82
4.10 AnalysisofRelativeMotionBetweenConsecutiveLinksDuring
LateralUndulation . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.11 ChapterSummary . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5 PathFollowingControlandAnalysisofSnakeRobotsBasedonthe
PoincaréMap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1 TheRelationBetweenThisChapterandPreviousLiterature . . . . 90
5.2 IntroductiontoPoincaréMaps . . . . . . . . . . . . . . . . . . . . 91
5.2.1 GeneralDescriptionofPoincaréMaps . . . . . . . . . . . 91
5.2.2 PracticalApplicationofPoincaréMaps . . . . . . . . . . . 93
5.3 StraightLinePathFollowingControlofSnakeRobots . . . . . . . 94
5.3.1 ControlObjective . . . . . . . . . . . . . . . . . . . . . . 94
5.3.2 TheStraightLinePathFollowingController . . . . . . . . 95
5.4 StabilityAnalysisofthePathFollowingControllerBasedonthe
PoincaréMap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
