Robot and Multibody Dynamics: Analysis and Algorithms

531 Pages·2011·3.11 MB·English

by  Abhinandan Jain (auth.)

Robot and Multibody Dynamics

Abhinandan Jain
Robot and Multibody
Dynamics
Analysis and Algorithms
123
AbhinandanJainPh.D.
JetPropulsionLaboratory
4800OakGroveDrive
Pasadena,California91109
USA
[email protected]
ISBN978-1-4419-7266-8 e-ISBN978-1-4419-7267-5
DOI10.1007/978-1-4419-7267-5
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2010938443
(cid:2)c SpringerScience+BusinessMedia,LLC2011
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
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Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
In memoryof GuillermoRodriguez,
anexceptional scholaranda gentleman.
To myparents,
and tomywife, Karen.

Preface
“Itisaprofoundlyerroneoustruism,repeatedbycopybooksandbyeminentpeoplewhen
they are making speeches, that we should cultivate thehabit of thinking of what we are
doing. The precise opposite is the case. Civilization advances by extending the number
ofimportantoperationswhichwecanperformwithoutthinkingaboutthem.Operationsof
thoughtarelikecavalrychargesinabattle–theyarestrictlylimitedinnumber,theyrequire
freshhorses,andmustonlybemadeatdecisivemoments.”
AlfredNorthWhitehead
Robotics,anditsneedforreal-timecontrol,hasexpandedresearchinmultibody
dynamicsbeyondmodelingandsystematicformulations,tocomputationalandcon-
trolissues.Whilesignificantprogresshasbeenmadeintheseareas,themathemat-
icalcomplexityofthesystemdynamics,andthepaucityofanalyticalconceptsand
mathematicaltoolstomanagethecomplexity,presentimposingchallenges.
The body of work known as the spatial operator algebra (SOA) providessuch
analyticalandmathematicaltechniquesthataddressthesechallenges.TheSOApro-
videsspatialoperatormathematicalconstructs,thatconciselydescribethesystem
dynamicsandenabledynamicsanalysisinaunifiedandgeneralsetting.
Thattheequationsofmultibodydynamicscanbedescribedbyanalgebraofspa-
tialoperatorsiscertainlyofmathematicalinterest.However,theSOAalsoprovides
themeanstomanipulateatahighlevelofabstractiontheequationsdescribingmulti-
bodybehavior.Thesignificanceofthisgoesbeyondthemathematicsandisuseful
inapracticalsense.Atanystageofthemanipulationofequations,spatiallyrecur-
sive algorithmsto implement the operator expressionscan be readily obtained by
inspection.Therefore,thetransitionfromabstractoperatormathematicstopractical
implementationisstraightforward,andoftenrequiresonlyasimplementalexercise.
Thefocusofthisbookisonprovidingacomprehensiveandcoherentdescriptionof
the SOA methodologyand techniques,and ofthe interplaybetweenmathematical
analysis,structuralproperties,andcomputationalalgorithms.
Thematerialinthisbookservesasapointofdepartureforfurtherexplorationof
topicsinmultibodydynamics.Thus,whilethetextiswritteninastylethatisacces-
sible to a newcomer,it wouldbe bestappreciatedby practitionersandresearchers
inthefield.
vii
viii Preface
Thebookisorganizedintothreeparts.Part1,consistingofChaps.1–7,isastudy
ofthedynamicsofrigid-link,serial-chainsystems.Thesearethesimplestexamples
of multi-linksystems. Theyserve to introducethe notionof spatialoperators,and
to developthe conceptsof mappingoperatorexpressionsinto low-ordercomputa-
tionalalgorithms.InPart2,consistingofChaps.8–13,theoperatortechniquesare
generalizedtoincludethebroaderclassofmultibodysystems.Graphtheoryideas
areusedtodescribethestructureoftheoperatorsatalevelofabstractionthatmakes
themindependentofthesize, thetopologicalstructure,andthedetailedproperties
of the linkages. Part 3 is an exploration of the application of SOA techniques to
advancedtopics.Theseincludemethodsforpartitioningandsub-structuringmulti-
bodymodels,constraintembeddingfortransformingclosed-chainsystemsintotree
systems,thedynamicsofunder-actuatedsystemsandfree-flyingsystems,derivation
ofanalyticalsensitivityexpressions,anddiagonalizeddynamicsformulations.
The text is interspersed with exercises that further explore a topic or present
a related idea. All solutions are provided at the end of the book. Key results are
summarizedinlemmaswithself-containedassumptionsandconclusions.
Rarelyisthereasingleapproachorsolutionthatworksforthevarietyofprob-
lems encounteredwhen workingwith robotand multibodysystem dynamics. The
emphasis of this book therefore is on deepeningthe theoretical and mathematical
understandingof the operatortools, and on the rich tapestry of inter-relationships
amongthem.Asingletopicisthussometimesexploredfromdifferentangles,and
themesandconceptscuttingacrossdifferentcontextsarehighlighted.
Acknowledgments
My introduction to the fields of robotics and multibody dynamics began when
IjoinedtheJetPropulsionLaboratory(JPL).GuillermoRodriguezhadrecentlydis-
coveredtherichparallelsbetweenthemathematicaltheoryunderlyingoptimalfil-
teringandestimationtheory,andthestructureofthedynamicalpropertiesofrobotic
systemsthatformedthebasisoftheSOA.Ihadthegoodfortuneofjoininginthis
pioneering research. and, until his untimely passing, had the incredible personal
experienceofcollaboratingandworkingwithGuillermo.
Overtheyears,Ihavebenefitedinnosmallmeasurefromthecontinuousinter-
actionsandsupportfrommanyexceptionalcolleaguesatJPL.KenKreutz-Delgado
introducedmetotheearlydevelopmentsoftheSOA methodology.GuyMan’svi-
sion helped initiate the “real-world” application of the SOA techniques to solve
challengingdynamicsmodelingproblemsforNASA’sspacemissions.Iamgrateful
tomycolleaguesatJPL’sDARTSLab,includingBobBalaram,JonathanCameron,
Christopher Lim, Marc Pomerantz, Hari Nayar, Jeff Biesiadecki and many others
whohavecontinuedtoadvancethemethodologyandmakepossibleitsapplication
tochallengesinspacerobotics.IthasalsobeenapleasuretoworkwithNagarajan
Vaidehiin the non-engineeringapplicationof the SOA ideas to the moleculardy-
namicsarena.I wouldliketo thankJohnWen andRich Volpefortheir persuasive
Preface ix
encouragementtoworkonandtopublishthisbook.Last,butnotleast,Iwouldlike
to thank my family, Karen, Aarti, and Nikhil, who valiantly helped with figures,
proof-reading,andstylisticsuggestionsforthetext,andfortheirincrediblepatience
andforbearancethroughthemonthsofitspreparation.