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1、1RapidCollisionDynamicsforMultipleContactswithFrictionDannyKaufmanandDineshK.Pai∗Summary.Weexaminetheinteractionofcomplextwo-dimensionalrigidbodieswithfriction.Giventheiridealizeddescription,manydifferentfeasiblesolutionsforfrictionalcontactandcollisionarepossi
2、ble.Theusualassumptionsofnon-interpenetrationandnegligibledeformationattheglobalscaleconstraincontactbehaviors,whileincompletedescriptionsofmaterialpropertiesatthelocalscaleallowforalargeamountoflatitudeinsolutionmethods.Existingtechniquesforthemultiplecontact
3、problemwithfrictioneitherdependuponcollisionordering(propagationmethods)orapplyLCPmethods.Weproposeamethodthatgeneral-izesMoreau’simpactlawtoformulateasimplebutcompletecontactlawinwhichbothmultipleconstraintsandmultiplecontactsarepossible.Ouralgorithmfindsasimu
4、ltaneoussolutionforasystemofcontacts.Itsimplementationissimpleandobtainsreal-timespeeds.1.1IntroductionContactproblemsariseinmanyareasofapplicationincludingrobotics,graph-icsandsurgicalsimulation.Appropriatehandlingofcontactscanplayanim-portantroleinthequality
5、ofasimulation.Wefocusourattentiononrigidbodymodels.Allrealobjectsdeformtosomedegreewhencollidingwhile,problematically,rigidbodiesdonot.Wecanconsiderrigidbodiestobethelimitingcaseofobjectswhosestiffnessapproachesinfinity.Another,perhapsmorehelpfulperspectiveistov
6、iewthecollisionresponseofarigidbodymodelasaglobaldescriptionofmanysmalllocaldeformationsandtheirresultingcontactresolutions.Tocompletelydescribeacontactweneedinitialconditiondataspecifictotheobjectsathand.Additionally,wewouldliketohaveanaccuratecon-stitutivemod
7、eltodescribethebehaviorofthissysteminresponsetoany∗D.KaufmanandD.K.PaiarewithRutgers,TheStateUniversityofNewJersey,Piscataway,NJ.ThisworkwassupportedinpartbyNSFgrantsIIS-0308157,ACI-0205671,EIA-0215887,andEIA-0321057.F.Barbaglietal.(Eds.):Multi-pointInteractio
8、nwithRealandVirtualObjects,STAR18,pp.3–19,2005.©Springer-VerlagBerlinHeidelberg20054D.KaufmanandD.K.Paishockimposeduponitbyacollision.Rigidbodiesbytheirverydefinitionareassumedtolac
