Optimization of a 2 DOF Micro Parallel Robot Using

25Optimizationofa2DOFMicroParallelRobotUsingGeneticAlgorithmsSergiu-DanStan,VistrianMătieşandRaduBălanTechnicalUniversityofCluj-NapocaRomania1.IntroductionOverthelastcoupleofdecadesparallelrobotshavebeenincreasinglystudiedanddevelopedfrombothatheoreticalviewpointaswellasforpracticalapplications(Merlet,1995).Advancesincomputertechnologyanddevelopmentofsophisticatedcontroltechniqueshaveallowedforthemorerecentpracticalimplementationofparallelmanipulators.Someoftheadvantagesofferedbyparallelmanipulators,whenproperlydesigned,includeanexcellentload-to-weightratio,highstiffnessandpositioningaccuracyandgooddynamicbehavior(Merlet1995,Stan2003).Theever-increasingnumberofpublicationsdedicatedtoparallelrobotsillustratedverywellthistrend.However,therearealsosomedisadvantagesassociatedwithparallelmanipulators,whichhaveinhibitedtheirapplicationinsomecases.Mostseriousoftheseisthattheparticulararchitectureofparallelmanipulatorsleadstosmallermanipulatorworkspacesthantheirserialcounterparts.Oneofthemaininfluentialfactorsontheperformanceofthemicroparallelrobotisitsstructuralconfiguration.Thekinematicrelations,statics,dynamicsandstructurestiffnessarealldependentuponit.Afteritschoice,thenextsteponthemanipulatordesignshouldbetoestablishitsdimensions.Usuallythisdimensioningtaskinvolvesthechoiceofasetofparametersthatdefinethemechanicalstructureoftheparallelrobots.Theparametervaluesshouldbechoseninawaytooptimizesomeperformancecriterion,dependentupontheforeseenapplication.Microparallelrobotscanalsobedifficulttodesign(Stan,2003),sincetherelationshipsbetweendesignparametersandtheworkspace,andbehaviorofthemanipulatorthroughouttheworkspace,arenotintuitivebyanymeans.ThisisoneofthereasonswhyMerlet(1995)arguesthatcustomizationofparallelmanipulatorsforeachapplicationisabsolutelynecessaryinordertoensurethatallperformancerequirementscanbemetbythemanipulator.Asaresult,developmentofdesignmethodologiesforsuchmanipulatorsisanimportantissueinordertoensureperformancetotheirfullpotential.Inparticular,thedevelopmentandrefinementofnumericalmethodsforworkspacedeterminationofvariousparallelmanipulatorsisofutmostimportance.Thereisastrongandcomplexlinkbetweenthetypeofrobot’sgeometricalparametersanditsperformance.It’sverydifficulttochoosethegeometricalparametersintuitivelyinsuchawayastooptimizetheperformance.Severalpapershavedealtwithparallelrobotstooptimizeperformances(Stan,2006).Forexample,variousmethodstodetermineworkspaceFrontiersinEvolutionaryRobotics466ofaparallelrobothavebeenproposedusinggeometricornumericalapproaches.EarlyinvestigationsofrobotworkspacewerereportedbyGosselin(1990),Merlet(1994)andCecarelli(2004).Stan(2003)presentedageneticalgorithmapproachformulti-criteriaoptimizationofPKM.Mostofthenumericalmethodstodetermineworkspaceofparallelmanipulatorsrestonthediscretizationoftheposeparametersinordertodeterminetheworkspaceboundary.Amethodwasproposedtodeterminetheworkspacebyusingoptimization(Stan,2006).Inthenextsections,theplanar2-dofmicroparallelrobotofinterest,andthekinematicsforthismanipulator,ispresented.The2-dofmicroparallelrobotconsideredinthisstudyisshowninFig.3,whereitsjoints(AandC)connectedtothegroundareactiveandtheothersarepassivejoints.Theinputmotionsoftheactivejointscanbeindependentfromeachotherorbeprovidedviaasetofgearsmaintainingaspecifiedphaseanglebetweenthetwoactivejoints.Theobjectiveofthischapteristoproposeanoptimizationmethodforaplanarmicroparallelrobotthatusesperformanceevaluationcriteriarelatedtotheworkspaceofmicroparallelrobot.Furthermore,ageneticalgorithmisproposedastheprincipleoptimizationtool.Thesuccessofthistypeofalgorithmforparallelrobotsoptimizationhasbeendemonstratedinvariouspapers(Stan,2006).2.GeneticAlgorithmsforOptimizationofMicroParallelRobots2.1OptimizationbasedonGeneticAlgorithmsOptimizationistheprocessofmakingsomethingbetter.Anengineerorscientistconjuresupanewideaandoptimizationimprovesonthatidea.Optimizationconsistsintryingvariationsonaninitialconceptandusingtheinformationgainedtoimproveontheidea.Optimizationistheprocessofadjustingtheinputstoorcharacteristicsofadevice,mathematicalprocess,orexperimenttofindtheminimumormaximumoutputorresult(Fig.1).Theinputconsistsofvariables,theprocessorfunctionisknownasthecostfunction,objectivefunction,orfitnessfunction,andtheoutputisthecostorfitness.Iftheprocessisanexperiment,thenthevariablesarephysicalinputstotheexperiment.Figure1.Diagramofafunctionorprocessthatistobeoptimized.OptimizationvariestheinputtoachieveadesiredoutputThegeneticalgorithm(GA)hasbeengrowinginpopularityoverthelastfewyearsasmoreandmoreresearchersdiscoverthebenefitsofitsadaptivesearch.Geneticalgorithms(GAs)wereinventedbyJohnHollandinthe1960sandweredevelopedbyHollandandhisstudentsandcolleaguesattheUniversityofMichiganinthe1960sandthe1970s.Incontrastwithevolutionstrategiesandevolutionaryprogramming,Holland'soriginalgoalwasnottodesignalgorithmstosolvespecificproblems,butrathertoformallystudythephenomenonfunctionorprocessinputorvariablesoutputorcostEvolvingBehaviorCoordinationforMobileRobotsusingDistributedFinite-