MODELLING AND CONTROL STRATEGY OF ROBOTIC YO-YO

ABSTRACT- In the paper we address a problem of controlling an oscillating motion with a robot. As the object we have selected a yo-yo. Yo-yo is a toy made of two discs connected with a short thin axle, which can be moved up and down by moving a string tied

ProceedingsofRAAD’03,12thInternationalWorkshoponRoboticsinAlpe-Adria-DanubeRegion

Cassino,May7-10,2003

MODELLINGANDCONTROLSTRATEGYOFROBOTICYO-YO

ˇLeonZlajpah

JoˇzefStefanInstitute

Jamova39,1000Ljubljana,Sloveniaemail:leon.zlajpah@ijs.si

ABSTRACT-Inthepaperweaddressaproblemofcontrollinganoscillatingmotionwitharobot.Astheobjectwehaveselectedayo-yo.Yo-yoisatoymadeoftwodiscsconnectedwithashortthinaxle,whichcanbemovedupanddownbymovingastringtiedtotheaxle.Althoughitisveryeasytoplaywithyo-yoforahuman,designingacontrolsystemforarobotisquiteachallenge.Wepresentasimpli edmodelofayo-yowhichisintendedforcontrolanalysisanddesign.Ourmodelhasonedegree-of-freedomandthebehaviourattheendofthestringismodelledasanimpact.Nextwediscussthecontrolstrategyandpresentacontrolmethodwhichallowsplayingtheyo-yoatselectedtopheight.

Keywords:Robotjuggling,Oscilatorysystems,Yo-yomodelling,VisualfeedbackINTRODUCTION

Inthelastyearstherehasbeenagrowinginterestinrobotsystemsthatarecapableofperformingthecyclictasks.Oneoftheexcitingtasksisjuggling[5,1,6]orplayingwithdifferenttoys[6,7,3],amongwhichisalsoayo-yo[2,4].Commontoallofthemisthatplayingwiththemisusuallymoreorlessaneasytaskforahuman,ly,dexterityofthesystemandsynchronizationwiththetoyarerequired.Ahumancanusehissensestolearnhowtooperateatoy.However,developingaroboticsystemthatcanperformthesamejobrequirescomplexsensorysystemsandadvancedcontrolstrategies.Yo-yoisatoymadeoftwodiscsconnectedwithathinshortaxle.Astringistiedtotheaxleandtheoperatorcontrolsthemotionoftheyo-yobymovingitupanddown(seeFig.1).Theobjectiveistoattainaperiodicmotionoftheyo-yo.Foranef cientroboticyo-yoacorrespondingmodelisneeded.Therearesomemod-elsofyo-yoavailableinliterature.Agoodinsightintothebehaviouroftheyo-yoisgivenin[4].Themotionoftheyo-yoisdividedintofourphases,andeachofthemisanalysed.Asthederivedmodelisverycom-plex,theauthorsproposeasimpli edmodel.Howev-er,someoftheirassumptionsaretoorestrictive,espe-ciallyneglectingthediameterofthestring.In[2],asimpli edmodelisgiven,buttheauthorsassumethattheenergylossisduetothefrictionandtheyneglecttheimpact.Additionally,theyproposecontrolmethodforroboticyo-yo.

Inthepaperwedealwithmodellingandcontrolstrate-giesfortheyo-yo.Inthe rstsectionweanalysethe

behaviouroftheyo-yo.Forthatwehavemademea-surementsofthemotionandforces.Nextweproposeasimpli edoneDOFmodel,whichcapturesallimpor-tantfeaturesoftheyo-yo.Inthethirdsectionwedis-cussthecontrolstrategiesandinthelastsectionweillustratetheproposedcontrolbyasimulation.ANALYSISOFYO-YOMOTION

Beforemodellingwehavemeasuredthemotionofayo-yowithandwithouthumaninteraction.Wehavemeasuredthepositiontrajectoriesandstringforces.Theexperimentalsetupforthemotionanalysiscon-sistsofanopticalsystemElitewhichcanmeasurea3Dpositionusingpassivemarkersandinfraredcam-eras.Forourmeasurementswehaveusedtwocam-eras.Fig.1showsacameraandayo-yowithamarkerattachedtothecenterofadisc.Thesystemoperatesat100Hzandtheaccuracyisaround1mm.Theparame-tersoftheyo-yoaregivenlater.

Wehaveanalysedtwosituations:themotionwithoutmovingthehand(stringisrigidlyrestrained)andwhenahumanplayswiththeyo-yo.Figure2showsthemotionoftheyo-yowithouthumaninteraction.Wecannoticethattheamplitudedecreaseswitheachperi-od.Furthermore,somesmalldisturbingoscillationsinxandydirectioncanbeseen.InFig.3theverticalmotionofthehandandtheyo-yoisshownwhenahumanisplayingwiththeyo-yo.Wecanseethatthehumancancontroltheyo-yowithupanddownmotionofthestringsothattheamplitudeoftheyo-yomotionisapproximatelyconstant.

Nextwehavemeasuredtheforcesinthestring