MODELLING AND CONTROL STRATEGY OF ROBOTIC YO-YO(5)

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

motionreasonsshouldcycleandthethepositionnotbeendshouldofdrasticthebehandandequal,atjerky.theForpracticalh(tbeginningofthestart)=h(tend).TounderstanddesigntheThehowclose-loopthecontrolleritisimportanttotionenergydependsmainpointistheyo-yoenergymotiontransfer.canbeThecontrolled.topposi-thestoredoninthetheenergyyo-yoatofthethetopyo-yo.positionThepotentialenergypotentialbylostduringenergylastinimpacttheprevioustopposition,issumtheofplaysthedownthehandessentialandyo-yoduringlastcycle.Observingandtheenergyhowsuppliedahumanthenup.(Fig.From3)weEq.can(7)seeitthatthehandgoesBasedweonwhenmeasurementsthehandfollowsthatitisandacceleratesusingtheanddecelerates.thehaveupwardenergyfoundfromoutthethathandthetomosttheyo-yoef cientderivedisiftransfermodel,themajoroftomafterimpactaccelerationisperformedjustbeforethebot-theoftoptimingtheimpact.andtheFordownwardillustration,accelerationwehavetakestestedplacehowheightsofany ofaccelerationtwoconsecutivepulsein uencescyclesµ

theratioµ=

y i+1

i

Fig.8aofshowstheheightoftheyo-yorelativethehand(maltanddelayandthatthethetime tbetweenFig.8bgivestheratioandµacceleration

versustheaccelerationofimpacttheendsthandaccelerationpulsep)i, justt=beforeti tp.theItimpact,isopti- bet=impact.

shown0.Similarly,thatitisforoptimaldownwardifitaccelerationstartsjustafteritcouldtheWeisde nedproposeas

acontrolstrategywherethehandmotionh=khhn(ktτ),

0≤τ≤1

(16)

wherenalhnisthenominalmotionpattern,τisthenomi-ofthethepatternhandtime,motion,khandisthegaintoadjusttheamplitudetimerealandnominaltime;ktisτthe=0scalingandτfactorbetweeniswhenthemotionstarts(t=1indicatethestart)andwhenonecycletcompleted(tt<tend),respectively.Betweentwocycles,

andend,i<h

¨=0.Itstartis,obviousi+1,handthatisnottmoving,h=0,h

˙=0thanend,i tstart,imustbetbeforethecycletheimpact.oftheyoyo.AsitTheisimpossiblemomenttbelesstostartpredictmustheightstartdirectly,thehandmotionisstartedatchangingbeforethetheamplitudetheyo-yoreaches(gainkbottomposition.acertainByh)bemotion(thefactorkandthedurationoft)theyo-yopeakheightcanincreasingcontrolled.kThepeakheightcanbeincreasedbyhordecreasingktandviceversa.

a)time

response

b)ratioµoftopversusheightstheofdelaytwoconsecutive tcycles

Figure8:TopheightversustimeofaccelerationSIMULATIONEXAMPLE

Tostrategyillustrateeterswegivethesomecapabilitiessimulationoftheresults.proposedThecontrol00..05kg,ofthe0036m,I=yo-yoand2.k610 used5kgmin2,theB=simulation0,L=0.are:param-7m,rm=o=r=1.610 4nominalm.WehaveselectedtheThishandmotionpatternasshowninFig.9.ments.pattern0.15maboveThehandsatis esthebottommotionallpreviouslymentionedrequire-position.

startedwhenyo-yohasbeenThemotion.desiredpeakheighty dhasaccordingly.Therefore,Wehavegainsusedkbeenthefollowingkchangedduringhandthadtodependencies

bechangedkh=0.5(y d y )+0.05kt=

1

dwhereNoteywhenthat dandky arethedesiredandactualpeakheights.handkstantduringpeakyo-yotheremainingheighttarechangedisreachedonlytime).

(theirinvaluethemomentiscon-TheseemotionthatsimulationwiththeresultsareshowninFig.10.Wecandesiredheight.

isstableproposedandthatthecontrolpeakstrategy,heighttrackstheyo-yothe