斯坦福大学网络视频课程之机器人学

1、斯坦福大学网络视频课程之机器人学Instructor (Oussama Khatib):Okay, lets get started. So todays movie segment isabout aa speccial aactuattor. PProbabbly yoou saww thiss on tthe fiirst llecturre, buut we will see ssomemore deetailss. So this is a flexiible aactuattor thhat coomes ffrom TToshibba, annd thiis wassdevelo

2、pped inn the earlyy 90ss. It was ppresennted aat 19991 viddeo prroceeddings.Video:This neew acttuatorr is mmade oof fibber ree-enfoorced rubbeer andd is ddrivenn pneuumaticcally orhydraullicallly. Itt has 3 deggrees of frreedomm; pittch, inauddible, andd streetch, whichh areadequatte forr roboot mec

3、chanissms suuch ass finggers, arms or leegs.The acttuatorr has threee inteernal chambbers, and tthe prressurre in each can bbe conntrollledindepenndentlly thoough fflexibble tuubes. The rrubberr is ccircullarly re-ennforceed witth fibber tooreduce deforrmatioon in the rradiall direectionn.The acttua

4、torr can be fllexed in evvery ddirecttion bby conntrollling tthe prressurre in each chambber.Inaudiible develloped actuaators rangiing inn sizee fromm 1 miillimeeter tto 20 milliimeterrs indiameteer. Thhis iss the formuula meeter aactuattor. TThe deesign is eaasily miniaaturizzed beecausee ofits sim

5、mple sstructture.This iss a moodifieed verrsion. The rubbeer is reinfforcedd spirrally with fiberr so tthat rrotatiionalmovemennt is possiible. We caan appply thhese fflexibble miicro-aactuattors tto minniaturre robbotmanipullatorss. By conneectingg themm seriially, we gget ann arm with many degreee

6、s off freeedomand snaake liike moovemennts.This iss a prrototyype coonsistting oof twoo actuuatorss and a minni griipper. It hhas 7 degreees offfreedomm inclludingg the grippper. IIt cann accoomplissh dellicatee taskks, whhich ccould be haandleddonly wiith grreat ddifficculty by coonventtionall robo

7、ots.Construuctingg miniiaturee roboot mannipulaators is eaasy beecausee the actuaators also act aas theerobot sstructture. On thhe othher haad, coombiniing thhe acttuatorrs in paralllel rresultts in a mulltifinngereddrobot hhand. They form a dexxterouus hannd witth a ddelicaate toouch. This protooty

8、peconsistts of four actuaators, eachh 12 mmillimmeterss in ddiametter, aand itt has 12 deegreess offreedomm.Its abble too handdle frragilee and compllicateed worrk witth easse, beecausee the actuaatorssdeformeed to suit the sshape of thhe worrk pieece ittself. The bolt is eaasily tighttened with onl

9、yrough ssettinngs off the posittion aand orrientaation of thhe hannd beccause the aactuattors hhave ssuchgood coompliaance.Miniatuure roobots with a sofft touuch annd no conveentionnal liinks ccan bee creaated uusing theseeactuatoors. PPeoplee see the uuse off flexxible microo-actuuatorss Instruccto

10、r (Oussaama Khhatib):So, what do yoou thiink? WWhat wwould be thhe advvantagges offusing ppneumaatic iin thiis wayy? Yess?Studentt:Probbably saferr for a lott moree objeects.Instrucctor (Oussaama Khhatib):Safeer, yoou saiid? Soo safeety iss a veery, vvery iimporttant aaspecttof the desiggn of a robb

11、ot, eespeciially if thhe robbot iss goinng to interract wwith hhumanss, andd youreally dontt wantt thiss roboot to just go crrazy aand hiit andd makee a laarge iimpactt. So softactuatiion ussing ppneumaatic iis verry goood beccause it baasicallly its complliant, righht.Now anoother impliicatioon of

12、the ffact tthat yyou arre usiing pnneumattic iss the struccture of thherobot iis goiing too be llighteer, beecausee if yyou thhink aabout operaating thesee finggers wwith tthemotors or iinaudiible I thiink abbout aan armm withh motoors. YYou neeed too carrry thee motoors,you neeed to put ggears, you

13、 need a lott of sstructture tto hanndle iit, soo defiinitelly thiis is lightter,safer, more flexiible, complliant, all of thhat.Any dissadvanntage you ccan seee? Yees?Studentt:Hardder too conttrol?Instrucctor (Oussaama Khhatib):Yeahh. Bassicallly wwell, I meaan, itt depeends wwhat yyou waantto achii

14、eve, but yyou caannot expecct to achieeve thhe tassks. WWhat kkind oof tassks yoou cannnotcontroll withh thiss typee of aactuattion?Studentt:Inaaudiblle mootion?Instrucctor (Oussaama Khhatib):Inaaudiblle mootion or faast dyynamiccs if you wwant ttochange direcctionss becaause? What is thhe prooblem

15、with that inauudiblee?Studentt:InaaudiblleInstrucctor (Oussaama Khhatib):So yyeah, I meaan bassicallly thee respponse of thhis iss goinng tobe sloww becaause yyou arre usiing aiir preessuree and you ccannott pushh the air ppressuure too a poointwhere yyou caan reaally gget faast dyynamiccs. Weell la

16、ater oon in the qquarteer we will see aa concceptthat coombinees thiis ideea of usingg pneuumaticc, whiich iss lighht to carryy, andd woulld ressult iintoa nice lightt struucturee, commbine it wiith otther ttype oof acttuatioon to bringg hybrrid acctuatiion inna way tthat ccombinnes booth thhe advva

17、ntagges off the lightt struucturee and the ffast ddynamiics thhatwe needd to aachievve alll the diffeerent taskss thatt woulld reqquire the rrobot to reespondd quicckly.Yes?Studentt:Is tthere any ggood wway too inaaudiblle thhat, llike, you ddont actuaally kknow wwhereyoure inauudiblee?Instrucctor (

18、Oussaama Khhatib):Welll thatt inaaudiblle, yyou woould ssee thhe robbot waas likketurningg. Okaay, annyone wouldd likee to aanswerr thiss quesstion? Im sure you hhave aan ideea, buut,this iss reallly noot funndamenntal tto thee roboot dessign. It iss moree on tthe faact thhat wee havee noexternaal f

19、eeedbackk or nno touuch, oor we are nnot ussing tthe innformaation aboutt the touchh torealizee thatt we aalreaddy lefft thaat conntact.But thiis is actuaally ssomethhing tthat yyou caan addd on ttop off the desiggn to likke wouuld What kiind off senssory yyou woould uuse?Studentt:Presssure sensoor?

20、Instrucctor (Oussaama Khhatib):Toucch sennsor, you mmean llike yyou waant too knoww if yyou arretouchinng or not?Studentt:Presssure wouldd be inauddible to kknow eexactlly likke howw far you aare, bbut wiithsomethiing liike thhat, inauddible. Likke innaudibble pput soomethiing thhat exxactlyy tellls

21、 youu thepositioon of the eend.Instrucctor (Oussaama Khhatib):So wwe cann put a sennsor aat thee end that is loocalizzed att thetip of the ffingerr and then we caan feeel wheether the ssensorr is oon or off. That is juust toouch,but if you wwant mmore iinformmationn abouut thee presssure, you need a

22、 sennsor, inauudibleesensor that wouldd meassure.But theen thee probblem I meean, nnow wee comee intoo a muuch haarder probllem, wwhich is thhefact iff youre hooldingg someethingg leets iimaginne witth youur twoo finggers yyouree holddingsomethiing. AAnd thhere iis alwways sslip, so yoou neeed to me

23、asuure thhe sliip so that you ccanapply llargerr presssure.And to do thhat yoou neeed thee sortt of ddynamiic innaudibble. So thhere hhas beeen a lot oof worrkactuallly in the ggroup of Maark Cookoskeey. A lot oof ressearchh on inauddible, dynnamicinaudiible and aalso tthe iddea off usinng preessure

24、e is aa veryy goodd ideaa becaause iin facct, byymeasuriing thhe preessuree and the ccontrool preessuree therre is a diffferennce beetweenn whatt youare exppectinng andd whatt you see.You willl be able to deeduce some inforrmatioon aboout coontactt. Theere waas a ccommennt theere?Studentt:Inaaudibll

25、e seensorss on tthe suurfacee and use tthose to fiind thhe possitionn?Instrucctor (Oussaama Khhatib):Um hhm. Noow if you iinstruument the eenviroonmentt,obvioussly yoou willl be able to geet a llot off infoormatiion abbout tthe ennvironnment, but that iscostly. So yyou waant moore too put the ssenso

26、rrs on the rrobot. But theree is aanotheer typpe ofsensor that will give you mmore iinformmationn abouut thee enviironmeent thhat especciallyy abouutwhetherr you are iin comm I mean, closse or not, like to loocalizze andd see wheree thinngs arre.To see wheree thinngs arre, whhat doo we ccall?Student

27、t:Inaaudiblle Innstrucction:Vision. Put couplle of camerras annd youu woulld seee wherre youu are with respeect too theworld. And sso youu havee a meechaniism, yyou haave thhe conntrolllers, but rreallyy you need toclose tthe looop. BBut too closse thee loopp you need perceeptionn, andd percceptioon

28、 couuld ussesensorss in tthe ennvironnment, senssor exxternaal thaat aree moniitorinng thee enviironmeent orrinstrummentattion oon thee roboot itsself.Anyway, thiss cutee desiign acctuallly wass purssued ffor a couplle of yearss. Theey buiilt evven abig robbot thhat iss walkking wwith tthose legs, a

29、nd Im nnot suure iff we wwill ssee itt. Theen thiisprojectt justt I mean, theyy didnnt goo any furthher.It is llike mmany oof thee desiigns tthat mmake uuse off air presssure, only you eend upp withh realllylimitattions, a loot of limittationns on the uuse off onn the abiliity off the robott to ffor

30、m ttasks.And in fact theree is aa lot of woork tooday iin thiis areea thaat is with artifficiall musccles tto creeatefaster musclles thhat usse airr presssure.And theere arre manny diffferennt sollutionns thaat willl pussh thiis litttle ffurtheer, buut stiill yoou havvelimitattions, and as I said, w

31、e wwill ddiscusss litttle bbit moore abbout tthose issuees of desiggn,especiaally iin thee conttext oof saffety bbecausse saffety rreallyy, reaally iis beccomingg a veeryimportaant asspect in roobot ddesignn becaause wwe havve beeen worrking with robott wiithinaudiible robotts.So inaaudiblle roobots

32、 are wworkinng aloone orr workking wwith pparts and oobjectts youu dontreally worryy too much if thhere iis an acciddent jjust bbetweeen wwell, the rrobot and tthatenvironnment. But if yoou aree goinng to work with humanns, yoou reaally hhave tto makke surrethat thhere iis no dangeer to the hhuman,

33、and that is reeally a chaallengging pprobleem, soo we wwillcome baack too thiss lateer.Any othher coommentt abouut thiis? Okkay. AAll riight, so leets ggo bacck to the llecturre. Soo lastttime wee saw this tool we caall hoomogenneous transsform, and the hhomogeeneouss trannsformmreally has sseveraal

34、 intterpreetatioons, oor cann fulffill sseveraal funnctionns.And thee firsst onee of tthem iis thee factt thatt trannsformmationn likee thiss alloows uss to ddescriibe thheframe, so frrame BB is ddescriibed wwith tthe reespectt of fframe A givven thhis trransfoormatiion. SSoif I knnow thhe hommogene

35、eous ttransfformattion bbetweeen B aand A, thatt is tthis ffour bby fouur TMeetricssthat deescribbes A B iin wwith aa relaation to A.Then I have descrriptioon of this framee B, aand thhis deescripption contaains tthe rootatioon of theaxis off framme B wwith rrespecct to A, annd thee locaation of thh

36、e oriigin oof fraame B with respeectto framme A. Now wwe saww alsoo thatt therre is anothher roole thhis hoomogenneous transsformaationcan plaay.And thiis seccond rrole thirrd rolle, whhateveer, doo you have an iddea whhat caan we use tthistransfoormatiion foor? Whhat caan we whaat cann thiss tranns

37、formmationn helpp us ddo?Studentt:Operrationns?Instrucctor (Oussaama Khhatib):Operrationns, thhat iss wee can inauudiblee theetransfoormatiion ass an ooperattor thhat iss actiing onn a veector and cchangiing thhis veector, rotaatingthe vecctor oor rottatingg and transslatinng thaat vecctor. So thhis

38、 iss a seecond interrpretaation of thhetransfoormatiion ass an ooperattor. OOr? Onne morre?So if yyou haave a vectoor in spacee, desscribee withh resppect tto somme fraame, BB, andd you want itsdescripption in a diffeerent framee, A, can yyou usse thiis traansforrmatioon? Soo thiss is tthemappingg,

39、whaat we call mappiing. TThat iis, wee takee the descrriptioon of vectoor P iin a fframe well, BB, andd we mmap itt to aa desccriptiion inn framme A.So the vectoor B, this greenn vecttor ovver thhere iis noww the red vvectorr thatt is tthis oone,describbing tthis ppoint in frrame AA.And youu can see

40、 hhere wwe havve twoo diffferentt vecttors. If thhere wwas noo trannslatiion, tthenbasicallly itt willl be tthe saame veector with two ddifferrent sset off compponentts. Annd as yousaid, wwe havve alsso thee desccriptiion off homoogeneoous trransfoormatiion ass an ooperattor.That iss we ttake aa vec

41、ttor P11 and changge it to a vectoor P2. So tthe veector P1 iss now P2 affterthis trranslaation. So tthese diffeerent roless of tthe hoomogenneous transsformaation use tthe saamemathemaatics, but the aappliccationn, thee inteerprettationn is ggoing to bee diffferentt and we haave toopay atttentioon

42、to the wway wee applly thee defiinitioon.So the next questtion tthat wwe havve to addreess iss how we noow usee. So if yoou remmemberr,when I talkeed aboout hoomogenneous transsformaation, I saaid byy buillding this metriics, ffour bbyfour meetricss in aa highher diimensiional spacee, we are aable t

43、to havve a hhomogeeneouss relaationbetweenn vecttors.So thiss propperty is gooing tto hellp us propaagate and ggo froom onee framme to anothher annd havvedescripptionss thatt are relatted byy the indivviduall trannsformmationns bettween framees. Soo heree isan exammple; you hhave tthis ccameraa moni

44、itorinng thee enviironmeent annd herre in fact you hhavea robott, a mmobilee maniipulattor, tthis iis Rommeo, tthat iis ddid I introoduce Romeoo and Julieet toyou? Noo? Nott yet?Okay, wwell mmaybe you wwill hhave aa channce laater. So Roomeo iis esssentiaally aa mobiileplatforrm, a holonnomic mobill

45、e plaatformm withh an aarm, aand itt alloows yoou to move in thheenvironnment and mmanipuulate the eenviroonmentt. Butt becaause oof thee plattform, thiss is ddoneeverywhhere iin thee worlld, noot likke wheen youu havee justt one arm ffixed on a tablee wherre youubring mmateriial too be pprocesssed.

46、Here yoou aree ablee to eexplorre thee humaan envvironmment. And, in faact, tthe roobot iis movvingand itss locaation is allways diffiicult. So tthe quuestioon is how ccan wee, forr insttance, locaate thhisrobot? So yoou neeed to find, actuually, the transsformaation betweeen thhe basse fraame off t

47、herobot wwith rrespecct to the ccameraa.This iss litttle biit diffficullt unlless yyou arre ablle to find elemeents aand diiffereent thhings. Sosupposee the camerra is monittoringg the endoffactorr. So you hhave tthe enndofacctor hhere aandyou cann see it. SSo if you hhave tthis rrelatiion thhat iss

48、 in aa giveen fraame, yyou arre ablle to see aandidentiffy thee end of faactor, whicch is, lets sayy thiss framme. Thhen thhroughh the otherr pathh thattis goinng froom herre to the bbase tthrouggh thoose trransfoormatiions tto thee endoofactoor, yoou havveanotherr pathh.You knoow thiis andd yoou kn

49、oow thiis theen youu can compuute thhis. AAnd wee needd to bbe ablle topropagaate annd ressolve this transsform equattion. Now tthis ccomes everyywheree, yeaah, weell,Romeo iis cappable inauudiblee. I will show you mmaybe laterr if wwe havve a cchancee, litttle ttimein the lectuure.So agaiin, whhere

50、 yyou arre innaudibble, wheree is tthe baase annd youu havee thiss loopp in ttheenvironnment if yoou aree obseervingg the envirronmennt, annd youu needd to bbe ablle to go thhroughhthe traansforrmatioons. FFrom tthe baase too the endoffactorr, youu havee alwaays thhe forrwardkinemattics tthrouggh al

51、ll the transsformaationss betwween llinks.But obvviouslly witth thee grouund yoou havve sliippagee and you ccannott deteerminee exacctly ttherelatioonshipp betwween aa fixeed cammera aand thhe loccationn of tthe baase.So firsst of all, how wwe commbine transsformaationss; letts coonsideer twoo framm

52、es, aand coonsideerthat noow were gooing tto inttroducce a tthird framee, C, so wee havee a trransfoormatiion frrom Cto B, wwe havve a ttransfformattion ffrom BB to AA, andd obviiouslyy Im interrestedd in tthetransfoormatiion frrom C to A, the totall trannsformmationn.I wouldd likee to ccombinne the

53、ese twwo traansforrmatioons. SSo if we haave a vectoor, veectordescribbed inn C, tthat iis, wee havee a pooint PP, desscribee in fframe C. Thhe queestionn is wwhat iis theedescripption of thhis veector in frrame AA?Well thhe ressult iis obvvious; I meean prrobablly youu alreeady gget itt. We are ggo

54、ing to muultipllythese ttwo trransfoormatiions. And tto proove itt, letts fiirst ccomputte whaat is the ttransfformattionto framme B. P andd B iss simpply gooing tto be obtaiined bby thee homoogeneoous trransfoormatiionfrom C to B, righht?Now if we wrrite tthe saame thhing ffor thhis pooint iin B, w

55、e caan go to A throuugh thhehomogenneous transsformaation, B too A. NNow iss we ssubstiitute this with the eexpresssion thatuses C, we wwill oobtainn thiss relaation; thatt is, the vvectorr in CC is ttransfformedd intoo thedescripption in frrame AA usinng thiis forrm, whhich mmean tthat eessenttiall

56、yy we aare gooing ffromdescripption in C to A. Thatt is, from C to A. Annd thaat meaans esssentiially, thetransfoormatiion coorresppondinng to thesee two framees, suuccesssive fframess, is goingg to bbe theeproductt of tthe maatricees, thhe hommogeneeous ttransfformattion, C, B and BB to AA.And youu

57、 can see tthis hhas a nice form. You just elimiinate the BB and yourre goiing frrom Cto A wiith thhis nootatioon. Soo, thaat is reallly thee advaantagee of ccom I meaan, hoomogenneoustransfoormatiion iss thatt you have a mattrix aand thhen whhen yoou havve mulltiplee frammes, oorwhat yoou neeed to d

58、o iss to mmultipply thhese mmatricces.So now if wee multtiply C to B, B to A, thiss is wwhat wwe willl obttain. We wiill seee herre thaatthe strructurre of this transsformaation is gooing tto maiintainn the struccture with respeect too therotatioons. SSo we have the ssame pproperrties of rootatioon.

59、 Itt is CC to AA throough CC/B annd B ttoA.And thiis vecctor, whichh is tthe orrigin, the vectoor loccatingg the origiin of C witth resspect to A,well itt is eessenttiallyy compputed by loocatinng thee origgin off C wiith reespectt to BB, rottatingg it ttothe rigght frrame, and tthen aaddingg the of

60、fseet duee to tthe orrigin of B with respeect too A.So I mean, the logicc is vvery ssimplee. Its vecctor ccomputtationn, butt agaiin, whhen yoou do themultipllicatiion, iit is autommaticaally ttaken into accouunt annd youu get thosee resuults. So noowthat wee havee thiss relaation that wouldd alloow