ExpBrai nRes(1981)42: 223- 227 E x m e n t a lB r a n R e s e a rc h9Springer-Verlag1981 ResearchNote SpatialControlofArmMovements* P. Morasso IstitutodiEl et t rot ecni caUniversitfidiGenova, Vi al eCausa13,1-16145Genova, Italy Summar y. Hu ma n subj ect swer ei nst r uct edt opoi ntonehandt odi f f er ent visualt ar get swhi chwer e r andoml ysequenced, usingapar adi gmwhi ch al l owedt wodegr eesof f r e e dom( shoul der , el bow).The t i mecour seof t hehandt r aj ect or yandt hej oi ntangul arcurveswer eobser ved. Thel at t er exhi bi t ed pat t er nswhi chchangemar kedl yf or di f f er ent move-ment s, wher east hef or me r pr eser vesimilarcharac- teristics(inpar t i cul ar , asinglepe a ke dt angent i alvel oci t ycurve). Thehypot hesi sist henf or mul at ed t hat t hecent ral c omma ndf or t hesemovement s is f or mul at edint er msof t r aj ect or i esof t hehandin space. Keywords: Ar mt r aj ect or i es-Mul t i pl edegr eesoff r eedommovement s -Tangent i al vel oci t y -Cent r almot or commands Movement s of t hear mcanbedescr i bedei t her in t er msofspat i al t r aj ect or i esoft hehandor of angul ar curvesoft hej oi nt s. Itist husi mpor t ant t odet er mi ne whet her t hemot or commands arecent ral l yr epr e-sent edint er msof j oi nt sangl esor of spat i al t raj ec- t ori es. Inor der toanswerthisquest i on, itispossi bl e t oobser vedi f f er ent movement s whi chcor r es pondt o t hesamemot or t askandt ol ook f orc ommonf eat ur es amongt hedi f f er ent movement s . Thi snot er epor t s t heresul t of exper i ment s Iinwhi chhumansubj ect s *Researchsupport edbyt heIt al i anResearchCouncil(Bi l at eralResearchCont ract )andbyN. I . H. Gr ant sNS09343andAM 26710 1Theexperi ment swereper f or medint hel abor at or yofProf.E. Bizzi( M. I . T. , PsychologyDepar t ment , Cambri dge, MA,USA). Stimulusact i vat i onanddat aacquisitionweremanaged bymeansofaPDP11/10comput erwi t haLPS11peri pheralunit. Subsequent dat aanalysisandst i mul at i onwasper f or med onaPDP11/34comput er, att heElectricalEngi neeri ng Depar t ment , GenoaUni versi t y, Italy Present address:Massachuset t sInst i t ut eofTechnol ogy, Depar t -ment ofPsychology,Cambri dge, MA02139,USA wer ei nst r uct edt opoi nt onehandt odi f f er entvisual t arget swhi chwer er andoml ysequenced.Theexper i ment al par adi gmwaschoseninsucha wayastosimplifyt hepr obl emasmuchaspossi bl e:onl yt wodegr eesof f r e e domwer eal l owed(wrist movement s wer epr e ve nt e dby means ofasplint)and t hei nfl uence ofgravi t y waskept const ant by wor ki ng int hehor i zont al pl ane. Inthisway, movement s oft hear mwer er educedt of l exi on- ext ensi onof t h eel bowandf l exi on- ext ensi on oft heshoul der (Fig.1). Mot i onsof t hear mwer et r ans ducedbymeansof a light-weightt wo-j oi nt sar t i cul at edst r uct ur e 2whose handl ewasgr aspedbyt hesubj ect s. Tr unkmove-ment swer epr event edbyappr opr i at est rappi ng.Sixadults 3 par t i ci pat edassubj ect sint heexper i -ment s, dur i ngwhi cht hesixt arget swer eact i vat ed accordi ngt oasequence 4whi chwasr epeat edfive t i mes, withasmallrest t i mebet weentrials.Thesubj ect sr ecei vednopar t i cul ar i nst r uct i onexceptsimplyt or eacht het ar get posi t i on. Nocont actoccur r ed bet weenhandandt ar get becauset het ar getwasont hepl at eandt hear mwasunder neat h. The pot ent i omet er s ont heshaftsof t het woj oi nt spr o-2Thearticulatedst ruct urewasdesi gnedbyProf.N.Hogan ( M. I . T. , Mechani cal Engi neer i ngDepar t ment , Cambri dge,MA, USA) andwasbui l t usingal umi numpipes.Theproxi malpi pe was28 cmlong,t he distal pi pewas36 cmlong andt heaxis oft hedistalpipewasdisplacedby3cmfromt hehi ngeoft he proximalpipe.Thesedi mensi onsandt herelativeposi t i on bet weent hemani pul andumand t he body werechosen in such a waytoavoidanyconst rai nt ont hefreedomofmot i onoft he handl e 3Dat aont hesubjects: Subject123456 SexMMMFFM Age252436233131 Humer usl engt h33.532.531263227 For ear ml engt h413438343337 4Theactivation sequenceof t he t arget s i ncl uded 30 t arget s, it was randomi zedinspaceandint i me, wi t hanaverageact i vat i on i nt ervalof3s 0014-4819/81/0042/0223/$1.00 224P. Mor asso: Spat i al Cont r ol o f Ar mMo v e me n t sFi g. I . Exper i ment al s et upf ort he st udyofr eachi ng move me nt si n t hehor i zont al pl ane. Re c or de dvari abl es: ( X, Y)Car t esi an Coor di nat es oft he Ha nd, (qs, 0)Angul a r Coor di nat es oft he Joi nt s (wristmove me nt s wer enot al l owed) . Vi sual t ar get s: 7"1,999T 6 .Thei r car t esi an coor di nat es , wi t h r egar dt ot hes houl derori gi n, ar e t hefol l owi ngones(incm) ; T 1 (0, 0), T2( - 30, 0) , T2( - 25, 30) , T 4(0,35),T5(30,29),T 6 (30, 0). Onl yonet ar get wasact i veatone t i me. Whe nonet ar get wass wi t ched off, a not he r onewasswi t ched onandt hesubj ect wasi ns t r uct edt omove t heha ndf r omt he f or mer t ot hel at t er. The t ar get pl at ewasabout 1i nchabovet he pl aneof t hear mandt hesubj ect shadnovi si onof t hei r ha nd videdthesourcesignalswhichweredigitizedat 10ms/sample,andallowedthecomput at i on(by meansofsimpletrigonometriccalculations)ofthe followingvariables:(1)thet raj ect oryofthehandin the X- Yplane,and(2) theanglesat theshoulderand elbow joints s.Thedigitizedangularsignals were then fittedbymeansofaleast-squares,second-order polynominalapproximationwhichallowedtheesti- mationofthefirstandsecondtimederivatives.The same techniquewas used withtheX- Ytrajectoriesin ordertoestimatethetangentialvelocity of thehand. Theresultsoftheexperimentsarepresent edin Figs.2and3.Figure2showsthespatialtrajectories ofthehandandFig.3showsthetimecourseofthe jointangularposition,jointangularvelocity,and handtangentialvelocity,forfourdifferentmove- ments.Jointangularvelocities(Fig.3,secondrow) forthesedifferentmovement sexhibitquitedifferent patterns;somejointangularvelocitiesaresingle peakedandsomearedoubl epeaked(whichmeans 5Unwa nt e dsmal lt r ansl at i onsoft hes houl der de t e r mi ne er r or sin t hees t i mat edj oi nt angl es. The s e er r or s ar enonl i near f unct i ons oft heangl esandof t hel engt hof t hear ms egment s . Togivean or der of magni t ude, itispossi bl et ocal cul at et hat , f or anar m conf i gur at i oninwhi cht hes houl der angl eisn/ 4andt heel bow angl e is n/ 2, as houl derdi s pl acementof1 cm de t e r mi ne san er r orof oneandt wodegr eesi nt het woangl es, r espect i vel y inversionofthejointmotion). Thefourmovement s ofthefigureexhibitallthefourpossiblecombina- tions(singlepeak/ doubl epeak)forthetwojoints. Incontrast,thetangentialhandvelocityforthe differentmovement shasasinglepeakedcurvethat varieslittleinshapebet weenmovements. Thedura- tionofthedifferentmovement swasratherconstant foreachsubject, what evertheshapeofthejoint angularpatterns.Thisisinaccordancewithprevious observations(Bryan1892;StetsonandMcDill1923). Ifwenowl ookatthetrajectoriesofthehand (Fig.2),weobservethatt heyapproximatestraight segmentswhichlinkinitialandfinalpositions. Insum,theobservationsabovemaybesum- marizedbysayingthatthecommonfeaturesamong thedifferentreachingmovement sarethesingle- peakedshapeof thehandtangentialvelocity andthe shapeof thehandtrajectory. Asaconsequence, one mayhypothesizethatthecentralcommandswhich underlietheobservedmovement saremorelikelyto specify thet raj ect oryof thehandthanthemot i onof thejoints(inshort,wemaycallita"spatialcontrol" hypothesis).Theideaof"spatialcont rol "canbe associatedwithearlytheoreticalandrecentexperi- mentalinvestigations.Notingthe"deepl yseat ed inherentindifferenceofthemot orcontrolcentreto thescaleandpositionofthemovement effect ed",Bernstein(1935)formul at edthehypothesisthat thereexist in thehigherlevels of theCNSproj ect i ons of spaceandnotprojectionsof jointsandmuscles". Consideringtheprobl emofserialorderin behaviour,Lashley(1951)hypothesizedtheexist- enceofsystemsofspacecoordinates:"theirinflu- encespervadethemot orsystemsothateverygross movement of limbsof body is madewithreference to thespacesystem.Theperceptionsfromthedistance receptors,vision,hearingandtoucharealsocon- stantlymodifiedandreferredtothesamespaceof coordinates". Morerecently,Russell(1976),study- ingtheaccuracyofpointingonehandtoatarget, startingfromdifferentinitialpositions,concluded that"spatiallocationisaviablealternativetothe storedmot orcommandsortheirsensoryconse- quencesintheproduct i onandcontrolofmove- ment ". Furt hermore, theexperimentsof Vivianiand Terzuolo(1980)provi deadetailedkinematic descriptionofthehandmot i onduringhandwriting whichshowsthatthebasickinematicvariables (tangentialvelocity ofthehandandcurvatureofthe trajectory)preservetheirt emporal pat t ernwhen positionandsizeofthemovement ischanged. Itisalsointerestingtonot ethatthesamekindof probl emisbeingfacedintherobot i cfield.Evenif mostindustrialrobot spresentlyusedarecontrolled accordingtojoint-orientedschemes,theneedof 9 -~'~i ~ !i~ ,'~::::i ................... 7,, ................. ' ~\ / .,..., ! ;.>':: ......... \ ~,. ,.ic T ~ o ~UBJ i ~",.~-~'\ .-'"'" ! ,"~ [ .... >,+- \ ,' i /"L; ........... L/" \ ~" ..................... ~.,..~1~ " ....... ~','.-~t~;:; i " "".- -"9 /..9 ". ! ~.: "-.... o SUBJ 4 ......... i "Nr'L ... i t" ! ~;.:::. ..................... _a < SHOULOER _ _ >> SHOULDER _ - i l l".; . rm i : ,5", " '",- ., ~_ - % i eJ , x . : :, f ' ; ; 7" , . . . ,- - - ~ k 2ABCD F i g . 3A-D. Joint rotationand handtrajectory.For subject1, this figure displays the temporal patternsof four typical movements (acolumn for each movement)which exhibit distinctive joint angularpatterns,thoughpreserving the shapeof thetangentialvelocity curve.For each movement,thefollowing curves aredisplayed:Row1:Jointangle(vertical scale:30deg);row 2:Jointangularvelocity (vertical scale:50 deg/s);row3:Jointangularacceleration(vertical scale:100deg/s/s);row4:Tangentialhandvelocity (vertical scale:30cm/s)(timescale: 1 s).ATarget1 totarget4.BTarget3totarget5.CTarget2totarget5.DTarget1 totarget5(seeFig.1 fortargetnumbering) P.Morasso:Spatiat Controlof ArmMovements227 t a s k - o r i e n t e d c o n t r o l s y s t e ms isf a v o r i n g t h e e me r -ge nc e of c o n c e p t s o f " s p a t i a l c o n t r o l " ( s e e , f ore x a mp l e , Ne v i n s a n d Wh i t n e y 1973; Pa u l 1979). Ont h e o t h e r h a n d , i t isi mp o r t a n t t or e a l i z e t h a t t h en o t i o n of " s p a t i a l c o n t r o l " i mp l i e s t h e e x i s t e n c e of a me c h a n i s mf or t r a n s f o r mi n g s p a t i a lmo t o r c o mma n d si nt oc o o r d i n a t e d j o i n t a n g u l a r p a t t e r n s ( s e e , f ore x a mp l e , t h e mo d e l s of Pe l l i o n i s z a n d Ll i nf i s( 1980)a ndof Be n a t i e t al . 1980a, b) .Fi n a l l y , i t i sp o s s i b l e t os p e c u l a t e t h a t t h er a t i o n a l e of t hi s s e e mi n g l y c o mp l i c a t e d c o n t r o la r c h i t e c t u r e l i es i nt h e p o t e n t i a l o f t h e " s p a t i a l c o d e "t os e r ve asac o mmo n l a n g u a g e a mo n g t h e d i f f e r e n ts our c e s of i n f o r ma t i o n wh i c h s u b s e r v e c o o r d i n a t e dmo v e me n t s ( e . g . , e x t e r o c e p t i v e a n d p r o p r i o c e p t i v ea f f e r e n c e s , mo t o r p r o g r a ms , e t c . ) .Acknowledgement. The author is greatly indebted to Prof. E. Bizzi (PsychologyDept.,MIT,Cambridge,USA), Prof.W.Chapple (Biol.Sci.Group,University of Connecticut,Storrs, USA), Prof. N.Hogan(MechanicalEngineeringDept.,MIT,Cambridge, USA),Prof.V.Tagliasco(Electrical EngineeringDept.,Genoa University,Italy) for discussing the general topics of motor control whichunderlietheexperimentsandforparticipating indefining suchexperiments andforcarrying themout. Re f e r e nc e stionandsolutionbymeansofananalogmodelofarm geometry. Technical Report,E. E. Department,GenoaUni versity Benati M,Gaglio S,Morasso P,TagliascoV,Zaccaria R(1980b) Anthropomorphic robotics. I.Representing mechanical com- plexity. II.Analysis of manipulator dynamicsandtheoutput motor impedance.Biol Cybern38:125-140,141-150 BernsteinN(1935) Theproblem of theinterrelation of coordina- tionandlocalization. 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Academic Press, NewYork,pp67-83 Stetson RH, McDill JA(1923)Mechanismsofdifferent types or movements.PsycholMonogr 32:18 VivianiP,TerzuoloCA(1980)Space-Time invariance in learned motorskills.In:StelmachGS,RequinJ(eds)Tutorialin motor behaviour.NorthHolland,Amsterdam,pp525-533 Benati M,Morasso P,Tagliasco V(t980a)Theinverse kinematic problem for anthropomorphic manipulator arma:representa-Received October 26,1980 /Accepted January26,1981