Handbook of Psychology, Volume 4: Experimental Psychology

MotorPreparation325

the inversion of the motor transformation is assumed to be an
integrated component of a motor-control structure. In the sec-
ond case, it is left to additional and separate processes. Al-
though the choice may be somewhat arbitrary, it implies an
assumption about whether the internal model of the inverse
motor transformation is specific for a particular type of
movement governed by a particular motor-control structure,
or whether it is generalized and thus applicable to different
types of movement.
There are some considerations and data that favor the
modeling of motor-control structures with end-effector kine-
matics as output. One consideration starts with the observa-
tion that both perception and action are externalized. For
example, we do not see the image on the retina, but objects
and their locations in the world. Similarly, awareness of our
own movements is typically not in terms of muscular con-
tractions and joint angles. Visual distances and movement
amplitudes in the external world are commensurate, whereas
proximal visual stimuli and patterns of muscular activity are
not (cf. Prinz, 1992). Thus, to be compatible with how we
perceive the world around us, movement should be repre-
sented in terms of world coordinates.
Anotherconsiderationstartswiththeassumptionthatthe
variablesusedinmotorpreparationorplanningshouldreveal
themselvesbythepossibilityofdescribingthemconciselyas
wellasbytheirconsistency.Forexample,forpointingina
two-dimensionalplaneasinFigure12.2,themovementpaths
approximatestraightlines,whereastherelationsbetween
joint-anglescanbefairlycomplex.Morespecifically,plotting
theycoordinatesoftheend-effectorasafunctionofthex
coordinatesresultsinstraightlinesatleastapproximately,
whereasplottingtheelbowangleasafunctionoftheshoul-
derangleresultsinstronglycurvedlines.Thissuggeststhat
motor-controlstructuresdealwiththetrajectoryoftheend-
effector,andthatthetime-coursesofjointanglesareaconse-
quencethereof(cf.Hollerbach&Atkeson,1987).Similarly,
kinematiccharacteristicsofsingle-jointmovementsare
highlysimilarformovementswithandagainstgravity,
whereasthepatternsofmuscularactivityaregrosslydifferent
(Virjii-Babul,Cooke,&Brown,1994).
Nomatterforwhichkindofvariableprototypicalfunc-
tionsaredefined,thenotionisintimatelyrelatedtotheinvari-
anceofrelativetiming.Theinvarianceisneverreallyperfect,
butoften.Itcanbetakenasareasonableapproximation.
However,therearealsocleardeviationsfrominvariance.For
example,whenthetargetsizeisreducedoraccuracyrather
thanspeedisemphasized,therelativedurationofthedeceler-
ationphaseofaimedmovementstendstoincrease(Fisk&
Goodale,1989;MacKenzieetal.,1987).Moreover,the
conceptofaprototypicalfunctiontakesaparticularrelative

timingasamandatorycharacteristicofacertaintypeof

movementwhichcannoteasilybechanged;however,when

aftersomepracticeinaparticulartemporalpatterntherelative

timingischanged,humansdonotencounterparticulardiffi-

culties(Heuer&Schmidt,1988).Thus,prototypicalfunc-

tionsdonotrepresentavalidtypeofmodelformotor-control

structuresingeneral,butneverthelesstheycancaptureim-

portantcharacteristicsofsometypesofmovement.

Generative Structures

Whereasaconceptualizationofmotor-controlstructuresin

termsofprototypicalfunctionspositsstoredtrajectories,con-

ceptualizationsintermsofgenerativestructurespositnet-

worksthatgeneratethetrajectories.Anexampleisamodel

bySaltzmanandKelso(1987)thatbelongstoaclassthey

calledthe“task-dynamicapproach.”Foranaimedmovement,

SaltzmanandKelsodefinedareachaxisthatrunsthroughthe

targetandthecurrentpositionoftheend-effectoraswellasan

axisorthogonaltoit.Theseaxesdefineanabstracttaskspace

inwhichtheend-effectorisrepresentedbya“taskmass.”The

targetpositionislocatedintheoriginofthetaskspaceandis

assumedtohavethecharacteristicsofapointattractor.Thus,

whereverthetaskmassisintaskspace,itwillmovetoward

thetargetgovernedbyasetofsimpleequationsofmotion;for

thereachaxisxitismTx ̈+bTx ̇+kTx=0,withtheindexT

designating parameters of the task space.

The task-dynamic approach goes beyond advance specifi-

cations of movements in task space. For example, joint

movements are derived by way of coordinate transforms.

However, for the present purpose only the highest level of the

scheme is important. At first glance there does not seem to be

much difference between describing a motor-control struc-

ture in terms of a differential equation that governs a genera-

tive structure or in terms of a solution of such an equation that

could be stored as a prototypical function. However, there

are differences. First, the parameterizations are different.

Whereas the prototypical function has a rate and an ampli-

tude parameter, the particular generative structure at hand

has abstract mass, mT, friction, bT, and stiffness, kT, parame-

ters. Variation of these parameters, for example, does not

necessarily result in relative-timing invariance. Second, and

perhaps more important, the generative structure is less

susceptible to the effects of transient perturbations. It

implements a movement characteristic called equifinality:

Movements tend to reach their target even when they are

transiently perturbed (Kelso & Holt, 1980; Polit & Bizzi,

1979; Schmidt & McGown, 1980).

Although the model of Saltzman and Kelso (1987) seems

to be more mathematically than physiologically inspired, this