grasping: insights into a redundant motor system

8/11/2019 Grasping: Insights into a redundant motor system

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Grasping: Insights into a redundant motor system

Jason Friedman

Macquarie Centre for Cognitive Science (MACCS)Macquarie University, Sydney, Australia

19th June, 2011

Jason Friedman Grasping and redundancy


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Motor homunculus

In Penfields homunculus, a very large area of the motorcortex is related to the hand and fingers.



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Redundancy in grasping

Redundancy = more solutions than necessary

When grasping, we are required to solve (at least) thesemostly redundant problems:

Select grasp points for a particular taskSelect the posture of the hand

Select the stiffness properties of the fingers and graspCoordinate the grip and tangential forces of the fingersShare the force produced by multiple fingers

and ideally do this in an efficient / optimal way



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Experiments

I will present the results of three studies looking at different

aspects of redundancy in grasping:1 Grasp selection - from all possible grasps (fingertip locations,

hand postures), which grasps do we select for objectmanipulation?

2 Control of load and grasp forces - how do we coordinate fingerforces to stabilise and manipulate an object?

3 Good and bad variance - what is the relation of good andbad variance to frequency?



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Experiment 1: Which grasps do we select for objectmanipulation?Friedman & Flash, Cortex, 2007

We need to select posture and impedanceproperties to successfully perform themanipulation

This work examined the grasp selected atthe start of the manipulation rather thanthe movement



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Experiment 1: MethodsFriedman & Flash, Cortex, 2007

Experimental setup

20cmtransmitterFastrak

(with Velcro)

Object position

(without Velcro)

Object position

Resting positionof arm

Objects



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Experiment 1: MethodsFriedman & Flash, Cortex, 2007

Kinematic recording

Joint angles recorded with the CyberGlove, position andorientation of the wrist recorded with the Fastrak

Stiffness recording

Forces applied to each fin-ger using the CyberGrasp



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Grasp JacobianFriedman & Flash, Cortex, 2007

Relationship between joints, contacts and object

The grasp Jacobian is the transformation from the joint velocitiesto the velocity of the object being grasped. It takes into account

the contact relationships between the fingers and the object.

Joints ObjectContacts

xc xo

fc FoG

GTJh

Gh

JTh

G1h



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Experiment 1: Results - Jar lid

What are the task requirements for unscrewing the lid of a jar,or lifting the lid of a jar

The grasp Jacobian can be visualised as an ellipsoid (its shapeand orientation will depend on the posture of the hand)

In order to most efficiently perform the task, the ellipsoid

should be aligned with the requirements of the task.Jason Friedman Grasping and redundancy


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Experiment 1: Results (Jar lid - torque)Friedman & Flash, Cortex, 2007

Unscrew Lift

0.20

0.2

0.2

00.2

0.2

0

0.2

xz

y

0.40.2

00.2

0.4

0.4

0.2

0

0.2

0.4

0.4

0.2

0

0.2

0.4

xz

y

When unscrewing, the major axis of the torque ellipsoid wasgenerally closely aligned with the axis of rotation (y).

A larger torque about the vertical (y) axis can be generatedusing the unscrew grasp compared to the lift grasp.



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Experiment 1: Results (Jar lid - stiffness)Friedman & Flash, Cortex, 2007

Unscrew Lift

500

0

500

500

0

500

500

0

500

xz

y

500

0

500

500

0

500

500

0

500

xz

y

More isotropic translational stiffness ellipsoids are observed forpicking up the lid.

x and zstiffness is greater than in the ydirection, thedirection of motion.



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Experiment 2:Control of grip and load forcesFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

When holding a glass, we need toapply vertical load forcesto actagainst gravity, and horizontal grip

forcesto prevent slipping.We also need to stop the objectfrom rotating

This is a redundant problem - howdo we share the forces among thefingers?

How do we deal with this problem

in a dynamic situation, forexample, holding a glass that isbeing filled with water (or liquid ofyour choice)?



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Experiment 2:Control of grip and load forcesFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

What must a grasp satisfy? (Physics)1 The sum of the tangential forces of the fingers must equal the

load force:L=Ftth+F

tVF

2 The static external moment Mstshould be equal and oppositeto the applied moment

Mst=F

n

thdn

th+Fn

VFdn

VF+Ft

thdt

th+Ft

VFdt

VF

3 The sum of the normal forces should equal zero

0 =Fn

th+Fn

VF

4 The sum of the normal forces should equal zero

0 =Fnth+FnVF



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Experiment 2:Statement of the problemFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

This setup models grasping a cupbeing filled with water.

For a pinch grasp (thumb andindex finger), the grip force applied

by the fingers increases linearlywith an increase in the load force(Johansson & Westling, 1984).

How will the grip force change

when grasping with five fingers?



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Experiment 2:Statement of the problemFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

In this setup, themoment arms(distance from centre

of mass to grippoints) is unequal forthe thumb and otherfingers.

Hence, simply scalingthe forces will notmaintain rotationalequilibrium.

There are (at least)two possiblesolutions:



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Experiment 2:Balance of moments - strategy 1Friedman, Latash & Zatsiorsky, Exp Br Res, 2009

Share the load forcesevenly between thethumb and virtual

fingerHowever, this willproduce a momentand cause the handle

to rotateA moment in theopposite directionmust then beproduced by changingthe sharing pattern ofthe grip forces



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Experiment 2:Balance of moments - strategy 2Friedman, Latash & Zatsiorsky, Exp Br Res, 2009

Produce more of theload force with thevirtual finger (0.6 to

0.4)This will not producea moment from theload forces

So do not need toalter the momentfrom the normal

forces, rather can usethe same sharingpattern for thenormal forces


E R l


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Experiment 2:ResultsFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

Most of the subjects used the second strategy


E i 2 R l


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Experiment 2:ResultsFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

A small number of subjects used the first strategy


E i 2 S i i


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Experiment 2: SuperpositionFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

The principle of superposition is that some actions can bedecomposed into elemental actions that can be independently

controlled.Systems that implement this principle are advantageous,because they are computationally simpler.


E i t 2 S iti


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If elemental variables (e.g. load and grip forces of the fingers,moments) have low correlations, this suggests that they arecontrolled independently.

If elemental variables have high correlations, this suggests that

they may be controlled together.

This can be tested using principal component analysis (PCA)with varimax rotation on the detrended data within a trial.


E i t 2 S iti


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Three independent sets can be observed:1 Ft

thand Mt

th

2 FtVF

, Mtth

and MnVF

3

Fn

th and Fn

VF

Note that FnVF

and MnVF

are in different sets

Variable PC1 PC2 PC3

Ftth 0.71 0.00 0.00

FtVF

0.02 -0.60 -0.05Fnth

0.00 0.01 -0.70FnVF

0.01 0.00 0.70

Mtth -0.71 0.00 0.00MtVF

0.02 -0.60 -0.05MnVF

0.03 -0.53 0.12


Experiment 2: Conclusions


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Experiment 2: ConclusionsFriedman, Latash & Zatsiorsky, Exp Br Res, 2009

Two different strategies are used to achieve rotational stabilitywhen grasping the object while a load is applied.

Superposition appears to be used, this allows the neural

controller to parition the task and independently control thecomponents.


Experiment 3: Relation of Good and bad variance to


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Experiment 3: Relation of Good and bad variance tofrequency

Friedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

When there are multiple effectorsin a redundant task, how can westabilise the output?

Coordination of the covariancebetween the effectors can allow usto take advantage of theredundancy.


Experiment 3:Prehension synergies


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Experiment 3:Prehension synergiesFriedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

Aprehension synergy

is a conjoint change of finger forcesand moments during multi-fingerprehension tasks

adjusts to changes in taskparameters

compensates for external orself-inflicted disturbances


Experiment 3:Uncontrolled Manifold (UCM)


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Experiment 3:Uncontrolled Manifold (UCM)Friedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009


Experiment 3:Uncontrolled Manifold (UCM)


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Experiment 3:Uncontrolled Manifold (UCM)Friedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

The uncontrolled manifoldapproach (Scholz and Schoner,1999) can be used to explain the variance observed when agiven task has more degrees of freedom than necessary.

It assumes that the neural controller wants to stabilize aparticular performance variable.

This can be achieved by selecting a subspace such that withinthe subspace, the value of the performance value isunchanged.

This subspace is known as the uncontrolled manifold, becauseselecting different values within this manifold will not change

the desired performance variable.Then the variance that does not change the performancevariable (VUCM) and variance that does change theperformance variable (VORT) can be calculated.


Experiment 3: Expected variance components


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Experiment 3: Expected variance componentsFriedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

In previous studies, it has been observed that:1 VUCM(good variance) is proportional to F2 VORT(bad varaince) is proportional to

dF

dt

Question: In a cyclic task, is VORTdue to frequency or dFdt?



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Experiment 3: Results


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Experiment 3: ResultsFriedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

As expected,VUCM

increasedapproximatelylinearly withthe force

VORTincreasedlinearly with

the force rate(dF/dt)



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Experiment 3: Conclusions


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pFriedman, SKM, Zatsiorsky & Latash, Exp Br Res, 2009

Within a trial, Fwas proportional to VUCM, dF

dt to VORT.Across trials, at the same amplitude, VORTdid not increaseas the frequency and dF

dt increased.

It seems that the bad variance (VORT), which is related to

timing errors, is modulated to keep the errors in performanceat an acceptable level, perhaps by increasing the timingaccuracy.


General conclusions


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Redundancy is observed at many levels in the planning andproduction of movement / forces, such as:

Posture selection

Which hand posture / grasp points do we select to perform a

particular manipulation?

The high level of redundancy allows us to optimize multiplerequirements, while grasping the same object.

Force sharing in graspingJason Friedman Grasping and redundancy


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Thanks


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Experiment 1 was performed at the Moross laboratory at the

Weizmann Institute of Science, Israel, as part of my PhDstudies, under the supervision of Prof. Tamar Flash.

Experiments 2 and 3 were performed in the Biomechanics andMotor Control laboratories at the Pennsylvania StateUniversity, USA, in the labs of Prof. Mark Latash and Prof.Vladimir Zatsiorsky. Experiment 3 was performed togetherwith Varadhan SKM.


grasping: insights into a redundant motor system

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