CONSTANT EFFORT COMPUTATION AS A DETERMINANT OF MOTOR BEHAVIOR

doutfanaticalMechanics

Nov 14, 2013 (3 years and 4 months ago)

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CONSTANT EFFORT COMPUTATION

AS A DETERMINANT OF MOTOR
BEHAVIOR

Emmanuel Guigon, Pierre Baraduc, Michel Desmurget

INSERM U483, UPMC, Paris, France

INSERM U534, «

Space and Action

», Bron, France

MOTOR BEHAVIOR: CONSTRAINED

AMPLITUDE / VELOCITY

AMPLITUDE / DURATION

Gordon et al. (1994)

Amplitude (cm)

MOTOR BEHAVIOR: CONSTRAINED

KINEMATIC

INVARIANCE

Gordon et al. (1994)

MOTOR BEHAVIOR: CONSTRAINED

CONSTRAINTS
ACROSS DIRECTIONS

Gordon et al. (1994)

MOTOR BEHAVIOR: CONSTRAINED

SPEED VS ACCURACY

Fitts (1954)

Jeannerod (1988)

MOTOR BEHAVIOR: FLEXIBLE

INDEPENDENT CONTROL

OF KINEMATICS AND
ACCURACY

Gribble et al. (2003)

KNOWN PRINCIPLES

Amplitude/duration

OC

(Harris&Wolpert 1998)

Kinematic invariance

OC

(Flash&Hogan 1985
-

Harris&Wolpert 1998)

Across directions

? (but see Todorov 1998)

Speed/accuracy

OFC

+
SEN

(Hoff&Arbib 1993) or
SDN

(Todorov 2003)

OC

+
SDN

(Harris&Wolpert 1998)

Kinematics/accuracy

?

Trajectory

OC

(Uno et al. 1989)
-

EPT

(Gribble et al. 1998)

EMG

OC

(Dornay et al. 1996)
-

EPT

(Flanagan et al. 1990)

Online correction

OFC

(Hoff&Arbib 1993
-

Todorov&Jordan 2002)

EPT

(Flanagan et al. 1993)

Redundancy

SOFC

(Todorov&Jordan 2002)

Central command

? (but see Todorov 2000)

OC
: optimal control
-

OFC
: optimal feedback control
-

SOFC
: stochastic OFC

EPT
: equilibrium
-
point theory
-

SDN
: signal
-
dependent noise
-

SEN
: state
-
estimation noise

CURRENT PRINCIPLES


Optimal feedback control


Constraints
: to reach the goal (
zero
-
error
)


Objective

(cost): to minimize the controls (
effort
)




Constant effort


For given instructions, all movements are


performed with the same
effort



Cocontraction

as an independent parameter



State
-
estimation noise


Inaccuracy in estimation of position and velocity


Increases with velocity


Decreases with cocontraction (fusimotor control)

Muscles as force generator.

No force/length effects.

No force/velocity effects.

No stretch reflex.

No biarticular muscles.

No static forces.

No viscosity.

Same formulation for OFC.

Solved numerically (Bryson 1999).

OPTIMAL CONTROL PROBLEM

KINEMATICS

EMGs

SHOULDER

ELBOW

AMPLITUDE / DURATION

KINEMATIC INVARIANCE

Also holds for changes

in inertial load.

DIRECTIONAL VARIATIONS

KINEMATICS & ACCURACY

-

OFC

+
SEN

-

Estimation of endpoint position: linear forward model

-

Gaussian noise on velocity

-

Variability: determinant of terminal covariance matrix

SHOULDER

ELBOW

-

Same amplitude

-

Same duration

-

Similar kinematics

-

Different accuracy

WHAT ARE THE CONTROLS?

Sergio&Kalaska (1998)

SHOULDER FLEXOR CONTROL

DIRECTIONAL TUNING

Sergio&Kalaska (1998)

FLEXOR

EXTENSOR

SHOULDER

ELBOW

SUMMARY


Known principles

OPTIMAL FEEDBACK CONTROL




STATE
-
ESTIMATION NOISE


Trajectory


EMG


Speed/accuracy


Central command



New principles


CONSTANT EFFORT





COCONTRACTION


Amplitude/duration


Kinematic invariance


Constraints across directions


Kinematics/accuracy


DISCUSSION


Kinematic invariance


Without desired trajectory.



Constant effort


Movements are selected not by


minimizing a cost, but by choosing


a cost level



Limitations / Extensions


-

Static forces


-

Limitations of force control (Ostry&Feldman 2003)


-

Accuracy/stability: viscoelastic properties


-

Adaptation to force fields and inertial loads