CONSTANT EFFORT COMPUTATION AS A DETERMINANT OF MOTOR BEHAVIOR Emmanuel Guigon, Pierre Baraduc, Michel Desmurget INSERM U483, UPMC, Paris, France INSERM.

CONSTANT EFFORT COMPUTATIONCONSTANT EFFORT COMPUTATIONAS A DETERMINANT OF MOTOR AS A DETERMINANT OF MOTOR

BEHAVIORBEHAVIOR

Emmanuel Guigon, Pierre Baraduc, Michel DesmurgetEmmanuel Guigon, Pierre Baraduc, Michel DesmurgetINSERM U483, UPMC, Paris, FranceINSERM U483, UPMC, Paris, France

INSERM U534, « Space and Action », Bron, FranceINSERM U534, « Space and Action », Bron, France

MOTOR BEHAVIOR: CONSTRAINEDMOTOR BEHAVIOR: CONSTRAINED

AMPLITUDE / VELOCITYAMPLITUDE / DURATION

Gordon et al. (1994)

Amplitude (cm)

MOTOR BEHAVIOR: CONSTRAINEDMOTOR BEHAVIOR: CONSTRAINED

KINEMATICINVARIANCE

Gordon et al. (1994)

MOTOR BEHAVIOR: CONSTRAINEDMOTOR BEHAVIOR: CONSTRAINED

CONSTRAINTS ACROSS DIRECTIONS

Gordon et al. (1994)

MOTOR BEHAVIOR: CONSTRAINEDMOTOR BEHAVIOR: CONSTRAINED

SPEED VS ACCURACY

Fitts (1954)Jeannerod (1988)

W = 2 inW = 1W = 0.5W = 0.25

*

MOTOR BEHAVIOR: FLEXIBLEMOTOR BEHAVIOR: FLEXIBLE

INDEPENDENT CONTROLOF KINEMATICS AND

ACCURACY

Gribble et al. (2003)

KNOWN PRINCIPLESKNOWN PRINCIPLESAmplitude/duration OCOC (Harris&Wolpert 1998)

Kinematic invariance OCOC (Flash&Hogan 1985 - Harris&Wolpert 1998)

Across directions ? (but see Todorov 1998)

Speed/accuracyOFC + SEN (Hoff&Arbib 1993) or SDNSDN (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 correctionOFC (Hoff&Arbib 1993 - Todorov&Jordan 2002)EPT (Flanagan et al. 1993)

Redundancy SOFC (Todorov&Jordan 2002)

Central command ? (but see Todorov 2000)

OCOC: optimal control - OFCOFC: optimal feedback control - SOFCSOFC: stochastic OFCEPTEPT: equilibrium-point theory - SDNSDN: signal-dependent noise - SENSEN: state-estimation noise

CURRENT PRINCIPLESCURRENT PRINCIPLES

• Optimal feedback controlOptimal feedback controlConstraints: to reach the goal (zero-error)Objective (cost): to minimize the controls (effort)

• Constant effortConstant effortFor given instructions, all movements areperformed with the same effort

• CocontractionCocontraction as an independent parameter

• State-estimation noiseState-estimation noiseInaccuracy in estimation of position and velocityIncreases with velocityDecreases 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 PROBLEMOPTIMAL CONTROL PROBLEM

KINEMATICSKINEMATICS

EMGsEMGs

SHOULDER ELBOW

AMPLITUDE / DURATIONAMPLITUDE / DURATION

KINEMATIC INVARIANCEKINEMATIC INVARIANCE

Also holds for changesin inertial load.

DIRECTIONAL VARIATIONSDIRECTIONAL VARIATIONS

KINEMATICS & ACCURACYKINEMATICS & ACCURACY

- OFCOFC + SENSEN- 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?WHAT ARE THE CONTROLS?

Sergio&Kalaska (1998)

SHOULDER FLEXOR CONTROL

DIRECTIONAL TUNINGDIRECTIONAL TUNING

Sergio&Kalaska (1998)

FLEXOR EXTENSOR

SH

OU

LD

ER

EL

BO

W

SUMMARYSUMMARY

• Known principles OPTIMAL FEEDBACK CONTROLOPTIMAL FEEDBACK CONTROLSTATE-ESTIMATION NOISESTATE-ESTIMATION NOISE

TrajectoryEMGSpeed/accuracyCentral command

• New principles CONSTANT EFFORTCONSTANT EFFORTCOCONTRACTIONCOCONTRACTION

Amplitude/durationKinematic invarianceConstraints across directionsKinematics/accuracy

DISCUSSIONDISCUSSION

• Kinematic invarianceWithout desired trajectory.

• Constant effortMovements are selected not byminimizing a cost, but by choosinga cost level

• Limitations / Extensions- Static forces- Limitations of force control (Ostry&Feldman

2003)- Accuracy/stability: viscoelastic properties- Adaptation to force fields and inertial loads