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
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