Transcript PPT presentation

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
Amplitude (cm)
Gordon et al. (1994)
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
W = 2 in
W= 1
* W = 0.5
W = 0.25
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)
OPTIMAL CONTROL PROBLEM
No
staticas
forces.
Muscles
force generator.
No viscosity.
force/length effects.
Same
formulationeffects.
for OFC.
No force/velocity
Solved
numerically
No stretch
reflex. (Bryson 1999).
No biarticular muscles.
KINEMATICS
EMGs
SHOULDER
ELBOW
AMPLITUDE / DURATION
KINEMATIC INVARIANCE
Also holds for changes
in inertial load.
DIRECTIONAL VARIATIONS
KINEMATICS & ACCURACY
SHOULDER
ELBOW
- Same amplitude
- Same duration
- Similar kinematics
- Different accuracy
- OFC + SEN
- Estimation of endpoint position: linear forward model
- Gaussian noise on velocity
- Variability: determinant of terminal covariance matrix
WHAT ARE THE CONTROLS?
SHOULDER FLEXOR CONTROL
Sergio&Kalaska (1998)
DIRECTIONAL TUNING
EXTENSOR
ELBOW
SHOULDER
FLEXOR
Sergio&Kalaska (1998)
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