1. 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

2. MOTOR BEHAVIOR: CONSTRAINED AMPLITUDE / VELOCITY AMPLITUDE / DURATION Gordon et al. (1994) Amplitude (cm)

3. MOTOR BEHAVIOR: CONSTRAINED KINEMATIC INVARIANCE Gordon et al. (1994)

4. MOTOR BEHAVIOR: CONSTRAINED CONSTRAINTS ACROSS DIRECTIONS Gordon et al. (1994)

5. MOTOR BEHAVIOR: CONSTRAINED SPEED VS ACCURACY Fitts (1954) Jeannerod (1988)

6. MOTOR BEHAVIOR: FLEXIBLE INDEPENDENT CONTROL OF KINEMATICS AND ACCURACY Gribble et al. (2003)

7. KNOWN PRINCIPLES Amplitude/duration OC OC (Harris&Wolpert 1998) Kinematic invariance OC OC (Flash&Hogan 1985 - Harris&Wolpert 1998) Across directions ? (but see Todorov 1998) Speed/accuracy SDN OFC + SEN (Hoff&Arbib 1993) or SDN (Todorov 2003) OC + SDN (Harris&Wolpert 1998) Kinematics/accuracy ? TrajectoryOC (Uno et al. 1989) - EPT (Gribble et al. 1998) EMGOC (Dornay et al. 1996) - EPT (Flanagan et al. 1990) Online correction OFC (Hoff&Arbib 1993 - Todorov&Jordan 2002) EPT (Flanagan et al. 1993) RedundancySOFC (Todorov&Jordan 2002) Central command? (but see Todorov 2000) OCOFCSOFC OC: optimal control - OFC: optimal feedback control - SOFC: stochastic OFC EPTSDNSEN EPT: equilibrium-point theory - SDN: signal-dependent noise - SEN: state-estimation noise

8. 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 Cocontraction as an independent parameter State-estimation noise Inaccuracy in estimation of position and velocity Increases with velocity Decreases with cocontraction (fusimotor control)

9. 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

10. KINEMATICS

11. EMGs SHOULDERELBOW

12. AMPLITUDE / DURATION

13. KINEMATIC INVARIANCE Also holds for changes in inertial load.

14. DIRECTIONAL VARIATIONS

15. KINEMATICS & ACCURACY OFCSEN - 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

16. WHAT ARE THE CONTROLS? Sergio&Kalaska (1998) SHOULDER FLEXOR CONTROL

17. DIRECTIONAL TUNING Sergio&Kalaska (1998) FLEXOREXTENSOR SHOULDER ELBOW

18. SUMMARY OPTIMAL FEEDBACK CONTROL Known principlesOPTIMAL FEEDBACK CONTROL STATE-ESTIMATION NOISE Trajectory EMG Speed/accuracy Central command CONSTANT EFFORT New principlesCONSTANT EFFORTCOCONTRACTION Amplitude/duration Kinematic invariance Constraints across directions Kinematics/accuracy

19. 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