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 OC (Harris&Wolpert 1998) Kinematic invariance OC OC (Flash&Hogan 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 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

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)

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 SHOULDERELBOW

AMPLITUDE / DURATION

KINEMATIC INVARIANCE Also holds for changes in inertial load.

DIRECTIONAL VARIATIONS

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

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

DIRECTIONAL TUNING Sergio&Kalaska (1998) FLEXOREXTENSOR SHOULDER ELBOW

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

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