Trajectory control in targeted force impulses. III: compensatory adjustments for initial errors

In the preceding study (Gordon and Ghez 1987), we showed that accurately targeted isometric force impulses produced by human subjects are governed by a pulse height control policy. Different peak forces were achieved by modulating the rate of rise of force while force rise time was maintained close to a constant value and independent of peak force. An early measure of the rate of rise of force, peak d2F/dt2, was scaled to the required force (target amplitude) and highly predictive of the peak force achieved. In six subjects examined, peak d2F/dt2 accounted for between 70% and 96% of the total variance in peak force. In the present study, we further examined these targeted responses to determine whether the residual variability not predicted by peak d2F/dt2 could be accounted for by adjustments to the force trajectories which compensated for initial errors in the scaling of the d2F/dt2. A statistical model of the determinants of peak force was tested. This model included two paths by which the target amplitude could independently influence the peak force achieved. The first path was preprogrammed pulse height control. In this path, target amplitude determined the initial rate of rise of force (peak d2F/dt2) which in turn determined the final peak force achieved. The second path was an independent influence of errors in the initial scaling of peak d2F/dt2 on peak force. Multiple regression analysis was performed on trajectory variables within the sets of responses by each subject in each condition to determine whether the second path contributed significantly to explaining the variance in peak force. In each subject and condition, there was a significant independent influence of error in d2F/dt2 on peak force, and the direction of this effect was to decrease the magnitudes of peak force errors. These compensatory adjustments accounted for between 1% and 14% of the total variance in peak force. Further multiple regression analyses revealed that inappropriate scaling of the initial phase of the trajectories was compensated for by shortening or prolonging the force rise time. These trajectory adjustments were in turn implemented by modulation of the timing and magnitude of the contractions in the agonist and antagonist muscles that produced the force trajectories. Because these compensatory adjustments were evident in the EMG pattern at latencies too short to be accounted for by peripheral feedback, we assume that they depend on internal monitoring of the unfol