Moving a hand-held object: Reconstruction of referent coordinate and apparent stiffness trajectories

This study used the framework of the referent configuration hypothesis and slow changes in the external conditions during vertical oscillation of a hand-held object to infer the characteristics of hypothetical control variables. The study had two main objectives: (1) to show that hypothetical control variables, namely, referent coordinates and apparent stiffness of vertical hand position and grip force can be measured in an experiment; and (2) to establish relation(s) between these control variables that yield the classic grip-force-load-force coupling. Healthy subjects gripped a handle and performed vertical oscillations between visual targets at one of five metronome-prescribed frequencies. A HapticMaster robot was used to induce slow changes in the vertical force applied to the handle, while the size of the handle was changed slowly leading to changes in the grip aperture. The subjects were instructed not to react to possible changes in the external forces. A linear, second-order model was used to reconstruct the referent coordinate and apparent stiffness values for each phase of the vertical oscillation cycle using across-cycle regressions. The reconstructed time profiles of the referent coordinates and apparent stiffness showed consistent trends across subjects and movement frequencies. To validate the method, these values were used to predict the vertical force and the grip force applied to the handle for movement cycles that were not utilized in the reconstruction process. Analysis of the coupling between the four variables, two referent coordinates and two apparent stiffness values, revealed a single strong constraint reflecting the coupling between the grip force and vertical force. We view these data as providing experimental support for the idea of controlling natural, multi-muscle actions with shifts in a low-dimensional set of referent coordinates.