On the nature of unintentional action: a study of force/moment drifts during multifinger tasks

Abstract

We explored the origins of unintentional changes in performance during accurate force production in isometric conditions seen after turning visual feedback off. The idea of control with referent spatial coordinates suggests that these phenomena could result from drifts of the referent coordinate for the effector. Subjects performed accurate force/moment production tasks by pressing with the fingers of a hand on force sensors. Turning the visual feedback off resulted in slow drifts of both total force and total moment to lower magnitudes of these variables; these drifts were more pronounced in the right hand of the right-handed subjects. Drifts in individual finger forces could be in different direction; in particular, fingers that produced moments of force against the required total moment showed an increase in their forces. The force/moment drift was associated with a drop in the index of synergy stabilizing performance under visual feedback. The drifts in directions that changed performance (non-motor equivalent) and in directions that did not (motor equivalent) were of about the same magnitude. The results suggest that control with referent coordinates is associated with drifts of those referent coordinates toward the corresponding actual coordinates of the hand, a reflection of the natural tendency of physical systems to move toward a minimum of potential energy. The interaction between drifts of the hand referent coordinate and referent orientation leads to counterdirectional drifts in individual finger forces. The results also demonstrate that the sensory information used to create multifinger synergies is necessary for their presence over the task duration.

Keywords: abundance; finger; redundancy; referent configuration; synergy; uncontrolled manifold hypothesis; visual feedback.

Fig. 1.

A: production of a magnitude of total force (F_TOT) with a set of fingers (I, index; M, middle; R, ring; L, little) in isometric conditions is associated with setting a referent coordinate (RC) for the fingertips and a magnitude of apparent stiffness k. Given the constant actual coordinate of the effector (AC), F_TOT = k(RC − AC). B: production to a magnitude of the moment of force, M_TOT is associated with a shift of the referent orientation of the plane of fingertip coordinates (RO) away from its actual orientation (AO) scaled with an apparent stiffness coefficient (k_O): M_TOT = k_O(RO − AO).

Fig. 2.

A: illustration of the experimental setup. The monitor presented total force (F_TOT) and total moment (M_TOT) feedback. B: hand configuration of the sensors. C and D: time series of the normalized F_TOT and M_TOT for a representative subject in a trial when no feedback was presented after 5 s. PR, pronation; SU, supination. Phase 1 was defined as the time interval 470–480 ms; phase 2 was defined as the time interval 2,470-2,480 ms. Note the downward drift in both F_TOT and M_TOT magnitudes.

Fig. 3.

The changes in F_TOT and M_TOT, ΔF_TOT and ΔM_TOT (both normalized by the initial values) for each hand and moment condition. Averaged across subjects values are shown with SE bars. Note the larger ΔF_TOT in the right hand (B) with no effect of the moment direction (PR, pronation; SU, supination). The drift in M_TOT was much larger for the SU moments (C and D).

Fig. 4.

The changes in the individual finger forces (A) and modes (B) for each moment condition (PR, pronation; SU, supination). Averaged across subjects values are shown with SE bars. Positive values correspond to an increase in the finger force (mode) while negative values indicate a drop in the finger force (mode). Note that positive values were typical for “moment antagonist” fingers, i.e., those producing moment against the required moment direction.

Fig. 5.

Two components of the normalized variance across trails, within (V_UCM) and orthogonal (V_ORT) to the UCM for the right hand. Averaged across subjects values are shown with SE bars. The results of the analysis for phase 1 and phase 2 for both hands and both moment conditions are shown in the mode space (A) and in the force space (B). The analysis was performed for the Jacobians computed with respect to F_TOT (J_F), M_TOT (J_M), and both {F_TOT; M_TOT} (J_FM). In phase 1, across conditions and analyses, there were synergies stabilizing both F_TOT and M_TOT (V_UCM > V_ORT, for all Jacobians) while there were no such synergies in phase 2. Similar results were observed for the left hand. PR, pronation; SU, supination.

Fig. 6.

The magnitudes of the z-transformed index of synergy (ΔV_Z) for the mode (A) and force (B) space analyses are shown at phase 1 (open bars) and phase 2 (black bars) for all the hand and moment conditions. Averaged across subjects values are shown with SE bars. Note that ΔV_Z > 0 in phase 1 but not in phase 2. The panels show the results for the {F_TOT; M_TOT}-based Jacobian (J_FM). Similar results were obtained for the analyses with respect to F_TOT-based (J_F) and M_TOT-based (J_M) Jacobians. PR, pronation; SU, supination.

Fig. 7.

The motor equivalent (ME) and non-motor equivalent (nME) components of the vector of mode (A and C) and force (B and D) difference between phase 2 and phase 1. Averaged across subjects values are shown with SE bars for the left hand (A and B) and for the right hand (C and D). Both ME and nME components were normalized by the square root of corresponding degrees of freedom. Note the larger nME for the right hand compared with the left hand and for the SU (supination) condition compared with the PR (pronation) condition.

Fig. 8.

An illustration of the production of F_TOT and M_TOT with changing RC and RO. After a drift in RC and RO (the right panel), a drop in the magnitude of both F_TOT and M_TOT is expected. Note consistent changes in the forces of “moment agonist” fingers (force drop) while changes in the forces of “moment antagonists” may depend on the relative rate of the RC and RO drifts. They can lead to an increase in the forces of those fingers.