Unintentional movements produced by back-coupling between the actual and referent body configurations: violations of equifinality in multi-joint positional tasks

Abstract

We tested several predictions of a recent theory that combines the ideas of control with referent configurations, hierarchical control, and the uncontrolled manifold (UCM) hypothesis. In particular, we tested a hypothesis that unintentional changes in hand coordinate can happen following a long-lasting transient perturbation. The subjects grasped a handle with the right hand, occupied an initial position against a bias force produced by the HapticMaster robot, and then tried not to react to changes in the robot-produced force. Changes in the force were smooth and transient; they always ended with the same force as the bias force. The force-change amplitude and the time the force was kept at the new level (dwell time) varied across conditions. After the transient force change was over, the handle rested in a position that differed significantly from the initial position. The amplitude of this unintentional movement increased with the amplitude of transient force change and with the dwell time. In the new position, the across-trials joint configuration variance was mostly confined to a subspace compatible with the average handle coordinate and orientation (the UCMs for these variables). We view these results as the first experimental support for the hypothesis on back-coupling between the referent and actual body configurations during multi-joint actions. The results suggest that even under the instruction "not to react to transient force changes," the subjects may be unable to prevent unintentional drift of the referent configuration. The structure of joint configuration variance after such movements was similar to that in earlier reports on joint configuration variance after intentional movements. We conclude that the intentional and unintentional movements are products of a single neural system that can lead to intentional and unintentional shifts of the referent body configuration.

Figure 1

An illustration of the initial posture. The subject sits in a chair, using the right arm to hold the handle in an initial position. The robot arm is aligned such that the subject’s hand moves primarily in a parasagittal plane. The marker clusters and additional markers that are used to determine the joint locations and segment lengths are shown. {G} and {r} show the Global and the Robot Coordinate Systems respectively.

Figure 2

A: A typical hand trajectory along X direction in the global coordinate system with zero dwell time (T_DWELL = TS). The time before T₀ is Preparation (shown by the left arrow), in which the subject holds a position against F_BASE. The time between T₀ and the time when the force returns to F_BASE is Perturbation (shown by the double-arrow line). The two dashed lines show the start and the end of the perturbation force (F_PERT). The directions of both F_BASE and F_PERT are along positive X (X+). The right arrow on the right of the second dashed line shows Recovery, when the force is back to F_BASE. Three phases for analysis were: Phase-1, the 0.5 s time interval prior to T₀; Phase-2, the 0.1 s time interval prior to the initiation of F_PERT drop, and Phase-3, the 0.5 s time interval that ended 0.5 s before the end of the trial. B: A typical hand trajectory along X direction in the global coordinate system with T_DWELL = 3 s (TM). Phase-2 is the 0.5 s time interval prior to the initiation of F_PERT drop. Perturbation time (PT) is the sum of movement time (MT) and T_DWELL. C: A typical hand trajectory with T_DWELL = 8 s (TL). Phase-2 is the 0.5 s time interval prior to the initiation of F_PERT drop.

Figure 3

The top left panel (A) shows the Euclidean distance for D12 and D13. The top middle (B) and right (C) panels show the distance for D12 and D13 along the X and Z directions separately. The bottom panels (D - F) show the absolute angle difference for D12 and for D13. Note that D12 > D13 in all conditions and for all variables. DS and DL indicate short and long perturbation distance, respectively. TS, TM and TL indicate short, medium and long dwell time, respectively. Averages across subjects are presented with standard error bars.

Figure 4

A: D13 averaged across all subjects with standard error bars. The data points correspond to the three perturbation times (the sum of movement time and T_DWELL) for the two different perturbation distances. For zero perturbation time we assume D13 = 0. Given the four points, an exponential regression D13 (PT) = a × (1 − e^{−b × PT}) was performed. The corresponding R² are provided. The solid line is for the short perturbation distance (DS); the dashed line is for the long perturbation distance (DL). B: The same data for a typical subject.

Figure 5

A: Indices of joint configuration variance for D12. Left panels: Variance within the UCM for position- and orientation-related analyses (V_UCMP and V_UCMO) and variance orthogonal to the UCM for position- and orientation-related analyses (V_ORTP and V_ORTO). Right panels: Z-transformed synergy indices for position- and orientation-related analyses (ΔV_ZP and ΔV_ZO). Averages across subjects with standard error bars are presented. Note that V_UCM > V_ORT (ΔV > 0) across all conditions and variables. B: Indices of joint configuration variance for D13.