Figure 1.
The Virtual Partner Interaction (VPI) paradigm.
Subject coordinates finger movement with a virtual partner visually via an animated display. Subject's behavior is digitized and fed to a real-time HKB computational circuit. The circuit computes corresponding virtual partner position and velocity
which is then used to animate the hand of the virtual partner. Circuit is coupled to the subject via the digitized inputs. Subject is coupled to the circuit visually via the display.
Table 1.
Virtual Partner Interaction experiment parameters.
Figure 2.
Simulation of the relative phase behavior of a reverse-coupled HKB system.
Relative phase approaches either −π/2 or π/2 depending on the initial condition. Except for the reversed coupling, the parameters used are identical and are given in Table I. The shifted attractors are reminiscent of the bi-stability at 0 and π found in the normally coupled HKB system. The convergence of the trajectories toward two attractors at −π/2 and π/2 reflects the (minimal) bistability present due to the choice of parameters.
Figure 3.
Response of the virtual partner (blue curve) to a sinusoidal input (orange curve).
Sine input has the same frequency and fixed amplitude. The plots are time series of positions. (A) After starting out at in-phase, the coordination pattern switches to the virtual partner's preference at anti-phase. This switch is accompanied first by reduction then by an increase in the amplitude. (B) If the sinusoidal input is periodically reset so as to be in-phase with the virtual partner, the virtual partner amplitude decreases and does not recover. For the full VPI experiment, this has the effect of degrading the visual information required by the subject to coordinate effectively with the virtual partner.
Figure 4.
Selection of experimental frequencies guided by the HKB collective variable dynamics.
Humans have shown remarkably consistent coordinative (relative phase) behavior in a wide variety of coordination tasks with rhythmic stimuli, a fact captured by the elementary HKB dynamics [11] illustrated here. When asked to synchronize at the same frequency with the stimulus, stable phase patterns are invariably present at (or close to) anti-phase and in-phase for low movement frequencies (typically <2 Hz). This is indicated by the solid lines of fixed points () when
and
for f below a critical frequency f*. For frequencies f>f*, only the fixed point at
is stable. In the VPI experiment, a separate scaling trial in which the frequency is systematically increased is used to determine f*. The value of f* is then used as an upper bound for the choice of frequency parameter, ensuring that pattern instability is not only due to the effect of high frequency in the subject but also comes from conflicting tasks.
Figure 5.
Experimental conditions defined by the direction of coupling or information flow.
In human-to-VP condition (A), the display is switched off but kinematic information about the subject's movement is received by the virtual partner. In the bidirectional condition (B), the subject sees the virtual partner's movements and the virtual partner receives kinematic information of the subject's movements. In the VP-to-human condition (C), a subject has vision of the virtual partner's movements but the virtual partner is decoupled (coupling term set to zero) from the subject.
Figure 6.
Relative phase distributions for unidirectional and bidirectional conditions at low and high movement frequencies.
Data are collapsed across subjects. For the Human-to-VP conditions, the distributions of relative phase suggest peaks at just below anti-phase (≈2.5 rad) for the low-frequency condition (A) and near anti-phase ( rad) for the high-frequency condition (B). The relatively flat distribution shows the weakness of the coupling of the virtual partner with the human. On the other hand, in the VP-to-Human conditions (E) and (F) the human subject is able to coordinate with the virtual partner when the latter functions like a passive visual metronome. The results for Bidirectional conditions are shown for low (C) and high (D) frequencies, respectively. The range of the vertical axis is doubled compared to unidirectional conditions because of the different number of trials used. The distributions are bimodal with a larger concentration of in-phase than anti-phase at both frequencies. For high (D) relative to low frequency (C) the concentration at in-phase decreases while phase dispersion and antiphase increase.
Figure 7.
Examples of relative phase time series showing the three basic behaviors found in bidirectional trials.
Stable coordination is shown in (A), intermittent switching between in-phase and anti-phase in (B) and unstable phase wrapping behavior in (C). Using the synchronization index and dwell time criteria, the percentage distributions were computed and are given in Table 2 (for comparison, data for the unidirectional conditions are also provided).
Table 2.
Distribution of coordination patterns for low and high frequency conditions classified according to combined criteria of synchronization index and dwell time.
Figure 8.
Behavioral patterns in bidirectional conditions.
Reciprocal interaction between human and VP gives rise to unstable (not shown), intermittent (A) and stable (B, C) collective behaviors. Shown are the time series for positions of the virtual partner (x, blue curve) and the subject (y, orange curve) and the relative phase of the subject with respect to the virtual partner. Motion near in-phase and anti-phase are highlighted in green and red, respectively. When a subject is in-phase with the virtual partner, the latter's amplitude eventually decreases due to the reversed coupling. To prevent amplitude collapse, subjects may temporarily switch to anti-phase (A). For extended in-phase coordination, spatial strategies were employed by the subjects. These include reducing one's amplitude to an optimal range (B), and shifting the center of oscillation downward toward flexion (C). None of the strategies were part of the instructions to coordinate but were discovered during the course of interaction.
Figure 9.
Simulations of spatial strategies during extended in-phase coordination.
A sine signal acts as a pseudo-subject for the virtual partner. The phase of the sine signal is reset to force in-phase synchronization. The plots show the position time series of the VP (blue) in response to amplitude and origin shift manipulations of the input signal (orange). (A) The amplitude decline of the VP is systematically delayed when the origin of the sine oscillation is changed by amounts P = 0, −0.7, and −1 (shifted down). At P = −1, the virtual partner's amplitude remains constant throughout the 100 sec simulated trial. (B) When the effective input amplitude Q is systematically reduced (Q = 4,2,1), the decline in the virtual partner's amplitude is also delayed. At the critical value Q = 1, the virtual partner maintains its amplitude throughout the run.