Fig 1.
Experimental paradigm and simulation framework to investigate physical interaction between humans mediated by the coupling dynamics.
(A) Experimental configuration to test physical interaction in 1 dimension. Subjects, recruited in pairs, were separated by a curtain and followed a common target using their wrist flexion/extension to control a cursor along a 1 dimensional arc. Their wrists were virtually coupled together through the dual robotic interface by a spring with computer-controlled elasticity. Only the target, which was a normally distributed cloud of spots, and one’s own cursor were displayed on each subject’s individual monitor. (B) The computational framework to test different strategies (in purple) that partners could adopt during interaction. In this approach, only the goal or what information is used to track the target is changed. The goal is tracked by a subject who generates a motor command to move their wrist. Two subjects are simulated in parallel, who experience the coupling force from the spring. In follow the leader, subjects switch to following the partner nearest to the target. In interpersonal goal integration, the partner’s target is inferred through haptics and is integrated with one’s own target estimated from vision. Neuromechanical goal sharing is similar to interpersonal goal integration, but the weighting between the visual target and the partner’s target is influenced by the coupling dynamics.
Fig 2.
Results of physical interaction between humans through different coupling dynamics.
(A) Improvement, defined as the tracking error in a solo trial minus the error in the preceding connected trial, as a function of the relative error, defined as the difference in tracking errors between the partners in the solo trial. The improvement was modulated as a function of the coupling stiffness such that the worse partner (positive in the horizontal axis) improved more with the hard than with the soft interaction. However, the hard interaction did not hinder the better partner’s performance. (B) Interaction effort, defined as the effort expended during a solo trial minus the effort in the preceding connected trial, as a function of the relative error. The effort was estimated as the sum of the mean muscle activations, normalized with respect to torque, from a wrist flexor and extensor pair. As with the improvement, the interaction effort is modulated by the softness of the interaction. Only the better partner in the hard and medium interactions exerted more effort in comparison to solo trials.
Fig 3.
The follow the leader and interpersonal goal integration models cannot replicate the hard and soft interactions.
(A) Prediction of the improvement and interaction effort from the follow the leader model, where subjects switch to following the partner’s cursor if they are nearest to the target. The prediction overestimates the interaction effort by a large amount, and greatly underestimates the performance improvement. (B) Predictions from the interpersonal goal integration model, where the visual and haptic information of the target are combined to yield a better prediction of the target’s motion. The haptic estimate of the target is obtained by forming a representation of the partner that identifies how the partner’s movement changes in response to the motion of the target, which is used to estimate the partner’s target. Unlike the data, this model does not exhibit any modulation in the improvement due to the coupling stiffness.
Fig 4.
Coupling dynamics influence haptic communication.
(A) Haptic tracking control experiment to measure how the tracking error, or the noise in the haptic information, increases with the coupling stiffness (plots are mean±standard error). 8 individually recruited subjects received no visual feedback of the target, instead relying only on the haptic feedback from the elastic connection between the wrist and the target. (B) The tracking errors from the haptic tracking experiment were considered in the neuromechanical goal sharing model, which combines information from vision with the haptic sensing of the partner’s goal to improve tracking performance while taking into account the additional noise in haptic sensing arising from the softness of the interaction. The predictions from this model closely resemble the data, exhibiting modulation of both the improvement and interaction effort due to the coupling stiffness. This shows that the effort expended during interaction is not a strategy per se, but the outcome of maximizing the sensory information of the target’s motion.