Motion Plan Changes Predictably in Dyadic Reaching

Abstract

Parents can effortlessly assist their child to walk, but the mechanism behind such physical coordination is still unknown. Studies have suggested that physical coordination is achieved by interacting humans who update their movement or motion plan in response to the partner's behaviour. Here, we tested rigidly coupled pairs in a joint reaching task to observe such changes in the partners' motion plans. However, the joint reaching movements were surprisingly consistent across different trials. A computational model that we developed demonstrated that the two partners had a distinct motion plan, which did not change with time. These results suggest that rigidly coupled pairs accomplish joint reaching movements by relying on a pre-programmed motion plan that is independent of the partner's behaviour.

Fig 1. Dyadic reaching apparatus and protocol.

(A) Schematic of the dual-wrist interface setup. (B) The experiment was split up into three types of blocks: training and solo blocks, a coupled block and push-pull blocks. Dyads were alternately disconnected (training and solo blocks) and connected (coupled and push-pull blocks). After the first push-pull block and subsequent solo block, dyads performed another push-pull block and solo block. (C) In the training and solo blocks, partners are disconnected and reach the target alone. Feedback was given to the subject if the movement is faster than 900 ms or slower than 1200 ms. In the coupled and push-pull blocks the partners were rigidly coupled. In the coupled block, partners were rigidly coupled and moved the averaged cursor to the target. In the push-pull block, dyads were constrained to produce a torque of 0.7 Nm prior to the reaching movement. One partner pushed towards the target and the other pulled away; once the initial opposing torque was balanced and the average cursor position at 0 degrees, the 3 second countdown was initiated. Partners switched the pushing and pulling instructions in the second push-pull block. In all blocks, a 3 second countdown was used to initiate the movement.

Fig 2. Trajectory and torque data for the coupled block.

(A) Trajectories of the average cursor for all dyads in the coupled block. The bold lines indicate the average trajectory of each bin; the thin lines show the individual trials. (B) Torque from all eight dyads, where each bold trace corresponds to the average of each bin; the bins progress chronologically from green to blue for the blue partner and from yellow to red for the red partner. With the exception of dyad VIII, no consistent trial-by-trial change in the torque was observed within dyads. Different dyads displayed specific torque patterns.

Fig 3. Dyadic reaching with initial opposing torque prior to movement.

Torque from dyads I–IV in the coupled and both push-pull blocks; each bold trace is the average trajectory of each bin. In all dyadic reaching blocks, the torque was unchanging between trials within each block.

Fig 4. Position and velocity priority in the motion plan explains endpoint bias.

(A) The (decoupled) blue controller prioritises position, which causes it to overshoot the target. The (decoupled) red controller prioritises velocity such that it converges to the target without any overshoot. When the position-priority and velocity-priority controllers are coupled (dashed black trace), a force pattern is observed (dashed blue and red traces). The only manner in which the controllers would end the movement with constant torque is if they decide to hold their position once the reach is fulfilled. (B) Endpoint bias at the end of the reaching movement from all 16 partners. Partners, at movement onset, who pushed towards the target overshot it, and those who pulled away undershot it.

Fig 5. Simulation of dyadic reaching.

Trajectories and torques from dyads I to IV (A–D) in the coupled and push-pull blocks. Solid trace is from the data showing the mean of all trials and the shaded area is the 95% confidence interval; the dashed traces are from simulations. First, we identify the state costs of both partners in coupled reaching, then identify the state cost in the push-pull blocks to see what effect the opposing torques prior to movement onset had. In all dyads, the initial opposing torque had a consistent effect: partners pushing towards the target prioritised position, and overshot the target; those pulling away prioritised velocity and undershoot the target.