Composition and decomposition in bimanual dynamic learning

Abstract

Our ability to skillfully manipulate an object often involves the motor system learning to compensate for the dynamics of the object. When the two arms learn to manipulate a single object they can act cooperatively, whereas when they manipulate separate objects they control each object independently. We examined how learning transfers between these two bimanual contexts by applying force fields to the arms. In a coupled context, a single dynamic is shared between the arms, and in an uncoupled context separate dynamics are experienced independently by each arm. In a composition experiment, we found that when subjects had learned uncoupled force fields they were able to transfer to a coupled field that was the sum of the two fields. However, the contribution of each arm repartitioned over time so that, when they returned to the uncoupled fields, the error initially increased but rapidly reverted to the previous level. In a decomposition experiment, after subjects learned a coupled field, their error increased when exposed to uncoupled fields that were orthogonal components of the coupled field. However, when the coupled field was reintroduced, subjects rapidly readapted. These results suggest that the representations of dynamics for uncoupled and coupled contexts are partially independent. We found additional support for this hypothesis by showing significant learning of opposing curl fields when the context, coupled versus uncoupled, was alternated with the curl field direction. These results suggest that the motor system is able to use partially separate representations for dynamics of the two arms acting on a single object and two arms acting on separate objects.

Figure 1.

Composition and decomposition experiments. In the uncoupled phase (A), the hands were unlinked and orthogonal curl field components were applied to each arm. The task involved making out-and-back movements with two cursors (displayed as the small filled circles with lines attached to the hand positions) from a central home position (shown as the unfilled circle) to one of eight targets (shown as the gray filled circles). In the coupled phase (B), the same task was performed, but the arms were linked with a stiff virtual spring and the arms experienced a full curl field.

Figure 2.

Curl field switching experiments. Center out-and-back movements were performed and the direction of the curl field could be switched between batches to investigate interference in dynamic learning. In a coupled condition (A), the hands were linked with a stiff virtual spring, and both hands acted together on a curl field. In an uncoupled condition (B), each arm was unlinked and experienced a half-strength curl field.

Figure 3.

All individual subject and mean outward right-hand paths at different stages of the experiment. To enable the mean to be calculated, each trajectory has been truncated to the shortest outward path across the subjects. A–C, Shown are the trajectories for the composition, decomposition, and decomposition control paradigms, respectively.

Figure 4.

Results for the composition–decomposition experiment. A, B, Shown are the MPEs for the left and right hands, respectively, illustrating the effect of switching between uncoupled and coupled contexts. The shading shows SE across subjects. C, DPFV during catch trials for the two arms.

Figure 5.

Results for the decomposition–composition experiment. A, B, Shown are the MPEs for the left and right hands, respectively, illustrating the effect of switching between coupled and uncoupled contexts. Shading shows SE across subjects. C, DPFV during catch trials for the two arms.

Figure 6.

Results for the decomposition–composition control experiment, using decomposition into half-strength full curl fields. A, B, Shown are the MPEs for the left and right hands, respectively, illustrating the effect of switching between coupled and uncoupled contexts. The shading shows SE across subjects.

Figure 7.

Results for the curl field switching experiments. A–C, Shown are the MPEs of the right hand over each batch in the uncoupled, coupled, and alternating conditions, respectively. Error bars show 1 SE on the mean across the subjects.

Figure 8.

Results for the curl field switching experiments. A, B, Shown are the MPEs over the first batch after switching for the left and right hands, respectively. Error bars show 1 SE on the mean across the subjects.