Figure 1. Multiple force-field (multi-FF) environment paradigm.

(a) Setup for the multi-FF environment experiments. We altered environmental dynamics by exposing participants to viscous curl FFs in which the force vector perturbing reaching movements was proportional in magnitude and perpendicular in direction to the velocity of the hand (see Materials and methods). (b) Diagram of unperturbed 1- and 2-target trial types. On 1-target trials (left panel), a single target located in the left (+30°), right (−30°), or center (0°) direction was presented, and participants were instructed to initiate rapid 20 cm reaching movements to the target after an auditory go cue. On 2-target trials (right panel), a pair of potential targets, always in the left and right target directions, was presented before the go cue. Then, 3 cm after movement onset, we extinguished one target and highlighted the other to indicate the final goal. Delaying the precise goal information in this manner typically leads to initial reaching movements directed in-between potential target locations before participants produce in-flight movement corrections towards the final target. (c) Individual-target FF perturbations. During 1-target trials, we perturbed movements to the left and right targets with FF_LATERAL (light blue and pink arrow and dotted trace sets, respectively) and the center target with FF_CENTER (light gray arrow and dotted trace sets). The directions of FF_LATERAL and FF_CENTER were counterbalanced across participants, but always with FF_CENTER = -FF_LATERAL. Training in this composite environment alters the adaptive responses (darker solid arrow trace sets) in accordance with the FF imposed on each target. Note that the adaptive response on 1- and 2-target trials was measured as the force patterns participants produced on error clamp and partial error clamp trials, respectively (see Materials and methods). (d) Predictions for motor averaging (MA) and performance optimization (PO) for feedforward motor planning during uncertainty. Because both potential targets (left and right) were associated with FF_LATERAL, MA (purple arrows) predicts a force pattern consistent with FF_LATERAL on 2-target trials. However, since the initial motion on these 2-target trials is in the direction of the center target, PO (green arrows) predicts the force pattern consistent with FF_CENTER, which is opposite the MA prediction.