Two models of feedforward motor planning. Arm position estimates X̂INV are computed by combining visual and proprioceptive signals. A movement vector describing the desired direction of the initial velocity (Ẋ*) or acceleration (ẍ*) of the hand is computed by subtracting X̂MV from the target location x*. An inverse model transforms this desired extrinsic vector into an intrinsic motor command specifying joint angle velocities (
) or torques (τ), depending on the model being implemented. This transformation makes use of a second position estimate, X̂ and X̂INV. Finally, the motor command is executed, determining the initial hand trajectory. Note that the loop through the “Vision” and “Proprioception” boxes does not imply feedback control; in these models, the position estimates are only used to plan the plan the initial, feedforward component of a movement.