Adaptation and generalization in acceleration-dependent force fields

Any passive rigid inertial object that we hold in our hand, e.g., a tennis racquet, imposes a field of forces on the arm that depends on limb position, velocity, and acceleration. A fundamental characteristic of this field is that the forces due to acceleration and velocity are linearly separable in the intrinsic coordinates of the limb. In order to learn such dynamics with a collection of basis elements, a control system would generalize correctly and therefore perform optimally if the basis elements that were sensitive to limb velocity were not sensitive to acceleration, and vice versa. However, in the mammalian nervous system proprioceptive sensors like muscle spindles encode a nonlinear combination of all components of limb state, with sensitivity to velocity dominating sensitivity to acceleration. Therefore, limb state in the space of proprioception is not linearly separable despite the fact that this separation is a desirable property of control systems that form models of inertial objects. In building internal models of limb dynamics, does the brain use a representation that is optimal for control of inertial objects, or a representation that is closely tied to how peripheral sensors measure limb state? Here we show that in humans, patterns of generalization of reaching movements in acceleration-dependent fields are strongly inconsistent with basis elements that are optimized for control of inertial objects. Unlike a robot controller that models the dynamics of the natural world and represents velocity and acceleration independently, internal models of dynamics that people learn appear to be rooted in the properties of proprioception, nonlinearly responding to the pattern of muscle activation and representing velocity more strongly than acceleration.