Linking Motor Learning to Function Approximation: Learning in an Unlearnable Force Field

It appears that in constructing the motor commands to guide the arm toward a target, the brain relies on an internal model (IM) of the dynamics of the task that it learns through practice [1]. The IM is presumably a system that transforms a desired limb trajectory in sensory coordinates to motor commands. The motor commands in turn create the complex activation of muscles necessary to cause action. A major issue in motor control is to infer characteristics of the IM from the actions of subjects. Recently, we took a first step toward mathematically characterizing the IM's rep- resentation in the brain [2]. We analyzed the sequence of errors made by subjects on successive movements as they reached to targets while holding a robotic arm. The robot produced a force field and subjects learned to compensate for the field (presumably by constructing an IM) and eventually produced straight movements within the field. Our analysis sought to draw conclusions about the structure of the IM from the sequence of errors generated by the subjects.