There is substantial evidence that humans possess an accurate and adaptable internal model of the dynamics of their arm that is utilized by the nervous system for controlling arm movements. However, it is not known if such model-based strategies are used for controlling dynamical systems outside the body. The need to predict events in the external world is not restricted to the execution of reaching movements or to the handling of rigid tools. Model-based control may also be critical for performing functional tasks with non-rigid objects such as stabilizing a cup of coffee. The present study investigated the strategies used by humans to control simple mass-spring objects. Subjects made straight line reaching movements to a target while interacting with a robotic manipulandum that simulated the dynamics of a one-dimensional mass on a spring. After learning, neither hand nor object kinematics returned to those of free reaching, suggesting that this task was not learned as a perturbation of free reaching. Although there are control strategies (such as slowing the movement of the hand) that would require little or no knowledge of object dynamics, subjects did not adopt these strategies. Instead, they tailored their motor commands to the particular object being manipulated. When object parameters were unexpectedly altered in a way that required no changes in kinematics to successfully complete the task, subjects nonetheless exhibited substantial kinematic deviations. These deviations were consistent with those predicted by a model of the arm-plus-object system driven by a low-impedance controller that incorporated an explicit inverse model of arm-plus-object dynamics. The observed behavior could not be reproduced by a controller that relied on modulating hand impedance alone with no inverse model. These results were therefore consistent with the hypothesis that subjects learn to control the kinematics of manipulated objects by forming an internal model that specified the forces to be exerted by the hand on the object to induce the desired motion of that object.
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