Studies of arm movements have shown that subjects learn to compensate predictable mechanical perturbations by developing a representation of the relation between the state of motion of the arm and the perturbing forces. Here, we tested the hypothesis that subjects construct internal representations of two different force fields and switch between them when presented with an alternating sequence of these fields. Our results do not support this hypothesis. Subjects performed reaching movements in four sessions over 4 days. On the 1st day the robotic manipulandum perturbed the movement by perpendicular force that alternated its direction after each movement. Subjects were unable to construct the two underlying models and switch between them. On the 2nd day only one field was applied and well learned. On the 3rd day only the other field was applied and well learned. Then the experiment of the 1st day was repeated on the 4th day. Even after this extensive training subjects showed no signs of improved performance with alternating fields. This result combined with previous studies suggests that the central nervous system has a strong tendency to employ a single internal model when dealing with a sequence of perturbations.

Faster relearning of an external perturbation, savings, offers a behavioral linkage between motor learning and memory. To explain savings effects in reaching adaptation experiments, recent models suggested the existence of multiple learning components, each shows different learning and forgetting properties that may change following initial learning. Nevertheless, the existence of these components in rhythmic movements with other effectors, such as during locomotor adaptation, has not yet been studied. Here, we study savings in locomotor adaptation in two experiments; in the first, subjects adapted to speed perturbations during walking on a split-belt treadmill, briefly adapted to a counter-perturbation and then readapted. In a second experiment, subjects readapted after a prolonged period of washout of initial adaptation. In both experiments we find clear evidence for increased learning rates (savings) during readaptation. We show that the basic error-based multiple timescales linear state space model is not sufficient to explain savings during locomotor adaptation. Instead, we show that locomotor adaptation leads to changes in learning parameters, so that learning rates are faster during readaptation. Interestingly, we find an intersubject correlation between the slow learning component in initial adaptation and the fast learning component in the readaptation phase, suggesting an underlying mechanism for savings. Together, these findings suggest that savings in locomotion and in reaching may share common computational and neuronal mechanisms; both are driven by the slow learning component and are likely to depend on cortical plasticity. computational motor control; locomotor adaptation; motor learning; split-belt

Rapid arm-reaching movements serve as an excellent test bed for any theory about trajectory formation. How are these movements planned? A minimum acceleration criterion has been examined in the past, and the solution obtained, based on the Euler-Poisson equation, failed to predict that the hand would begin and end the movement at rest (i.e., with zero acceleration). Therefore, this criterion was rejected in favor of the minimum jerk, which was proved to be successful in describing many features of human movements. This letter follows an alternative approach and solves the minimum acceleration problem with constraints using Pontryagin's minimum principle. We use the minimum principle to obtain minimum acceleration trajectories and use the jerk as a control signal. In order to find a solution that does not include nonphysiological impulse functions, constraints on the maximum and minimum jerk values are assumed. The analytical solution provides a three-phase piecewise constant jerk signal (bang-bang control) where the magnitude of the jerk and the two switching times depend on the magnitude of the maximum and minimum available jerk values. This result fits the observed trajectories of reaching movements and takes into account both the extrinsic coordinates and the muscle limitations in a single framework. The minimum acceleration with constraints principle is discussed as a unifying approach for many observations about the neural control of movements.

The stiffness of the environment with which we come in contact is the local derivative of a force field. The boundary of an elastic field is a singular region where local stiffness is ill-defined. We found that subjects interacting with delayed force fields tend to underestimate stiffness if they do not move across the boundary. In contrast, they tend to overestimate stiffness when they move across the elastic field boundary. We propose a unifying computational model of stiffness perception based on an active process that combines the concurrent operations of a force and of a position-control system.