Different Predictions by the Minimum Variance and
Minimum Torque-Change Models
on the Skewness of Movement Velocity Profiles
Hirokazu Tanaka, Meihua Tai and Ning Qian, Neural Computation, 2004,
16:2021-2040.
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paper (PDF file).
Abstract
We investigated the differences between two well-known
optimization principles for understanding movement planning: the
minimum variance (MV) model of Harris \& Wolpert and the minimum
torque-change (MTC) model of Uno et al. Both models accurately
describe the properties of human reaching movements in ordinary
situations (e.g. nearly straight paths and bell-shaped velocity
profiles). However, we found that the two models can make very
different predictions when external forces are applied or when the
movement duration is increased. We considered a second-order linear
system for the motor plant that has been used previously to simulate
eye movements and single-joint arm movements, and were able to derive
analytical solutions based on the MV and MTC assumptions. With the
linear plant, the MTC model predicts that the movement velocity
profile should always be symmetric, independent of the external forces
and movement duration.
In contrast, the MV model strongly depends on the movement
duration and the system's degree of stability; the latter in turn
depends on the total forces. The MV model thus predicts a skewed
velocity profile under many circumstances. For example, it predicts
that the peak location should be skewed toward the end of the
movement when the movement duration is increased in the absence of any
elastic force. It also predicts that with appropriate viscous and
elastic forces applied to increase the system stability, the velocity
profile should be skewed toward the beginning of the movement. The
velocity profiles predicted by the MV model can even show oscillations
when the plant becomes highly oscillatory. Our analytical and
simulation results suggest specific experiments for testing the
validity of the two models.
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