Experimentally Confirmed Mathematical Model for Human Control of a Non-Rigid Object
J
Neurophysiol 91: 1158–1170, 2004
Jonathan B. Dingwell,
Christopher D. Mah, and Ferdinando A. Mussa-Ivaldi
Determining the principles
used to plan and execute movements is a fundamental question in neuroscience
research. When humans reach to a target with their hand, they exhibit
stereotypical movements that closely follow an optimally smooth trajectory.
Even when faced with various perceptual or mechanical perturbations, subjects
readily adapt their motor output to preserve this stereotypical trajectory.
When humans manipulate non-rigid objects, however, they must control the
movements of the object as well as the hand. Such tasks impose a fundamentally
different control problem than that of moving one’s arm alone. Here, we
developed a mathematical model for transporting a mass-on-a-spring to a target
in an optimally smooth way. We demonstrate that the well-known “minimum-jerk”
model for smooth reaching movements cannot accomplish this task. Our model
extends the concept of smoothness to allow for the control of non-rigid
objects. Although our model makes some predictions that are similar to minimum
jerk, it predicts distinctly different optimal trajectories in several specific
cases. In particular, when the relative speed of the movement becomes fast
enough or when the object stiffness becomes small enough, the model predicts
that subjects will transition from a uni-phasic hand motion to a bi-phasic hand
motion. We directly tested these predictions in human subjects. Our subjects
adopted trajectories that were well-predicted by our model, including all of
the predicted transitions between uni- and bi-phasic hand motions. These
findings suggest that smoothness of motion is a general principle of movement
planning that extends beyond the control of hand trajectories.
Dingwell,
J. B., Mah, C.D. and Mussa-Ivaldi, F.A.. Experimentally confirmed mathematical
model for human control of a non-rigid object. J Neurophysiol 91: 1158–1170,
2004