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Journal of Neuroscience, Vol 5, 1688-1703, Copyright © 1985 by Society for Neuroscience
The coordination of arm movements: an experimentally confirmed mathematical model
T Flash and N Hogan
This paper presents studies of the coordination of voluntary human arm
movements. A mathematical model is formulated which is shown to predict
both the qualitative features and the quantitative details observed
experimentally in planar, multijoint arm movements. Coordination is modeled
mathematically by defining an objective function, a measure of performance
for any possible movement. The unique trajectory which yields the best
performance is determined using dynamic optimization theory. In the work
presented here, the objective function is the square of the magnitude of
jerk (rate of change of acceleration) of the hand integrated over the
entire movement. This is equivalent to assuming that a major goal of motor
coordination is the production of the smoothest possible movement of the
hand. Experimental observations of human subjects performing voluntary
unconstrained movements in a horizontal plane are presented. They confirm
the following predictions of the mathematical model: unconstrained
point-to-point motions are approximately straight with bell-shaped
tangential velocity profiles; curved motions (through an intermediate point
or around an obstacle) have portions of low curvature joined by portions of
high curvature; at points of high curvature, the tangential velocity is
reduced; the durations of the low-curvature portions are approximately
equal. The theoretical analysis is based solely on the kinematics of
movement independent of the dynamics of the musculoskeletal system and is
successful only when formulated in terms of the motion of the hand in
extracorporal space. The implications with respect to movement organization
are discussed.
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