Article,
Relative damping improves linear mass-spring models of goal-directed movements
Human Movement Science, (2002)
Abstract
A limitation of a simple linear mass-spring model in describing goal
directed movements is that it generates rather slow movements when
the parameters are kept within a realistic range. Does this imply
that the control of fast movements cannot be approximated by a linear
system? In servo-control theory, it has been proposed that an optimal
controller should control movement velocity in addition to position.
Instead of explicitly controlling the velocity, we propose to modify
a simple linear mass-spring model. We replaced the damping relative
to the environment (absolute damping) with damping with respect to
the velocity of the equilibrium point (relative damping). This gives
the limb a tendency to move as fast as the equilibrium point. We
show that such extremely simple models can generate rapid single-joint
movements. The resulting maximal movement velocities were almost
equal to those of the equilibrium point, which provides a simple
mechanism for the control of movement speed. We further show that
peculiar experimental results, such as an ?N-shaped? equilibrium
trajectory and the difficulties to measure damping in dynamic conditions,
may result from fitting a model withabsolute damping where one withrelative
damping would be more appropriate. Finally, we show that the model
with relative damping can be used to model subtle differences between
multi-joint interceptions. The model with relative damping fits the
data much better than a version of the model with absolute damping
