Relative damping improves linear mass-spring models of goal-directed movements

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 with absolute damping where one with relative 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.