It has long been noted that human attempts at repeated movement are subject to considerable variability. While the nature of this variability has been extensively studied and plays important roles in some theories of motor control and motor learning, little is understood about the processes by which the motor control system generates variability having the observed properties. A plausible explanation is that noise inherent in the activity of the nervous system corrupts motor commands. But it is not known how motor command variability interacts with the dynamics of a movement to produce the observed patterns of behavior. Most of the theories in the literature explain properties of variability, such as speed-accuracy relationships, in purely kinematic terms that do not take the dynamic behavior of the motor plant into account. We describe a set of computational experiments aimed at studying the hypothesis that key properties of variability in fast reaching movements are due to nonlinear dynamical properties of the motor plant.
Specifically, we studied ballistic single degree-of-freedom movements generated by a fractional-power damping model of the plant driven by variable pulse-step motor commands. This model is motivated by the nonlinear properties of muscles and spinal reflex loops. After noting that dynamic models with linear damping do not generate significant final position variability under these conditions, we show that fractional-power damping naturally produces both linear and logarithmic relationships between movement velocity and endpoint variance. Fractional-power damping gives rise to dynamic behavior that includes a "stiction region": an extended region in the state space where movement effectively stops away from the system's equilibrium state. For each fixed control signal, the stiction region has well-defined borders, and final position variability can only take place within the stiction region. For an ensemble of movements generated by noisy command signals, the speed-accuracy relationship critically depends on the proportion of movements that hit the inner area of the stiction region versus the proportion of movements that undershoot or overshoot the region, thereby effectively stopping on an edge of the region. These results provide a new perspective on possible mechanisms for both the linear and logarithmic speed-accuracy relationships observed in reaching.
Letter size one page poster (all the files are gzipped): postscript (2.1M), pdf (669K).