Sensory uncertainty and stick balancing at the fingertip

Abstract

The effects of sensory input uncertainty, [Formula: see text], on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, [Formula: see text], that can be stabilized in the inverted position for a given time delay, [Formula: see text]. Five control strategies often discussed in the context of human motor control are examined: three time-invariant controllers [proportional-derivative, proportional-derivative-acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that [Formula: see text]-13 %. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25-0.5 m when [Formula: see text] s). However, a PDA controller becomes more effective when [Formula: see text]. A comparison between [Formula: see text] for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of [Formula: see text], and a variability of the fluctuations in the vertical displacement angle, an estimate of [Formula: see text], may make it possible to study the changes in control strategy as motor skill develops.