Sensory uncertainty and stick balancing at the fingertip

Abstract

The effects of sensory input uncertainty, $\varepsilon$, on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, $\ell _\mathrm{crit}$, that can be stabilized in the inverted position for a given time delay, $\tau$. 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 $\varepsilon \approx 7$–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 $\tau \approx 0.08$ s). However, a PDA controller becomes more effective when $\varepsilon > 15\,\%$. A comparison between $\ell _\mathrm{crit}$ 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 $\ell _\mathrm{crit},\,\tau$, and a variability of the fluctuations in the vertical displacement angle, an estimate of $\varepsilon$, may make it possible to study the changes in control strategy as motor skill develops.