Sensory uncertainty and stick balancing at the fingertip

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