ORIGINAL PAPER Sensory uncertainty and stick balancing at the fingertip

Abstract The effects of sensory input uncertainty, ε, on the stability of time-delayed human motor control are inves-tigated by calculating the minimum stick length, crit, that can be stabilized in the inverted position for a given time delay, τ. Five control strategies often discussed in the con-text of human motor control are examined: three time-invariant controllers [proportional–derivative, proportional– derivative–acceleration (PDA), model predictive (MP) con-trollers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncer-tainties 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 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 τ ≈ 0.08 s). However, a PDA controller becomes more effective when ε> 15 %. A comparison between 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 crit, τ, and a variability of the fluctuations in the vertical displacement angle, an estimate of ε, may make it possible to study the changes in control strategy as motor skill develops