Human stick balancing: tuning Lèvy flights to improve balance control

State-dependent, or parametric, noise is an essential component of the neural control mechanism for stick balancing at the fingertip. High-speed motion analysis in three dimensions demonstrates that the controlling movements made by the fingertip during stick balancing can be described by a Lèvy flight. The Lèvy index, alpha, is approximately 0.9; a value close to optimal for a random search. With increased skill, the index alpha does not change. However, the tails of the Lèvy distribution become broader. These observations suggest a Lèvy flight that is truncated by the properties of the nervous and musculoskeletal system; the truncation decreasing as skill level increases. Measurements of the cross-correlation between the position of the tip of the stick and the fingertip demonstrate that the role of closed-loop feedback changes with increased skill. Moreover, estimation of the neural latencies for stick balancing show that for a given stick length, the latency increases with skill level. It is suggested that the neural control for stick balancing involves a mechanism in which brief intervals of consciously generated, corrective movements alternate with longer intervals of prediction-free control. With learning the truncation of the Lèvy flight becomes better optimized for balance control and hence the time between successive conscious corrections increases. These observations provide the first evidence that changes in a Lèvy flight may have functional significance for the nervous system. This work has implications for the control of balancing problems ranging from falling in the elderly to the design of two-legged robots and earthquake proof buildings.