Control at stability's edge minimizes energetic costs: expert stick balancing.
Stick balancing on the fingertip is a complex voluntary motor task that requires the stabilization of an unstable system. For seated expert stick balancers, the time delay is 0.23 s, the shortest stick that can be balanced for 240 s is 0.32 m and there is a [Formula: see text]° dead zone for the estimation of the vertical displacement angle in the saggital plane. These observations motivate a switching-type, pendulum-cart model for balance control which uses an internal model to compensate for the time delay by predicting the sensory consequences of the stick's movements. Numerical simulations using the semi-discretization method suggest that the feedback gains are tuned near the edge of stability. For these choices of the feedback gains, the cost function which takes into account the position of the fingertip and the corrective forces is minimized. Thus, expert stick balancers optimize control with a combination of quick manoeuvrability and minimum energy expenditures.
W. M. Keck Science Department, The Claremont Colleges, Claremont, CA 91711, USA jmilton@kecksci.claremont.edu.
John
0000-0001-5037-2548
J
Milton
Pomona College, Claremont, CA 91711, USA.
Ryan
R
Meyer
Harvey Mudd College, Claremont, CA 91711, USA.
Max
M
Zhvanetsky
Scripps College, Claremont, CA 91711, USA.
Sarah
S
Ridge
Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary.
Tamás
T
Insperger
D000293:Adolescent; D000328:Adult; D004734:Energy Metabolism; D005260:Female; D005385:Fingers; D006801:Humans; D008297:Male; D008954:Models, Biological
microchaos; predictor feedback; sensory dead zone; stick balancing; time delay