Control at stability's edge minimizes energetic costs: expert stick balancing
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- John Milton
- W. M. Keck Science Department, The Claremont Colleges, Claremont, CA 91711, USA
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- Ryan Meyer
- Pomona College, Claremont, CA 91711, USA
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- Max Zhvanetsky
- Harvey Mudd College, Claremont, CA 91711, USA
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- Sarah Ridge
- Scripps College, Claremont, CA 91711, USA
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- Tamás Insperger
- Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
説明
<jats:p> 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 <jats:inline-formula> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rsif20160212ie1.gif" /> </jats:inline-formula> ° 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. </jats:p>
収録刊行物
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- Journal of The Royal Society Interface
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Journal of The Royal Society Interface 13 (119), 20160212-, 2016-06
The Royal Society