Document Detail

The time-delayed inverted pendulum: implications for human balance control.
MedLine Citation:
PMID:  19566270     Owner:  NLM     Status:  MEDLINE    
The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, tau(n), be greater than a critical delay tau(c) that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when theta exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.
John Milton; Juan Luis Cabrera; Toru Ohira; Shigeru Tajima; Yukinori Tonosaki; Christian W Eurich; Sue Ann Campbell
Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't; Research Support, U.S. Gov't, Non-P.H.S.    
Journal Detail:
Title:  Chaos (Woodbury, N.Y.)     Volume:  19     ISSN:  1089-7682     ISO Abbreviation:  Chaos     Publication Date:  2009 Jun 
Date Detail:
Created Date:  2009-07-01     Completed Date:  2009-10-01     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  100971574     Medline TA:  Chaos     Country:  United States    
Other Details:
Languages:  eng     Pagination:  026110     Citation Subset:  IM    
Joint Science Department, W. M. Keck Science Center, The Claremont Colleges, Claremont, California 91711, USA.
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MeSH Terms
Biophysical Phenomena
Locomotion / physiology
Middle Aged
Models, Biological*
Nonlinear Dynamics
Postural Balance / physiology*
Young Adult

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