Stick balancing, falls and Dragon-Kings

Cabrera, Juan Luis; Milton, John

doi:10.1140/epjst/e2012-01573-7

Cited by 29 publications

(32 citation statements)

References 42 publications

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“…These differences become most apparent when the structures shown, respectively, in Figures 5b and d are hung at their stable (downward) positions [90]. Whereas (18) predicts that the oscillations occur about the pivot point, (28) predicts that they occur near the mid-point of the pendulum as observed experimentally [48]. Moreover, the period of the oscillations predicted by (18) …”

Section: Stick Balancing At the Fingertipmentioning

confidence: 74%

“…Despite the similarity between (18) and (28) there are important differences between the dynamics of an inverted pendulum and a pendulum on a cart. These differences become most apparent when the structures shown, respectively, in Figures 5b and d are hung at their stable (downward) positions [90].…”

Section: Stick Balancing At the Fingertipmentioning

confidence: 99%

“…In stick balancing emphasis has been drawn to the transient nature of the 'balanced state' [15,17,18]. In particular, a number of empirical observations have suggested that, counter-intuitively, the control parameters for many subjects correspond to choices for which the upright position would not be stable [15,17].…”

Section: Stick Balancing At the Fingertipmentioning

confidence: 99%

“…First, it is possible that the intermittency may be event-driven, namely corrective forces are generated whenever the controlled variable crosses a threshold [4,10,12,33,34,39,68,69,71]. A well known example of threshold crossing in human balance control is the "safety-net" character of the ankle-hip-step control strategy used by humans to maintain balance in the face of increasingly large perturbations [18,86]. In the case of stick balancing on the fingertip the intermittency manifests as a power law [12,19,75].…”

Section: Introductionmentioning

confidence: 99%

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Human Balance Control: Dead Zones, Intermittency, and Micro-chaos

Milton

Insperger

Stépàn

2015

Mathematical Approaches to Biological Systems

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Summary. The development of strategies to minimize the risk of falling in the elderly represents a major challenge for aging, in industrialized societies. The corrective movements made by humans to maintain balance are small amplitude, intermittent and ballistic. Small amplitude, complex oscillations (micro-chaos) frequently arise in industrial settings when a time-delayed digital processor attempts to stabilize an unstable equilibrium. Taken together these observations motivate considerations of the effects of a sensory threshold on the stabilization of an inverted pendulum by time-delayed feedback. In the resulting switching-type delay differential equations, the sensory threshold is a strong small-scale nonlinearity which has no effect on large-scale stabilization, but may produce complex, small amplitude dynamics including limit cycle oscillations and micro-chaos. A close mathematical relationship exists between a scalar model for balance control and the micro-chaotic map that arises in some models of digitally controlled machines. Surprisingly, transient, timedependent, bounded solutions (transient stabilization) can arise even for parameter ranges where the equilibrium is asymptotically unstable. In other words the combination of a sensory threshold with a time-delayed sampled feedback can increase the range of parameter values for which balance can be maintained, at least transiently. Neuro-biological observations suggest that sensory thresholds can be manipulated either passively by changing posture or actively using efferent feedback. Thus it may be possible to minimize the risk of falling by means of strategies that manipulate sensory thresholds by using physiotherapy and appropriate exercises.

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Section: Stick Balancing At the Fingertipmentioning

confidence: 74%

Section: Stick Balancing At the Fingertipmentioning

confidence: 99%

Section: Stick Balancing At the Fingertipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Human Balance Control: Dead Zones, Intermittency, and Micro-chaos

Milton

Insperger

Stépàn

2015

Mathematical Approaches to Biological Systems

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“…Indeed, the existence of ankle -hip-step strategies to maintain balance in response to increasingly large perturbations [63] strongly points to a nested, or 'safety net', control network topology. In other words, the number of feedback loops that participate in control increases as the vertical displacement angle increases [64]. An important distinguishing point is that the thresholds in these strategies are not related to sensory dead zones, but rather are likely to be set in a manner to influence stability.…”

Section: Resultsmentioning

confidence: 99%

Acceleration feedback improves balancing against reflex delay

Insperger

Milton

Stépàn

2013

J. R. Soc. Interface.

121

111

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A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportionalderivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.

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