Modelling human balance using switched systems with linear feedback control

Kowalczyk, Piotr; Glendinning, Paul; Brown, M.; Medrano-Cerda, Gustavo A.; Dallali, Houman; Shapiro, Johanna

doi:10.1098/rsif.2011.0212

Cited by 61 publications

(69 citation statements)

References 38 publications

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“…Periodic solutions are also observed for (2) for PD feedback [45]. However, power spectral analysis of postural sway does not typically show the presence of a strong periodic component (for a notable exception see [98]).…”

Section: In the Interval X J ∈ [−2 2] This Map Is Identical To The mentioning

confidence: 96%

“…In general there can be a different threshold associated with each of θ(t),θ(t) andθ(t); however, here we have shown only a threshold for θ(t). In the mathematical literature, the study of the effects of a threshold on feedback control falls under the heading of switching [31,45,28], or hybrid [35] control. The threshold is a strong small-scale nonlinearity since it destroys the fixed-point.…”

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: In the Interval X J ∈ [−2 2] This Map Is Identical To The mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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

Milton

Insperger

Stépàn

2015

Mathematical Approaches to Biological Systems

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“…More recently, it has been shown (Pinter, van Swigchem, van Soest, and Rozendaal, 2008;Günther, Grimmer, Siebert, and Blickhan, 2009;Blickhan, 2011, 2012) that a multiple segment multiple input model is required to model unconstrained quiet standing and this clearly has implications for the corresponding human control system. Intermittent control has been suggested as the basic algorithm , and and related algorithms have been analysed by Insperger (2006); Stepan and Insperger (2006), Asai et al (2009) and Kowalczyk et al (2012).…”

Section: Examples: Human Standingmentioning

confidence: 99%

Event-Based Data Acquisition and Reconstruction—Mathematical Background

Thao¹

2018

Event-Based Control and Signal Processing

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Intermittent control has a long history in the physiological literature and there is strong experimental evidence that some human control systems are intermittent. Intermittent control has also appeared in various forms in the engineering literature. This article discusses a particular mathematical model of Event-driven Intermittent Control which brings together engineering and physiological insights and builds on and extends previous work in this area. Illustrative examples of the properties of Intermittent Control in a physiological context are given together with suggestions for future research directions in both physiology and engineering. i arXiv:1407.3543v1 [q-bio.QM]

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“…The latter has been proposed for stabilization of quiet upright stance [18][19][20][21], based on the assumption that small deviations from upright position are not detected by the control unit and that active corrective torques are generated only when the position [19] or the velocity [20] exceeds a given threshold, i.e. when jaðtÞj .…”

Section: Neurobiologymentioning

confidence: 99%

Balancing on tightropes and slacklines

Paoletti

Mahadevan

2012

J. R. Soc. Interface.

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Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.

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Modelling human balance using switched systems with linear feedback control

Cited by 61 publications

References 38 publications

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

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

Event-Based Data Acquisition and Reconstruction—Mathematical Background

Balancing on tightropes and slacklines

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