Improved Assessment of Orbital Stability of Rhythmic Motion with Noise

Ahn, Jooeun; Hogan, Neville

doi:10.1371/journal.pone.0119596

Cited by 17 publications

(29 citation statements)

References 30 publications

(36 reference statements)

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“…For example, it has been shown that Floquet analysis of a simple nonlinear walking model with stochastic noise over-estimates orbital stability. 43,44 In addition, human walking is not exactly periodic, 45 and it has even been suggested that it might not be a stable limit cycle. 46…”

Section: B Poincaré Maps and Floquet Multipliersmentioning

confidence: 99%

Stability and predictability in human control of complex objects

Bazzi

Ebert

Hogan

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Previous research on movement control suggested that humans exploit stability to reduce vulnerability to internal noise and external perturbations. For interactions with complex objects, predictive control based on an internal model of body and environment is needed to preempt perturbations and instabilities due to delays. We hypothesize that stability can serve as means to render the complex dynamics of the body and the task more predictable and thereby simplify control. However, the assessment of stability in complex interactions with nonlinear and underactuated objects is challenging, as for existent stability analyses the system needs to be close to a (known) attractor. After reviewing existing methods for stability analysis of human movement, we argue that contraction theory provides a suitable approach to quantify stability or convergence in complex transient behaviors. To test its usefulness, we examined the task of carrying a cup of coffee, an object with internal degrees of freedom. A simplified model of the task, a cart with a suspended pendulum, was implemented in a virtual environment to study human control strategies. The experimental task was to transport this cart-and-pendulum on a horizontal line from rest to a target position as fast as possible. Each block of trials presented a visible perturbation, which either could be in the direction of motion or opposite to it. To test the hypothesis that humans exploit stability to overcome perturbations, the dynamic model of the free, unforced system was analyzed using contraction theory. A contraction metric was obtained by numerically solving a partial differential equation, and the contraction regions with respect to that metric were computed. Experimental results showed that subjects indeed moved through the contraction regions of the free, unforced system. This strategy attenuated the perturbations, obviated error corrections, and made the dynamics more predictable. The advantages and shortcomings of contraction analysis are discussed in the context of other stability analyses.

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Section: B Poincaré Maps and Floquet Multipliersmentioning

confidence: 99%

Stability and predictability in human control of complex objects

Bazzi

Ebert

Hogan

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another non-intuitive effect of noise on estimation was highlighted in a recent study on Floquet multipliers, a method for assessing orbital stability of rhythmic movements. Noise induces a bias in the estimation of orbital stability [ 57 ]. Another example for the surprising effect of noise is the two-thirds power law that is widely observed in human movements [ 58 – 61 ].…”

Section: Discussionmentioning

confidence: 99%

Noise Induces Biased Estimation of the Correction Gain

2016

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The detection of an error in the motor output and the correction in the next movement are critical components of any form of motor learning. Accordingly, a variety of iterative learning models have assumed that a fraction of the error is adjusted in the next trial. This critical fraction, the correction gain, learning rate, or feedback gain, has been frequently estimated via least-square regression of the obtained data set. Such data contain not only the inevitable noise from motor execution, but also noise from measurement. It is generally assumed that this noise averages out with large data sets and does not affect the parameter estimation. This study demonstrates that this is not the case and that in the presence of noise the conventional estimate of the correction gain has a significant bias, even with the simplest model. Furthermore, this bias does not decrease with increasing length of the data set. This study reveals this limitation of current system identification methods and proposes a new method that overcomes this limitation. We derive an analytical form of the bias from a simple regression method (Yule-Walker) and develop an improved identification method. This bias is discussed as one of other examples for how the dynamics of noise can introduce significant distortions in data analysis.

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“…From the perspective of biomechanical engineering, orbital stability is defined using estimated Floquet multipliers from measured data of physical rotation and orbital movement [11][12][13]. The study by [11] provided a method that generated accurate estimates with noisy experimental data. However, there is no generalized method to choose the proper Poincaré section.…”

Section: Introductionmentioning

confidence: 99%

Development of Floquet Multiplier Estimator to Determine Nonlinear Oscillatory Behavior in Power System Data Measurement

Choi¹,

Cho²,

Lee³

2019

Energies

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Measurement-based technology has been developed in the area of power transmission systems with phasor measurement units (PMU). Using high-resolution PMU data, the oscillatory behavior of power systems from general electromagnetic oscillations to sub-synchronous resonances can be observed. Studying oscillations in power systems is important to obtain information about the orbital stability of the system. Floquet multipliers calculation is based on a mathematical model to determine the orbital stability of a system with the existence of stable or unstable periodic solutions. In this paper, we have developed a model-free method to estimate Floquet multipliers using time series data. A comparative study between calculated and estimated Floquet multipliers has been performed to validate the proposed method. The results are provided for a sample three-bus power system network and the system integrated with a doubly fed induction generator.

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Improved Assessment of Orbital Stability of Rhythmic Motion with Noise

Cited by 17 publications

References 30 publications

Stability and predictability in human control of complex objects

Stability and predictability in human control of complex objects

Noise Induces Biased Estimation of the Correction Gain

Development of Floquet Multiplier Estimator to Determine Nonlinear Oscillatory Behavior in Power System Data Measurement

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