Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Hajdu, Dávid; Milton, John; Insperger, Tamás

doi:10.1109/tnsre.2016.2541083

Cited by 16 publications

(19 citation statements)

References 51 publications

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“…p = p 0 + (1/2)Δ p and d = d 0 + (1/2)Δ d , then larger than δ p relative error in the tuning of p or larger than δ d relative error in the tuning of d destabilizes the system. Parameters Δ p and Δ d at the same time show the robustness of the system against static sensorimotor uncertainties [18,19,36,37]. Figure 1 b shows the robust stability boundaries associated with δ p = 0, δ p = 0.1 and δ p = 0.5 by solid, dashed and dotted lines, respectively.…”

Section: Introductionmentioning

confidence: 99%

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

2019

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Sensory uncertainties and imperfections in motor control play important roles in neural control and Bayesian approaches to neural encoding. However, it is difficult to estimate these uncertainties experimentally. Here, we show that magnitude of the uncertainties during the generation of motor control force can be measured for a virtual stick balancing task by varying the feedback delay, τ. It is shown that the shortest stick length that human subjects are able to balance is proportional to τ 2. The proportionality constant can be related to a combined effect of the sensory uncertainties and the error in the realization of the control force, based on a delayed proportional-derivative (PD) feedback model of the balancing task. The neural reaction delay of the human subjects was measured by standard reaction time tests and by visual blank-out tests. Experimental observations provide an estimate for the upper boundary of the average sensorimotor uncertainty associated either with angular position or with angular velocity. Comparison of balancing trials with 27 human subjects to the delayed PD model suggests that the average uncertainty in the control force associated purely with the angular position is at most 14% while that associated purely with the angular velocity is at most 40%. In the general case when both uncertainties are present, the calculations suggest that the allowed uncertainty in angular velocity will always be greater than that in angular position.

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Section: Introductionmentioning

confidence: 99%

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

2019

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“…The control parameters could be tuned into even slightly unstable regions where the sensory threshold (not considered in this study) helps to achieve micro-chaotic or long transient chaotic oscillations, which is satisfactory from practical balancing viewpoint [21]. All these considerations explain why the parameter point M in figure 3 is selected at P ¼ 20 s 22 and D ¼ 3.33 s 21 , which correspond to the plausible gains K p ¼ 1200 Nm rad 21 and K d ¼ 200 Nms rad 21 in accordance with (3.4) (see also [19,41,42]).…”

Section: Linear Stability Of Quiet Standing and Parameter Selectionmentioning

confidence: 68%

Saturation limits the contribution of acceleration feedback to balancing against reaction delay

Zhang

Stépàn

Insperger

2018

J. R. Soc. Interface.

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A nonlinear model for human balancing subjected to a saturated delayed proportional–derivative–acceleration (PDA) feedback is analysed. Compared to the proportional–derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typically introduces subcritical Hopf bifurcation into the system, which can also lead to falling for large enough perturbations. The subcriticality becomes stronger as the acceleration feedback gain increases or the saturation torque limit decreases. These explain some features of human balancing failure related to the increased reaction delay of inactive elderly people.

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“…We pose three hypotheses related to the location of the fitted control gains. We base our hypotheses on three observations: 1) PD controllers with gains located in the lower left quadrant of the stability diagram are most robust to the effects of random perturbations 43 ; 2) expert pole balancers increase maneuverability while minimizing energetic costs for balance control by adapting gains in the lower left quadrant of the stability diagram 44 ; and 3) the control gains for subjects who do ball-and-beam balancing are progressively tuned towards the node-spiral separation line as their skill improves 45 . Statistical analysis show that H1 and H3 are accepted and H2 is rejected.…”

Section: Introductionmentioning

confidence: 99%

Response to Perturbation During Quiet Standing Matches Delayed State Feedback With Precisely Tuned Control Gains

Zelei¹,

Milton

Stépàn

et al. 2021

Preprint

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Postural sway is a result of a complex action-reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics is modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to “large” perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness.

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Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Cited by 16 publications

References 51 publications

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

Virtual stick balancing: sensorimotor uncertainties related to angular displacement and velocity

Saturation limits the contribution of acceleration feedback to balancing against reaction delay

Response to Perturbation During Quiet Standing Matches Delayed State Feedback With Precisely Tuned Control Gains

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