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Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing.

Yoshikawa N, Suzuki Y, Kiyono K, Nomura T - Front Comput Neurosci (2016)

Bottom Line: To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors.We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing.We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University Toyonaka, Japan.

ABSTRACT
The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy.

No MeSH data available.


Related in: MedlinePlus

Parameter dependency of stability and the non-Gaussianity index  for the movement variability of the pendulum in the type-1 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1s). Values of the index  were calculated for the model with various parameter vectors  = (a, Pθ, Dθ, Dx, σ, type = 1), which are plotted by color-code in the Pθ-Dθ planes for a set of combinations of the values of a (columns) and Dx (rows). The noise intensity is σ = 0.011 for the upper sets (A) of the Pθ-Dθ planes and σ = 0.001 for the lower sets (B) of the Pθ-Dθ planes. Because the index values can be calculated only when the models exhibit stable dynamics, the colored regions also represent the stability regions of the model. The parameter points indicated by the arrows with (A–D) are used for generating the time-series shown in Figures 5A–D, respectively. Those with (s1), (s2), and (s4) are the parameter points that best fit the experimental behaviors for Subjects 1, 2, and 4, respectively. Note that the best-fit noise intensities for (s1), (s2), and (s4) are not the values used for these panels (see Table 3 for the exact values). See the text for details.
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Figure 4: Parameter dependency of stability and the non-Gaussianity index for the movement variability of the pendulum in the type-1 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1s). Values of the index were calculated for the model with various parameter vectors = (a, Pθ, Dθ, Dx, σ, type = 1), which are plotted by color-code in the Pθ-Dθ planes for a set of combinations of the values of a (columns) and Dx (rows). The noise intensity is σ = 0.011 for the upper sets (A) of the Pθ-Dθ planes and σ = 0.001 for the lower sets (B) of the Pθ-Dθ planes. Because the index values can be calculated only when the models exhibit stable dynamics, the colored regions also represent the stability regions of the model. The parameter points indicated by the arrows with (A–D) are used for generating the time-series shown in Figures 5A–D, respectively. Those with (s1), (s2), and (s4) are the parameter points that best fit the experimental behaviors for Subjects 1, 2, and 4, respectively. Note that the best-fit noise intensities for (s1), (s2), and (s4) are not the values used for these panels (see Table 3 for the exact values). See the text for details.

Mentions: Figures 4, 5 show the parameter dependency of the non-Gaussianity index for the movement variability of the pendulum in the type-1 intermittent and type-2 intermittent feedback-control models, respectively, with two typical noise intensities for each model. Because the index can be calculated only for the models with parameter vectors that exhibit stable dynamics, Figures 4, 5 also represent the stability regions of the models. That is, the regions indicated by colors denote stability irrespective of the color. Figure 4 shows how the non-Gaussianity index changes as values of a, Pθ, Dθ, and Dx change for the type-1 intermittent control model with parameter vectors with a small noise intensity (upper panels), and with with a medium noise intensity (lower panels). Similarly, Figure 5 provides corresponding information for the type-2 intermittent control model with parameter vectors and Each figure consists of a number of panels corresponding to the Pθ−Dθ parameter planes spanned by the proportional and derivative gain parameters in the range of Pθ ∈ [0, 12.0] and Dθ ∈ [0, 3.0]. The model for a given set of Pθ-Dθ parameter values is represented by the corresponding grid in the Pθ-Dθ plane, and the colored grid indicates that the model with that parameter values exhibits stable dynamics. For each parameter set for stable dynamics, a set of values for the index vector (Pθ, Dθ) was calculated, and particularly the value of the non-Gaussianity index is depicted using the color-code as a function of Pθ and Dθ in Figures 4, 5. In Figures 4, 5, for the small and medium noise intensities, the Pθ − Dθ planes in the first column (leftmost column) are for a = −∞, meaning that those Pθ-Dθ planes represent the stability regions of the continuous control model with different values of the gain parameter Dx.


Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing.

Yoshikawa N, Suzuki Y, Kiyono K, Nomura T - Front Comput Neurosci (2016)

Parameter dependency of stability and the non-Gaussianity index  for the movement variability of the pendulum in the type-1 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1s). Values of the index  were calculated for the model with various parameter vectors  = (a, Pθ, Dθ, Dx, σ, type = 1), which are plotted by color-code in the Pθ-Dθ planes for a set of combinations of the values of a (columns) and Dx (rows). The noise intensity is σ = 0.011 for the upper sets (A) of the Pθ-Dθ planes and σ = 0.001 for the lower sets (B) of the Pθ-Dθ planes. Because the index values can be calculated only when the models exhibit stable dynamics, the colored regions also represent the stability regions of the model. The parameter points indicated by the arrows with (A–D) are used for generating the time-series shown in Figures 5A–D, respectively. Those with (s1), (s2), and (s4) are the parameter points that best fit the experimental behaviors for Subjects 1, 2, and 4, respectively. Note that the best-fit noise intensities for (s1), (s2), and (s4) are not the values used for these panels (see Table 3 for the exact values). See the text for details.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4835456&req=5

Figure 4: Parameter dependency of stability and the non-Gaussianity index for the movement variability of the pendulum in the type-1 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1s). Values of the index were calculated for the model with various parameter vectors = (a, Pθ, Dθ, Dx, σ, type = 1), which are plotted by color-code in the Pθ-Dθ planes for a set of combinations of the values of a (columns) and Dx (rows). The noise intensity is σ = 0.011 for the upper sets (A) of the Pθ-Dθ planes and σ = 0.001 for the lower sets (B) of the Pθ-Dθ planes. Because the index values can be calculated only when the models exhibit stable dynamics, the colored regions also represent the stability regions of the model. The parameter points indicated by the arrows with (A–D) are used for generating the time-series shown in Figures 5A–D, respectively. Those with (s1), (s2), and (s4) are the parameter points that best fit the experimental behaviors for Subjects 1, 2, and 4, respectively. Note that the best-fit noise intensities for (s1), (s2), and (s4) are not the values used for these panels (see Table 3 for the exact values). See the text for details.
Mentions: Figures 4, 5 show the parameter dependency of the non-Gaussianity index for the movement variability of the pendulum in the type-1 intermittent and type-2 intermittent feedback-control models, respectively, with two typical noise intensities for each model. Because the index can be calculated only for the models with parameter vectors that exhibit stable dynamics, Figures 4, 5 also represent the stability regions of the models. That is, the regions indicated by colors denote stability irrespective of the color. Figure 4 shows how the non-Gaussianity index changes as values of a, Pθ, Dθ, and Dx change for the type-1 intermittent control model with parameter vectors with a small noise intensity (upper panels), and with with a medium noise intensity (lower panels). Similarly, Figure 5 provides corresponding information for the type-2 intermittent control model with parameter vectors and Each figure consists of a number of panels corresponding to the Pθ−Dθ parameter planes spanned by the proportional and derivative gain parameters in the range of Pθ ∈ [0, 12.0] and Dθ ∈ [0, 3.0]. The model for a given set of Pθ-Dθ parameter values is represented by the corresponding grid in the Pθ-Dθ plane, and the colored grid indicates that the model with that parameter values exhibits stable dynamics. For each parameter set for stable dynamics, a set of values for the index vector (Pθ, Dθ) was calculated, and particularly the value of the non-Gaussianity index is depicted using the color-code as a function of Pθ and Dθ in Figures 4, 5. In Figures 4, 5, for the small and medium noise intensities, the Pθ − Dθ planes in the first column (leftmost column) are for a = −∞, meaning that those Pθ-Dθ planes represent the stability regions of the continuous control model with different values of the gain parameter Dx.

Bottom Line: To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors.We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing.We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University Toyonaka, Japan.

ABSTRACT
The stabilization of an inverted pendulum on a manually controlled cart (cart-inverted-pendulum; CIP) in an upright position, which is analogous to balancing a stick on a fingertip, is considered in order to investigate how the human central nervous system (CNS) stabilizes unstable dynamics due to mechanical instability and time delays in neural feedback control. We explore the possibility that a type of intermittent time-delayed feedback control, which has been proposed for human postural control during quiet standing, is also a promising strategy for the CIP task and stick balancing on a fingertip. Such a strategy hypothesizes that the CNS exploits transient contracting dynamics along a stable manifold of a saddle-type unstable upright equilibrium of the inverted pendulum in the absence of control by inactivating neural feedback control intermittently for compensating delay-induced instability. To this end, the motions of a CIP stabilized by human subjects were experimentally acquired, and computational models of the system were employed to characterize the experimental behaviors. We first confirmed fat-tailed non-Gaussian temporal fluctuation in the acceleration distribution of the pendulum, as well as the power-law distributions of corrective cart movements for skilled subjects, which was previously reported for stick balancing. We then showed that the experimental behaviors could be better described by the models with an intermittent delayed feedback controller than by those with the conventional continuous delayed feedback controller, suggesting that the human CNS stabilizes the upright posture of the pendulum by utilizing the intermittent delayed feedback-control strategy.

No MeSH data available.


Related in: MedlinePlus