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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

Typical time-series data of the models with their corresponding phase portraits, cart-acceleration distributions, PSD functions, and ICM distributions. Panels are prepared for six sets of the parameter vectors  indicated at the top of each trace. The configuration in each of the (A–F) is exactly the same as in Figure 3. Each ICM distribution includes a number of small dots that were obtained from 100 simulated sample paths with a duration of 60 s. (A,B): Continuous feedback control models. (C,D): Type-1 intermittent control models. (E,F): Type-2 intermittent control models. See the legend of Figure 3 and the text for details. Dynamics in the (D,E) best fit the experimental behaviors of Subject 1 (Figure 3A) and Subject 6 (Figure 3B), respectively. For the intermittent control models in the (C–F), red vertical lines in the θ-waveforms represent the off-phases during which the active feedback control is switched off, and the black and red curves in the phase portraits represent the trajectories during the on-phases and off-phases, respectively.
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Figure 6: Typical time-series data of the models with their corresponding phase portraits, cart-acceleration distributions, PSD functions, and ICM distributions. Panels are prepared for six sets of the parameter vectors indicated at the top of each trace. The configuration in each of the (A–F) is exactly the same as in Figure 3. Each ICM distribution includes a number of small dots that were obtained from 100 simulated sample paths with a duration of 60 s. (A,B): Continuous feedback control models. (C,D): Type-1 intermittent control models. (E,F): Type-2 intermittent control models. See the legend of Figure 3 and the text for details. Dynamics in the (D,E) best fit the experimental behaviors of Subject 1 (Figure 3A) and Subject 6 (Figure 3B), respectively. For the intermittent control models in the (C–F), red vertical lines in the θ-waveforms represent the off-phases during which the active feedback control is switched off, and the black and red curves in the phase portraits represent the trajectories during the on-phases and off-phases, respectively.

Mentions: Parameter-dependency of stability and the non-Gaussianity index for the movement variability of the pendulum in the type-2 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1 s). The figure is arranged in the same way as Figure 4. 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. The parameter points indicated by arrows with (A,B,E,F) are used for generating the time-series shown in Figures 6A,B,E,F, respectively. Those with (s3), (s5), and (s6) are the parameter points that best fit the experimental behaviors for Subjects 3, 5, and 6, respectively. Note that the best-fit noise intensities for (s3), (s5), and (s6) are not the values used for these panels (see Table 3 for the exact values). See the legend of Figure 4 and the main text for details.


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)

Typical time-series data of the models with their corresponding phase portraits, cart-acceleration distributions, PSD functions, and ICM distributions. Panels are prepared for six sets of the parameter vectors  indicated at the top of each trace. The configuration in each of the (A–F) is exactly the same as in Figure 3. Each ICM distribution includes a number of small dots that were obtained from 100 simulated sample paths with a duration of 60 s. (A,B): Continuous feedback control models. (C,D): Type-1 intermittent control models. (E,F): Type-2 intermittent control models. See the legend of Figure 3 and the text for details. Dynamics in the (D,E) best fit the experimental behaviors of Subject 1 (Figure 3A) and Subject 6 (Figure 3B), respectively. For the intermittent control models in the (C–F), red vertical lines in the θ-waveforms represent the off-phases during which the active feedback control is switched off, and the black and red curves in the phase portraits represent the trajectories during the on-phases and off-phases, respectively.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: Typical time-series data of the models with their corresponding phase portraits, cart-acceleration distributions, PSD functions, and ICM distributions. Panels are prepared for six sets of the parameter vectors indicated at the top of each trace. The configuration in each of the (A–F) is exactly the same as in Figure 3. Each ICM distribution includes a number of small dots that were obtained from 100 simulated sample paths with a duration of 60 s. (A,B): Continuous feedback control models. (C,D): Type-1 intermittent control models. (E,F): Type-2 intermittent control models. See the legend of Figure 3 and the text for details. Dynamics in the (D,E) best fit the experimental behaviors of Subject 1 (Figure 3A) and Subject 6 (Figure 3B), respectively. For the intermittent control models in the (C–F), red vertical lines in the θ-waveforms represent the off-phases during which the active feedback control is switched off, and the black and red curves in the phase portraits represent the trajectories during the on-phases and off-phases, respectively.
Mentions: Parameter-dependency of stability and the non-Gaussianity index for the movement variability of the pendulum in the type-2 intermittent feedback control models with two typical noise intensities (delay-time Δ = 0.1 s). The figure is arranged in the same way as Figure 4. 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. The parameter points indicated by arrows with (A,B,E,F) are used for generating the time-series shown in Figures 6A,B,E,F, respectively. Those with (s3), (s5), and (s6) are the parameter points that best fit the experimental behaviors for Subjects 3, 5, and 6, respectively. Note that the best-fit noise intensities for (s3), (s5), and (s6) are not the values used for these panels (see Table 3 for the exact values). See the legend of Figure 4 and the main text for details.

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