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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

Off- and on-regions in the θ-ω plane and the θ-v plane to define the switching conditions between the off-phase and on-phase of the feedback control. In each plane, the white and gray regions represent the on-region and the off-region, respectively. (A,B) Continuous control model with Dx = 0 and Dx > 0, respectively: the on-region occupies the whole of the θ-ω and the θ-v planes for both cases. (C,D) Type-1 intermittent control model with Dx = 0 and Dx > 0, respectively: the off-regions in the θ-ω plane are located near the stable manifold (depicted as a solid line with a negative slope passing though the origin) for the inverted pendulum with no feedback control. The θ-v plane does not have off-regions. (E,F) Type-2 intermittent control model with Dx = 0 and Dx > 0, respectively: onset of the off-phase is determined based on the off-regions in the θ-ω phase and those in the θ-v plane. For each panel, the thick curve with arrowheads represents a sample trajectory of the model, and the black and red curves represent the trajectories during on-phases and off-phases, respectively. The circular shape of the black trajectories is due to the delay-induced instability with delay feedback control, and the hyperbolic shape of the red trajectories move along the stable manifold and/or the unstable manifold (depicted as a dotted line with a positive slope) during off-phases. See text for details.
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Figure 2: Off- and on-regions in the θ-ω plane and the θ-v plane to define the switching conditions between the off-phase and on-phase of the feedback control. In each plane, the white and gray regions represent the on-region and the off-region, respectively. (A,B) Continuous control model with Dx = 0 and Dx > 0, respectively: the on-region occupies the whole of the θ-ω and the θ-v planes for both cases. (C,D) Type-1 intermittent control model with Dx = 0 and Dx > 0, respectively: the off-regions in the θ-ω plane are located near the stable manifold (depicted as a solid line with a negative slope passing though the origin) for the inverted pendulum with no feedback control. The θ-v plane does not have off-regions. (E,F) Type-2 intermittent control model with Dx = 0 and Dx > 0, respectively: onset of the off-phase is determined based on the off-regions in the θ-ω phase and those in the θ-v plane. For each panel, the thick curve with arrowheads represents a sample trajectory of the model, and the black and red curves represent the trajectories during on-phases and off-phases, respectively. The circular shape of the black trajectories is due to the delay-induced instability with delay feedback control, and the hyperbolic shape of the red trajectories move along the stable manifold and/or the unstable manifold (depicted as a dotted line with a positive slope) during off-phases. See text for details.

Mentions: A simple and conventional model of the manual CIP system, referred to as the continuous (delayed) feedback-control model (or continuous control model), is used as a reference against models with intermittent controllers. In the continuous control model, the manual force u defined by Equation (5) is always applied to the cart, independent of the cart position and the posture of the inverted pendulum (Figure 2). Although, the origin (θ, ω, x, v) = 0 is a fixed point of the continuous control model, we are not necessarily interested in its stability, since the cart position may vary along the rail track while the pendulum is stabilized by the subject. Instead, we analyze behaviors of the pendulum using a pseudo-equilibrium point of the system in the θ-ω plane, which is defined as a solution of the zeros in the right-hand-side of the first and second rows of Equation (3). Namely,(6)θ˙=ω=0,(7)ω˙=2gℓθ−23mℓ(Pθθ△+Dθω△+Dxv△)=0.


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)

Off- and on-regions in the θ-ω plane and the θ-v plane to define the switching conditions between the off-phase and on-phase of the feedback control. In each plane, the white and gray regions represent the on-region and the off-region, respectively. (A,B) Continuous control model with Dx = 0 and Dx > 0, respectively: the on-region occupies the whole of the θ-ω and the θ-v planes for both cases. (C,D) Type-1 intermittent control model with Dx = 0 and Dx > 0, respectively: the off-regions in the θ-ω plane are located near the stable manifold (depicted as a solid line with a negative slope passing though the origin) for the inverted pendulum with no feedback control. The θ-v plane does not have off-regions. (E,F) Type-2 intermittent control model with Dx = 0 and Dx > 0, respectively: onset of the off-phase is determined based on the off-regions in the θ-ω phase and those in the θ-v plane. For each panel, the thick curve with arrowheads represents a sample trajectory of the model, and the black and red curves represent the trajectories during on-phases and off-phases, respectively. The circular shape of the black trajectories is due to the delay-induced instability with delay feedback control, and the hyperbolic shape of the red trajectories move along the stable manifold and/or the unstable manifold (depicted as a dotted line with a positive slope) during off-phases. See 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 2: Off- and on-regions in the θ-ω plane and the θ-v plane to define the switching conditions between the off-phase and on-phase of the feedback control. In each plane, the white and gray regions represent the on-region and the off-region, respectively. (A,B) Continuous control model with Dx = 0 and Dx > 0, respectively: the on-region occupies the whole of the θ-ω and the θ-v planes for both cases. (C,D) Type-1 intermittent control model with Dx = 0 and Dx > 0, respectively: the off-regions in the θ-ω plane are located near the stable manifold (depicted as a solid line with a negative slope passing though the origin) for the inverted pendulum with no feedback control. The θ-v plane does not have off-regions. (E,F) Type-2 intermittent control model with Dx = 0 and Dx > 0, respectively: onset of the off-phase is determined based on the off-regions in the θ-ω phase and those in the θ-v plane. For each panel, the thick curve with arrowheads represents a sample trajectory of the model, and the black and red curves represent the trajectories during on-phases and off-phases, respectively. The circular shape of the black trajectories is due to the delay-induced instability with delay feedback control, and the hyperbolic shape of the red trajectories move along the stable manifold and/or the unstable manifold (depicted as a dotted line with a positive slope) during off-phases. See text for details.
Mentions: A simple and conventional model of the manual CIP system, referred to as the continuous (delayed) feedback-control model (or continuous control model), is used as a reference against models with intermittent controllers. In the continuous control model, the manual force u defined by Equation (5) is always applied to the cart, independent of the cart position and the posture of the inverted pendulum (Figure 2). Although, the origin (θ, ω, x, v) = 0 is a fixed point of the continuous control model, we are not necessarily interested in its stability, since the cart position may vary along the rail track while the pendulum is stabilized by the subject. Instead, we analyze behaviors of the pendulum using a pseudo-equilibrium point of the system in the θ-ω plane, which is defined as a solution of the zeros in the right-hand-side of the first and second rows of Equation (3). Namely,(6)θ˙=ω=0,(7)ω˙=2gℓθ−23mℓ(Pθθ△+Dθω△+Dxv△)=0.

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