Intermittent Feedback-Control Strategy for Stabilizing Inverted Pendulum on Manually Controlled Cart as Analogy to Human Stick Balancing.
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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.
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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 |
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Mentions: Figure 1 illustrates the CIP system that we consider in this study. The equations of motion of the CIP are described as follows:(1)m3ℓ2θ¨+mℓ2x¨=mgℓ2θ,(2)mℓ2θ¨+(M+m)x¨=u+σξ,where θ is the tilt-angle of the pendulum, x is the cart position from the origin along the rail, ℓ/2 is the distance from the joint to the center of mass of the pendulum, mℓ2/3 is the moment of inertia of the inverted pendulum around the joint, m is the pendulum mass, M (= 2m) is the cart mass, g is the gravitational acceleration, and u is the manual force exerted by the subject, which is a control input to the CIP system. See Milton et al. (2009) for detail. Moreover, we consider an additive force noise σξ, where ξ represents a Gaussian white noise with zero mean and unit variance and σ is the noise intensity (standard deviation of the noise). In our coordinate system, the positive (x > 0) and negative (x < 0) directions of the cart position correspond to the positive (θ > 0) and negative (θ < 0) directions of the tilt angle of the inverted pendulum. Equations (1) and (2) can then be rewritten in the state-space representation, as follows:(3)[θ˙ω˙x˙v˙]=[01A210000000A4100100] [θωxv]+[0B20B4](u+σξ),where and v = ẋ are the angular velocity of the pendulum and the moving velocity of the cart, respectively. The elements of the system matrix and the input matrix are defined as:A21=2gℓ, A41=−g3B2=−23mℓ B4=49m. |
View Article: PubMed Central - PubMed
Affiliation: Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University Toyonaka, Japan.
No MeSH data available.