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

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          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.

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          Most cited references 23

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          Intermittent control: a computational theory of human control.

          The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.
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            Human control of an inverted pendulum: is continuous control necessary? Is intermittent control effective? Is intermittent control physiological?

            Human motor control is often explained in terms of engineering 'servo' theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high band-width, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visuo-manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s(-1). However, when optimising position or velocity regulation, a modal contact rate of 2 s(-1) was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s(-1). Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.
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              Forward models in visuomotor control.

              In recent years, an increasing number of research projects investigated whether the central nervous system employs internal models in motor control. While inverse models in the control loop can be identified more readily in both motor behavior and the firing of single neurons, providing direct evidence for the existence of forward models is more complicated. In this paper, we will discuss such an identification of forward models in the context of the visuomotor control of an unstable dynamic system, the balancing of a pole on a finger. Pole balancing imposes stringent constraints on the biological controller, as it needs to cope with the large delays of visual information processing while keeping the pole at an unstable equilibrium. We hypothesize various model-based and non-model-based control schemes of how visuomotor control can be accomplished in this task, including Smith Predictors, predictors with Kalman filters, tapped-delay line control, and delay-uncompensated control. Behavioral experiments with human participants allow exclusion of most of the hypothesized control schemes. In the end, our data support the existence of a forward model in the sensory preprocessing loop of control. As an important part of our research, we will provide a discussion of when and how forward models can be identified and also the possible pitfalls in the search for forward models in control.
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                Author and article information

                Contributors
                Journal
                Front Comput Neurosci
                Front Comput Neurosci
                Front. Comput. Neurosci.
                Frontiers in Computational Neuroscience
                Frontiers Media S.A.
                1662-5188
                19 April 2016
                2016
                : 10
                Affiliations
                Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University Toyonaka, Japan
                Author notes

                Edited by: Andre Longtin, University of Ottawa, Canada

                Reviewed by: John Milton, Claremont College, USA; Toru Ohira, Nagoya University, Japan

                *Correspondence: Taishin Nomura taishin@ 123456bpe.es.osaka-u.ac.jp
                Article
                10.3389/fncom.2016.00034
                4835456
                27148031
                Copyright © 2016 Yoshikawa, Suzuki, Kiyono and Nomura.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                Page count
                Figures: 6, Tables: 3, Equations: 0, References: 33, Pages: 19, Words: 14025
                Categories
                Neuroscience
                Original Research

                Neurosciences

                stick balancing, posture control, non-gaussianity, stable manifold, intermittency

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