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Possible functional roles of the phase resetting control during rhythmic movements have been attracting much attention in the field of robotics. The phase resetting control is a control mechanism in which the phase shift of periodic motion is induced depending on the timing of a given perturbation, leading to dynamical stability such as a rapid transition from an unstable state to a stable state in rhythmic movements. A phase response curve (PRC) is used to quantitatively evaluate the phase shift in the phase resetting control. It has been demonstrated that an optimal PRC for bipedal walking becomes bimodal. The PRCs acquired by reinforcement learning in simulated biped walking are qualitatively consistent with measured results obtained from experiments. In this study, we considered how such characteristics are obtained from a mathematical point of view. First, we assumed a symmetric Bonhoeffer-Van der Pol oscillator and phase excitable element known as an active rotator as a model of the central pattern generator for controlling rhythmic movements. Second, we constructed feedback control systems by combining them with manipulators. Next, we numerically computed the PRCs of such systems and compared the resulting PRCs. Furthermore, we approximately calculated analytical solutions of the PRCs. Based on the results, we systematically investigated the parameter dependence of the analytical PRCs. Finally, we investigated the requirements for realizing an optimal PRC for the phase resetting control during rhythmic movements.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.2 pp.398-406

- Publication Date
- 2020/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2019MAI0002

- Type of Manuscript
- Special Section INVITED PAPER (Special Section on Mathematical Systems Science and its Applications)

- Category

Kazuki NAKADA

Tsukuba University of Technology

Keiji MIURA

Kwansei Gakuin University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Kazuki NAKADA, Keiji MIURA, "Mathematical Analysis of Phase Resetting Control Mechanism during Rhythmic Movements" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 2, pp. 398-406, February 2020, doi: 10.1587/transfun.2019MAI0002.

Abstract: Possible functional roles of the phase resetting control during rhythmic movements have been attracting much attention in the field of robotics. The phase resetting control is a control mechanism in which the phase shift of periodic motion is induced depending on the timing of a given perturbation, leading to dynamical stability such as a rapid transition from an unstable state to a stable state in rhythmic movements. A phase response curve (PRC) is used to quantitatively evaluate the phase shift in the phase resetting control. It has been demonstrated that an optimal PRC for bipedal walking becomes bimodal. The PRCs acquired by reinforcement learning in simulated biped walking are qualitatively consistent with measured results obtained from experiments. In this study, we considered how such characteristics are obtained from a mathematical point of view. First, we assumed a symmetric Bonhoeffer-Van der Pol oscillator and phase excitable element known as an active rotator as a model of the central pattern generator for controlling rhythmic movements. Second, we constructed feedback control systems by combining them with manipulators. Next, we numerically computed the PRCs of such systems and compared the resulting PRCs. Furthermore, we approximately calculated analytical solutions of the PRCs. Based on the results, we systematically investigated the parameter dependence of the analytical PRCs. Finally, we investigated the requirements for realizing an optimal PRC for the phase resetting control during rhythmic movements.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019MAI0002/_p

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@ARTICLE{e103-a_2_398,

author={Kazuki NAKADA, Keiji MIURA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Mathematical Analysis of Phase Resetting Control Mechanism during Rhythmic Movements},

year={2020},

volume={E103-A},

number={2},

pages={398-406},

abstract={Possible functional roles of the phase resetting control during rhythmic movements have been attracting much attention in the field of robotics. The phase resetting control is a control mechanism in which the phase shift of periodic motion is induced depending on the timing of a given perturbation, leading to dynamical stability such as a rapid transition from an unstable state to a stable state in rhythmic movements. A phase response curve (PRC) is used to quantitatively evaluate the phase shift in the phase resetting control. It has been demonstrated that an optimal PRC for bipedal walking becomes bimodal. The PRCs acquired by reinforcement learning in simulated biped walking are qualitatively consistent with measured results obtained from experiments. In this study, we considered how such characteristics are obtained from a mathematical point of view. First, we assumed a symmetric Bonhoeffer-Van der Pol oscillator and phase excitable element known as an active rotator as a model of the central pattern generator for controlling rhythmic movements. Second, we constructed feedback control systems by combining them with manipulators. Next, we numerically computed the PRCs of such systems and compared the resulting PRCs. Furthermore, we approximately calculated analytical solutions of the PRCs. Based on the results, we systematically investigated the parameter dependence of the analytical PRCs. Finally, we investigated the requirements for realizing an optimal PRC for the phase resetting control during rhythmic movements.},

keywords={},

doi={10.1587/transfun.2019MAI0002},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - Mathematical Analysis of Phase Resetting Control Mechanism during Rhythmic Movements

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 398

EP - 406

AU - Kazuki NAKADA

AU - Keiji MIURA

PY - 2020

DO - 10.1587/transfun.2019MAI0002

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E103-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2020

AB - Possible functional roles of the phase resetting control during rhythmic movements have been attracting much attention in the field of robotics. The phase resetting control is a control mechanism in which the phase shift of periodic motion is induced depending on the timing of a given perturbation, leading to dynamical stability such as a rapid transition from an unstable state to a stable state in rhythmic movements. A phase response curve (PRC) is used to quantitatively evaluate the phase shift in the phase resetting control. It has been demonstrated that an optimal PRC for bipedal walking becomes bimodal. The PRCs acquired by reinforcement learning in simulated biped walking are qualitatively consistent with measured results obtained from experiments. In this study, we considered how such characteristics are obtained from a mathematical point of view. First, we assumed a symmetric Bonhoeffer-Van der Pol oscillator and phase excitable element known as an active rotator as a model of the central pattern generator for controlling rhythmic movements. Second, we constructed feedback control systems by combining them with manipulators. Next, we numerically computed the PRCs of such systems and compared the resulting PRCs. Furthermore, we approximately calculated analytical solutions of the PRCs. Based on the results, we systematically investigated the parameter dependence of the analytical PRCs. Finally, we investigated the requirements for realizing an optimal PRC for the phase resetting control during rhythmic movements.

ER -