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Dynamic delayed feedback control for stabilizing the giant swing motions of an underactuated three-link gymnastic robot

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Abstract

This paper investigates the dynamics of the giant swing motions of an underactuated three-link gymnastic robot moving in a vertical plane by means of dynamic delayed feedback control (DDFC). DDFC, being one of useful methods to overcome the so-called odd number limitation in controlling a chaotic discrete-time system, is extended to control a continuous-time system such as a 3-link gymnastic robot with passive joint. Meanwhile, a way to calculate the error transfer matrix and the input matrix which are necessary for discretization is proposed, based on a Poincaré section which is defined to regard the target system as a discrete-time system. Moreover, the stability of the closed-loop system by the proposed control strategy is discussed. Furthermore, some numerical simulations are presented to show the effectiveness in controlling a chaotic motion of the 3-link gymnastic robot to a periodic giant swing motion.

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Acknowledgments

This work is supported in part by the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, and in part by the Scientific Research Foundation for Young Teachers, Shanghai JiaoTong University. The authors thank the anonymous reviewers for their useful comments and suggestions.

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Authors and Affiliations

  1. Institute of Medical Precision Engineering and Intelligent System, School of Electronic Information and Electrical Engineering, Shanghai JiaoTong University, Shanghai , 200240, China

    Dasheng Liu

  2. School of Electronic Information and Electrical Engineering, Shanghai JiaoTong University, Shanghai , 200240, China

    Guozheng Yan

  3. Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1-I3-10, Ookayama, Meguro-ku, Tokyo , 152-8552, Japan

    Hiroshi Yamaura

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  1. Dasheng Liu
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Correspondence to Dasheng Liu.

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Liu, D., Yan, G. & Yamaura, H. Dynamic delayed feedback control for stabilizing the giant swing motions of an underactuated three-link gymnastic robot. Nonlinear Dyn 78, 147–161 (2014). https://doi.org/10.1007/s11071-014-1428-8

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