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A study of basin of attraction of the simplest walking model based on heterogeneous computation

Li Qing-Du Zhou Hong-Wei Yang Xiao-Song

A study of basin of attraction of the simplest walking model based on heterogeneous computation

Li Qing-Du, Zhou Hong-Wei, Yang Xiao-Song
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  • Passive dynamic walking becomes an important development for walking robots due to its simple structure and high energy efficiency, but it often falls. The key to this problem is to ascertain its stable gaits and basins of attraction. In order to handle the discontinuity, massive numerical computation is unavoidable. In this paper, we first propose an algorithm to compute Poincar maps in heterogeneous platforms with CPU and GPU, which can take the best performance of the newest heterogeneous platforms and improve the computing speed by more than a hundred times. With this algorithm, we study the simplest walking model by sampling massive points from the state space. We obtain high resolution images of the basin of attraction, and reveal its fractal structure. By computing the relation between the stable gaits and their basins and by varying the slop k, we find a new three-period stable gait and a period-doubling route to chaos, and we also study the new gait and its basin.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61104150, 10972082), the Natural Science Foundation Project of CQ CSTC (Grant No. cstcjjA40044), and the Independent Innovation Foundation of HUST(Grant No. 011906).
    [1]

    Winter D 1991 Biomechanics and Motor Control of Human Movement (2nd ed) (New York: Wiley)

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    McGeer T 1990 I. J. Robotic Res. 9 62

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    Garcia M, Chatterjee A, Ruina A, Coleman M 1998 J. Biomech. Eng. 120 281

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    Goswami A, Thuilot B, Espiau B 1998 I. J. Robotic Res. 17 1282

    [5]

    Schwab A,Wisse M 2001 Basin of attraction of the simplest walking model. In: International Conference on Noise and Vibration, (Pennsylvania: ASME)

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    Liu N, Li J F, Wang T S 2008 Mechanics in Engineering 30 18 (in Chinese) [柳宁, 李俊峰, 王天舒 2009 力学与实践 30 18]

    [7]

    Liu N, Li J F, Wang T S 2009 Acta Phys. Sin. 58 3772 (in Chinese) [柳宁, 李俊峰, 王天舒 2009 物理学报 58 3772]

    [8]

    Hong L 2010 Chin. Phys. B 19 030513

    [9]

    Kirk D, HwuWM 2010 Programming Massively Parallel Processors (Burlington: Elsevier)

    [10]

    Munshi A 2010 The OpenCL Specification Version 1.1. (Khronos OpenCL Working Group)

    [11]

    Li Q, Tan Y, Yang F 2011 Acta Phys. Sin. 60 030206 (in Chinese) [李清都, 谭宇玲, 杨芳艳 2011 物理学报 60 030206]

  • [1]

    Winter D 1991 Biomechanics and Motor Control of Human Movement (2nd ed) (New York: Wiley)

    [2]

    McGeer T 1990 I. J. Robotic Res. 9 62

    [3]

    Garcia M, Chatterjee A, Ruina A, Coleman M 1998 J. Biomech. Eng. 120 281

    [4]

    Goswami A, Thuilot B, Espiau B 1998 I. J. Robotic Res. 17 1282

    [5]

    Schwab A,Wisse M 2001 Basin of attraction of the simplest walking model. In: International Conference on Noise and Vibration, (Pennsylvania: ASME)

    [6]

    Liu N, Li J F, Wang T S 2008 Mechanics in Engineering 30 18 (in Chinese) [柳宁, 李俊峰, 王天舒 2009 力学与实践 30 18]

    [7]

    Liu N, Li J F, Wang T S 2009 Acta Phys. Sin. 58 3772 (in Chinese) [柳宁, 李俊峰, 王天舒 2009 物理学报 58 3772]

    [8]

    Hong L 2010 Chin. Phys. B 19 030513

    [9]

    Kirk D, HwuWM 2010 Programming Massively Parallel Processors (Burlington: Elsevier)

    [10]

    Munshi A 2010 The OpenCL Specification Version 1.1. (Khronos OpenCL Working Group)

    [11]

    Li Q, Tan Y, Yang F 2011 Acta Phys. Sin. 60 030206 (in Chinese) [李清都, 谭宇玲, 杨芳艳 2011 物理学报 60 030206]

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  • Received Date:  22 October 2010
  • Accepted Date:  15 June 2011
  • Published Online:  15 April 2012

A study of basin of attraction of the simplest walking model based on heterogeneous computation

  • 1. Key Laboratory of Network Control & Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
  • 2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
  • 3. Institute for Nonlinear Circuits and Systems, Chongqing University Posts and Telecommunications, Chongqing 400065, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61104150, 10972082), the Natural Science Foundation Project of CQ CSTC (Grant No. cstcjjA40044), and the Independent Innovation Foundation of HUST(Grant No. 011906).

Abstract: Passive dynamic walking becomes an important development for walking robots due to its simple structure and high energy efficiency, but it often falls. The key to this problem is to ascertain its stable gaits and basins of attraction. In order to handle the discontinuity, massive numerical computation is unavoidable. In this paper, we first propose an algorithm to compute Poincar maps in heterogeneous platforms with CPU and GPU, which can take the best performance of the newest heterogeneous platforms and improve the computing speed by more than a hundred times. With this algorithm, we study the simplest walking model by sampling massive points from the state space. We obtain high resolution images of the basin of attraction, and reveal its fractal structure. By computing the relation between the stable gaits and their basins and by varying the slop k, we find a new three-period stable gait and a period-doubling route to chaos, and we also study the new gait and its basin.

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