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被动行走机器人由于结构简单、能量利用率高而倍受青睐, 但其很容易跌倒, 因此准确把握最终步态与吸引区域成了关键. 由于面对非光滑系统, 大规模数值计算很难避免, 为此本文先提出基于CPU+GPU异构平台的Poincar映射算法. 该算法可发挥最新平台计算潜力, 比传统CPU上算法快上百倍. 得益于此, 本文针对双足被动行走的最基本模型, 大规模地选取样点进行计算, 不仅清晰地得出吸引区域的形状轮廓和细节特征, 揭示了其内在分形结构, 还得到系统吸引集和吸引区域随倾角k的变化关系, 发现了新的稳定三周期步态和倍周期分岔混沌现象, 并研究了吸引区域.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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Keywords:
- Poincar map /
- passive dynamic walking /
- bipeds /
- chaos
[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 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 60 030206]
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[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 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 60 030206]
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