基于异构计算的简单行走模型的吸引区域研究

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Poincaré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.

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

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 Poincaré 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.