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

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.