New walking dynamics in the simplest passive bipedal walking model |
| |
Authors: | Qingdu Li Xiao-Song Yang |
| |
Institution: | 1. Key Laboratory of Network Control and Intelligent Instrument, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China |
| |
Abstract: | This paper revisits the simplest passive walking model by Garcia et al. which displays chaos through period doubling from a stable period-1 gait. By carefully numerical studies, two new gaits with period-3 and -4 are found, whose stability is verified by estimates of eigenvalues of the corresponding Jacobian matrices. A surprising phenomenon uncovered here is that they both lead to higher periodic cycles and chaos via period doubling. To study the three different types of chaotic gaits rigorously, the existence of horseshoes is verified and estimates of the topological entropies are made by computer-assisted proofs in terms of topological horseshoe theory. |
| |
Keywords: | Periodic gaits Chaos Topological horseshoe Basin of attraction Passive bipedal model |
本文献已被 ScienceDirect 等数据库收录! |
|