Detection of Unstable Periodic Orbits and Chaos Control in a Passive Biped Model

Abstract

Dynamic analysis of passive biped models plays a significant role both in understanding human locomotion and in developing humanoid robots. In this investigation, two chaos control algorithms based on linearization of Poincare map (OGY method) and artificial neural networks (ANNs) are utilized to control the motion of a passive biped model. To this end, the chaotic characteristics of the system are analyzed using several nonlinear dynamics tools such as Poincare map, bifurcation diagram, and Lyapunov exponents, and then, unstable periodic orbits (UPOs) of the system are detected. Detection of these orbits helps to extract a desired walking pattern and also is utilized for chaos elimination of the system. The robustness of the proposed ANN-based control algorithm is verified by applying toe-off impulses to the biped during the gait. Furthermore, the effect of network parameters on the biped walking performance is investigated to get design guidelines for the ANN-based controller.