Stability Analysis of Bipedal Robots Using the Concept of Lyapunov Exponents

Abstract

The dynamics and stability of passive bipedal robot have an important impact on the mass distribution, leg length, and the angle of inclination. Lyapunov’s second method is difficult to be used in highly nonlinear multibody systems, due to the lack of constructive methods for deriving Lyapunov fuction. The dynamics equation is established by Kane method, the relationship between the mass, length of leg, angle of inclination, and stability of passive bipedal robot by the largest Lyapunov exponent. And the Lyapunov exponents of continuous dynamical systems are estimated by numerical methods, which are simple and easy to be applied to the system stability simulation analysis, provide the design basis for passive bipedal robot prototype, and improve design efficiency.