Stability Analysis of Bipedal Standing via Lyapunov Exponents Calculated from a Time Series Using Nonlinear Mapping - A Case Study

摘要

The stability analysis is important for the development of robotic systems. Due to the limitations on the derivations of Lyapunov functions, the stability analysis of robotic systems has been extremely limited. On the other hand, Lyapunov exponents can characterize the system stability provided that the numerical artifact is under control [1]. The most attractive advantage of using a time series is that the data for only one state is required, which can often be measured experimentally [2, 3]. However, it has been documented that the current methods for calculating Lyapunov exponents using a time series are valid for chaotic systems, i.e., for calculating positive Lyapunov exponents. They have been considered not reliable for calculating negative and zero exponents.