On the chaotic behavior of the hybrid inverted pendulum and its relation to the lateral dynamics of the walking robots

摘要

Dynamics of the so-called hybrid inverted pendulum is studied here. Motivation is the lateral stability of the planar walking strategies applied to more realistic settings. The influence of the lateral harmonic forcing of the hybrid inverted pendulum is analyzed. It is shown numerically that reasonable sized forcing imposes the bounded oscillatory behavior. The main contribution is the detection of the possible chaotic behavior created in the above way. The extensive simulations present quite complex bounded behaviors and for some of them their largest Lyapunov exponent is shown to be positive. This supports the idea that the chaotic behavior is present there. The positive Lyapunov exponent is determined as the smallest coupling coefficient enforcing the synchronization of the simple master-slave configuration of the hybrid inverted pendulum and its copy.