Lyapunov Exponents for Further Study of the Gait Complexity of the Passive Compass-Like Biped Walker.

The compass-like bipedal walker is described as an impulsive hybrid nonlinear system and is characterized by a passive gait while descending an inclined surface. To study its passive bipedal gait, an identification of the one-periodic walk should be first carried out using the Poincaré map. Moreover, bifurcation diagrams are generally employed to investigate the steady gaits of such passive gait by varying the slope angle or other parameters, and hence to confirm the display of unexpected occurrences like chaos and bifurcations. In this work, to further analyze these complex phenomena, we employ, along with the bifurcation diagrams, the Lyapunov exponents by varying the slope angle and the lower-leg segment length. Thus, we demonstrate and confirm the presence of quasi-periodic gaits and hence the exhibition of the Neimark-Sacker bifurcation.