Existence and stability of limit cycles in the model of a planar passive biped walking down a slope

Periodic gaits and flip bifurcation of a biped robot walking on level ground with two feasible switching patterns of motion

In this article, a biped robot walking on horizontal ground with two feasible switching patterns of motion (two-phase gait and three-phase gait) is presented. By using the first-order Taylor approximate at the equilibrium point, a simplified linear continuous dynamic equation is obtained to discuss the walking dynamics of the biped robot. Conditions for the existence and stability of period-1 gaits ( P ( 1 , 2 ) , P ( 1 , 3 ) ) and period-2 gaits ( P ( 2 , 2 , 2 ) , P ( 2 , 2 , 3 ) , P ( 2 , 3 , 3 ) ) are obtained by using a discrete map. Among the periodic gaits, the P ( 2 , 2 , 3 ) type gait has never been reported in previous studies. Flip bifurcation of periodic gait is investigated. Numerical results for periodic gaits and bifurcation diagram are in good agreement with the theoretical analysis.