Passive dynamic walking of compass-like biped robot on slippery downhill

In this paper, we discuss the possibility and fundamental properties of passive bipedal walking on a slippery downhill. First, we develop a mathematical model of the passive compass-like biped robot that contacts with the ground incorporating sliding friction which is specified as the Coulomb model. Second, we discuss the possibility of instantaneous stance-leg exchange through mathematical analysis of the collision dynamics. Third, we perform numerical simulations using the model developed, and show that a stable walking gait can be generated with suitable initial conditions and physical parameters. Furthermore, we numerically show that period-doubling bifurcation occurs with the decrease of the coefficient of sliding friction.