The kinetic energy of passive gaits in downhill walking gains from gravity and dissipates during the impact with ground. Hence, the passive gait is supposed to consume the least amount of energy in gait control. The simulated downhill walking trajectory seems to have a certain pattern though irregular. It has been observed that even a small deviation from an existed gait cycle may lead to instability easily. It would not be proper to conclude any gait cycle is stable except its pattern is a limit cycle in the phase plane. Also, the change during impact for different ground conditions was not addressed yet. We propose to use the coefficient of restitution to account for the impact change on different terrain while the conservation of the angular momentum at the contact point and kinematic constraints are observed. This paper demonstrates the existence of any limit cycle in passive downhill walking while including the ground impact conditions and a backstepping controller is designed to track the trajectory for the sake of power saving.
