The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually increased, the gaits exhibit universal period doubling bifurcations leading to chaos. Meanwhile, the phenomena of period doubling bifurcations also occur by increasing either the foot length or the mass ratio of the robot. Theory analysis and numerical simulations are given to verify our conclusion.