Passive dynamic walking with knee and fixed flat feet

Bipedal walking robots are inherently hybrid systems due to their intermittent, switching dynamics resulting from the impact between the robot foot and the ground as the robot foot lands on the ground. It is well known that stable (passive) limit cycles for the biped robots can be induced on shallow slopes without actuation. Recently the studies in passive dynamic walking have considered the robots with knee and point or curved feet. In this paper, we study the passive dynamic walking for biped robots with knee and fixed flat feet, which includes heel and toe rocking motions and the effect of foot length on the passive limit cycles. We derive the dynamic equations of motion for this model. We show by simulation that the proposed robot model can walk down a slope passively and also verify the stability of this walking by calculating the eigenvalues of the Jacobian of the Poincarè map. By using a numerical search method, we find the initial conditions of the stable limit cycles for various slope angles and foot lengths.