Passive Dynamic Walking with Symmetric Fixed Flat Feet

Biped robots are inherently hybrid systems due to their intermittent, switching dynamics resulting from foot/ground impacts. It is well known that stable (passive) limit cycles for such mechanisms can be induced on shallow slopes without actuation. Most studies of passive dynamics to date have considered point or curved feet. In this paper, we consider passive bipeds with fixed flat feet. We study heel and toe rocking motions and the effect of relative foot length on the passive limit cycles. We first derive the dynamic equations of motion and explain the typical limit cycle generated by this model. We show by simulation that the proposed robot model can walk down a slope passively and then verify the stability of this walking through numerical calculations of 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.