Approximating the stance map of a SLIP Monopod: A perturbation approach

In this paper, a novel method with perturbation technique is proposed to obtain analytic approximate solutions to the SLIP dynamics in stance phase with considering the effect of gravity. The perturbation solution achieves higher accuracy in predicting the apex trajectory and stance locomotion by comparing with other existing analytic approximations. Particularly, our solution is validated for non-symmetric case in a large angle range. Additionally, the approximate apex return map is established, of which the fixed point stability is analyzed base on the approximations.