Altendorfer, RichardKoditschek, Daniel EHolmes, Philip2023-05-222023-05-222003-09-142005-06-01https://repository.upenn.edu/handle/20.500.14332/33305In this paper, we report on a new stability analysis for hybrid legged locomotion systems based on factorization of return maps. We apply this analysis to a family of models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. We obtain a necessary condition for the asymptotic stability of those models, which is formulated as an exact algebraic expression despite the non-integrability of the SLIP dynamics. We outline the application of this analysis to other models of legged locomotion and its importance for the stability of legged robots and animals.GRASPKodlabPresentation