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In order to achieve stable control, the Poincare-mapping function is built by using spatial operator algebra (SOA) and the swing phase and impact phase dynamics equation of the passive walking robot are deduced. At last, the numerical analysis method is used to solve the stable fixed point of the mapping function, and the local stability of the model is analyzed. The result shows that, by using the theory of SOA, the Poincare-mapping function can be established effectively and fast, and avoids the complicated calculation of solving partial derivative in the modeling process by Lagrangian mechanics. At the same time, the analysis of local stability shows that passive walking robot must has stable fixed point for cycle stable walking, otherwise, it will occur period bifurcation.