You will use the perturbation theory developed in [2] in order to classify the walking gaits that a bipedal robot on a shallow slope (as modeled in [1]) can exhibit.
Reading:
[1] M. Garcia, A. Chatterjee, A. Ruina, The simplest walking model: Stability, complexity, and scaling,
J. Biomech. Eng. 120 (1998), no. 2, 281-288.
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Preprint
[2] M. Kamenskii, O. Makarenkov, P. Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems. J. Dynam. Differential Equations, 23 (2011), no. 3, 425-435.
Journal link
Preprint