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Stability Analysis of Legged Locomotion Models by Symmetry-Factored Return Maps

机译：基于对称 - 因式返回映射的腿式运动模型稳定性分析

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We present a new stability analysis for hybrid legged locomotion systems based on the 'symmetric' factorization of return maps. We apply this analysis to 2 and 3 degree of freedom (DOF) models of the Spring Loaded Inverted Pendulum (SLIP) with different leg recirculation strategies. Despite the non-integrability of the SLIP dynamics, we obtain a necessary condition for asymptotic stability (and a sufficient condition for instability) at a fixed point, formulated as an exact algebraic expression in the physical parameters. We use this expression to study a variety of 2 DOF SLIP models that have previously been posited as low dimensional representations of running, focusing on the sensory 'cost' required to achieve 'fast' transients as measured by the degree of singularity of the linearized dynamics. We introduce a new 3 DOF SLIP model with pitching dynamics whose stability properties, revealed by this analysis, provide for the first time the beginnings of a formal explanation for the surprisingly stable gaits of the open loop controlled robot, RHex.

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