  In this manuscript, we present a novel method for estimating the stochastic
stability characteristics of metastable legged systems using the unscented
transformation. Prior methods for stability analysis in such systems often
required high-dimensional state space discretization and a broad set of initial
conditions, resulting in significant computational complexity. Our approach
aims to alleviate this issue by reducing the dimensionality of the system and
utilizing the unscented transformation to estimate the output distribution.
This technique allows us to account for multiple sources of uncertainty and
high-dimensional system dynamics, while leveraging prior knowledge of noise
statistics to inform the selection of initial conditions for experiments. As a
result, our method enables the efficient assessment of controller performance
and analysis of parametric dependencies with fewer experiments. To demonstrate
the efficacy of our proposed method, we apply it to the analysis of a
one-dimensional hopper and an underactuated bipedal walking simulation with a
hybrid zero dynamics controller.
