Stochastic stability analysis of legged locomotion using unscented transformation

TL;DR

This paper introduces a new method using the unscented transformation to efficiently analyze the stochastic stability of complex legged locomotion systems, reducing computational load and experimental requirements.

Contribution

The paper presents a novel approach that simplifies stability analysis of high-dimensional legged systems by combining dimensionality reduction with the unscented transformation.

Findings

Effective stability estimation for a 1D hopper

Successful application to bipedal walking simulation

Reduced computational complexity compared to prior methods

Abstract

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.