Phase Uncertainty to State Stability of Continuous Periodic Orbits

TL;DR

This paper establishes conditions for the stability of continuous periodic orbits in bipedal robots under phase uncertainty caused by sensor noise, demonstrating that such orbits remain input-to-state stable despite imperfect phase estimation.

Contribution

It provides new sufficiency conditions for the stability of periodic orbits under phase uncertainty, specifically addressing the challenges of noisy phase variables in robotic trajectories.

Findings

Stable periodic orbits are input-to-state stable under phase uncertainty.

Phase-based uncertainty affects the stability analysis of continuous periodic orbits.

The paper offers a theoretical framework for analyzing stability with noisy phase information.

Abstract

The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous function. This monotonous function, called the phase variable, is often affected by intermittent perturbations due to noisy sensors. We will mainly focus on continuous periodic orbits obtained via parameterized trajectories, and then analyze their stability properties under a noisy phase estimation. In other words, our focus is on examples where phase variables are difficult to compute, and therefore are imperfect. We will show that stable periodic orbits subject to phase based uncertainty are input to state stable.