# An Input-to-State Stability Perspective on Robust Locomotion

arXiv: https://arxiv.org/abs/2303.10231 · HTML: https://mlsanity.com/paper/2303.10231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [NaviGait: Navigating Dynamically Feasible Gait Libraries using Deep Reinforcement Learning](https://mlsanity.com/paper/2510.11542/) (2025)

## Abstract (arXiv)

Uneven terrain necessarily transforms periodic walking into a non-periodic motion. As such, traditional stability analysis tools no longer adequately capture the ability of a bipedal robot to locomote in the presence of such disturbances. This motivates the need for analytical tools aimed at generalized notions of stability -- robustness. Towards this, we propose a novel definition of robustness, termed δ-robustness, to characterize the domain on which a nominal periodic orbit remains stable despite uncertain terrain. This definition is derived by treating perturbations in ground height as disturbances in the context of the input-to-state-stability (ISS) of the extended Poincar'e map associated with a periodic orbit. The main theoretic result is the formulation of robust Lyapunov functions that certify δ-robustness of periodic orbits. This yields an optimization framework for verifying δ-robustness, which is demonstrated in simulation with a bipedal robot walking on uneven terrain.