# Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots

arXiv: https://arxiv.org/abs/2201.08538 · HTML: https://mlsanity.com/paper/2201.08538/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Hybrid Systems Neural Control with Region-of-Attraction Planner](https://mlsanity.com/paper/2303.10327/) (2023)
- [Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walker](https://mlsanity.com/paper/2409.16301/) (2024)
- [V-MORALS: Visual Morse Graph-Aided Estimation of Regions of Attraction in a Learned Latent Space](https://mlsanity.com/paper/2602.23524/) (2026)

## Abstract (arXiv)

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we cast the computation of region-ofattraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.