# Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walker

arXiv: https://arxiv.org/abs/2409.16301 · HTML: https://mlsanity.com/paper/2409.16301/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 25 of 25)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots](https://mlsanity.com/paper/2103.14295/) (2021)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [Blind Bipedal Stair Traversal via Sim-to-Real Reinforcement Learning](https://mlsanity.com/paper/2105.08328/) (2021)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Humanoid Locomotion as Next Token Prediction](https://mlsanity.com/paper/2402.19469/) (2024)
- [Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions](https://mlsanity.com/paper/2004.07584/) (2020)
- [Fast and Efficient Locomotion via Learned Gait Transitions](https://mlsanity.com/paper/2104.04644/) (2021)
- [Reach-Avoid Problems with Time-Varying Dynamics, Targets and Constraints](https://mlsanity.com/paper/1410.6445/) (2014)
- [Lyapunov Design for Robust and Efficient Robotic Reinforcement Learning](https://mlsanity.com/paper/2208.06721/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures](https://mlsanity.com/paper/1910.09045/) (2019)
- [Parameter-Conditioned Reachable Sets for Updating Safety Assurances Online](https://mlsanity.com/paper/2209.14976/) (2022)
- [Generating Formal Safety Assurances for High-Dimensional Reachability](https://mlsanity.com/paper/2209.12336/) (2022)
- [Reliable Trajectories for Dynamic Quadrupeds using Analytical Costs and Learned Initializations](https://mlsanity.com/paper/2002.06719/) (2020)
- [Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots](https://mlsanity.com/paper/2201.08538/) (2022)
- [Reactive Locomotion Decision-Making and Robust Motion Planning for Real-Time Perturbation Recovery](https://mlsanity.com/paper/2110.03037/) (2021)
- [On infinitesimal contraction analysis for hybrid systems](https://mlsanity.com/paper/1811.03956/) (2018)
- [Hybrid Systems Neural Control with Region-of-Attraction Planner](https://mlsanity.com/paper/2303.10327/) (2023)
- [A Unified Perspective on Multiple Shooting In Differential Dynamic Programming](https://mlsanity.com/paper/2309.07872/) (2023)

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

- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)

## Abstract (arXiv)

Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in designing a learning-based locomotion controller whose stability can be examined and guaranteed. This can be achieved by verifying regions of attraction (RoAs) of legged robots to their stable walking gaits. This is a non-trivial problem for legged robots due to their hybrid dynamics. Although previous work has shown the utility of Hamilton-Jacobi (HJ) reachability to solve this problem, its practicality was limited by its poor scalability. The core contribution of our work is the employment of a deep learning-based HJ reachability solution to the hybrid legged robot dynamics, which overcomes the previous work's limitation. With the learned reachability solution, first, we can estimate a library of RoAs for various gaits. Second, we can design a one-step predictive controller that effectively stabilizes to an individual gait within the verified RoA. Finally, we can devise a strategy that switches gaits, in response to external perturbations, whose feasibility is guided by the RoA analysis. We demonstrate our method in a two-link walker simulation, whose mathematical model is well established. Our method achieves improved stability than previous model-based methods, while ensuring transparency that was not present in the existing learning-based approaches.