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

TL;DR

This paper introduces a deep learning-based Hamilton-Jacobi reachability approach to verify and enhance the stability of legged robots, enabling gait switching and improved stabilization in a two-link walker simulation.

Contribution

It presents a scalable deep learning method for reachability analysis in hybrid legged robot dynamics, allowing for verified gait stability and switching strategies.

Findings

Achieves improved stability over previous model-based methods

Enables verified gait switching in response to perturbations

Provides transparent stability guarantees in learning-based control

Abstract

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.