# 3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization

arXiv: https://arxiv.org/abs/2101.09588 · HTML: https://mlsanity.com/paper/2101.09588/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2021.

## Built on by (most cited first, 9 of 9)

- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model](https://mlsanity.com/paper/2104.09771/) (2021)
- [Autonomous Navigation of Underactuated Bipedal Robots in Height-Constrained Environments](https://mlsanity.com/paper/2109.05714/) (2021)
- [CLF-RL: Control Lyapunov Function Guided Reinforcement Learning](https://mlsanity.com/paper/2508.09354/) (2025)
- [MARCH: Model-Assisted Reinforcement Learning for the Perceptive Control of Humanoids over Sparse Footholds](https://mlsanity.com/paper/2606.10288/) (2026)
- [A Gait Driven Reinforcement Learning Framework for Humanoid Robots](https://mlsanity.com/paper/2506.08416/) (2025)
- [HybridMimic: Hybrid RL-Centroidal Control for Humanoid Motion Mimicking](https://mlsanity.com/paper/2603.06775/) (2026)
- [Terrain Consistent Reference-Guided RL for Humanoid Navigation Autonomy](https://mlsanity.com/paper/2605.15517/) (2026)
- [Model-Informed Safe Reinforcement Learning for Bipedal Locomotion via Step-to-Step Prediction](https://mlsanity.com/paper/2609.34486/) (2026)

## Abstract (arXiv)

In this paper, we holistically present a Hybrid-Linear Inverted Pendulum (H-LIP) based approach for synthesizing and stabilizing 3D foot-underactuated bipedal walking, with an emphasis on thorough hardware realization. The H-LIP is proposed to capture the essential components of the underactuated and actuated part of the robotic walking. The robot walking gait is then directly synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive the stepping stabilization via its step-to-step (S2S) dynamics, which is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass (COM) of the robotic walking. The approximation facilities a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is fully evaluated in both simulation and experiment on the 3D underactuated bipedal robot Cassie, which demonstrates dynamic walking behaviors with both high versatility and robustness.