# Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safety

arXiv: https://arxiv.org/abs/2105.01697 · HTML: https://mlsanity.com/paper/2105.01697/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2021.

## Built on by (most cited first, 7 of 7)

- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions](https://mlsanity.com/paper/2212.11365/) (2022)
- [Multi-Constraint Safe Reinforcement Learning via Closed-form Solution for Log-Sum-Exp Approximation of Control Barrier Functions](https://mlsanity.com/paper/2505.00671/) (2025)
- [MARCH: Model-Assisted Reinforcement Learning for the Perceptive Control of Humanoids over Sparse Footholds](https://mlsanity.com/paper/2606.10288/) (2026)
- [LEARN: Learning End-to-End Aerial Resource-Constrained Multi-Robot Navigation](https://mlsanity.com/paper/2511.17765/) (2025)
- [Beyond Safety Filtering: Control Barrier Function-Informed Reinforcement Learning for Connected and Automated Vehicles](https://mlsanity.com/paper/2605.16894/) (2026)

## Abstract (arXiv)

This paper combines episodic learning and control barrier functions in the setting of bipedal locomotion. The safety guarantees that control barrier functions provide are only valid with perfect model knowledge; however, this assumption cannot be met on hardware platforms. To address this, we utilize the notion of projection-to-state safety paired with a machine learning framework in an attempt to learn the model uncertainty as it affects the barrier functions. The proposed approach is demonstrated both in simulation and on hardware for the AMBER-3M bipedal robot in the context of the stepping-stone problem, which requires precise foot placement while walking dynamically.