# Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control

arXiv: https://arxiv.org/abs/2011.00032 · HTML: https://mlsanity.com/paper/2011.00032/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2020.

## Built on by (most cited first, 25 of 25)

- [Learning to Jump from Pixels](https://mlsanity.com/paper/2110.15344/) (2021)
- [VLSA: Vision-Language-Action Models with Plug-and-Play Safety Constraint Layer](https://mlsanity.com/paper/2512.11891/) (2025)
- [GLiDE: Generalizable Quadrupedal Locomotion in Diverse Environments with a Centroidal Model](https://mlsanity.com/paper/2104.09771/) (2021)
- [Reinforcement Learning for Safe Robot Control using Control Lyapunov Barrier Functions](https://mlsanity.com/paper/2305.09793/) (2023)
- [PI-ARS: Accelerating Evolution-Learned Visual-Locomotion with Predictive Information Representations](https://mlsanity.com/paper/2207.13224/) (2022)
- [One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments](https://mlsanity.com/paper/2412.09989/) (2024)
- [Gaitor: Learning a Unified Representation Across Gaits for Real-World Quadruped Locomotion](https://mlsanity.com/paper/2405.19452/) (2024)
- [Enhancing Autonomous Navigation by Imaging Hidden Objects using Single-Photon LiDAR](https://mlsanity.com/paper/2410.03555/) (2024)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Imitation and Adaptation Based on Consistency: A Quadruped Robot Imitates Animals from Videos Using Deep Reinforcement Learning](https://mlsanity.com/paper/2203.05973/) (2022)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [A Transferable Legged Mobile Manipulation Framework Based on Disturbance Predictive Control](https://mlsanity.com/paper/2203.03391/) (2022)
- [VAE-Loco: Versatile Quadruped Locomotion by Learning a Disentangled Gait Representation](https://mlsanity.com/paper/2205.01179/) (2022)
- [Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filters](https://mlsanity.com/paper/2501.02620/) (2025)
- [T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terrain](https://mlsanity.com/paper/2503.06083/) (2025)
- [Learning to enhance multi-legged robot on rugged landscapes](https://mlsanity.com/paper/2409.09473/) (2024)
- [MARCH: Model-Assisted Reinforcement Learning for the Perceptive Control of Humanoids over Sparse Footholds](https://mlsanity.com/paper/2606.10288/) (2026)
- [Safe Execution of RL Policies Via Acceleration-Based CBF-QP Constraint Enforcement for Real-World Robotic Deployments](https://mlsanity.com/paper/2607.14488/) (2026)
- [Modular Safety-Critical Control of Legged Robots](https://mlsanity.com/paper/2303.02386/) (2023)
- [Multi-Resolution Planar Region Extraction for Uneven Terrains](https://mlsanity.com/paper/2311.12562/) (2023)
- [Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systems](https://mlsanity.com/paper/2505.09734/) (2025)
- [Response-Aware Risk-Constrained Control Barrier Function With Application to Vehicles](https://mlsanity.com/paper/2603.24598/) (2026)
- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)
- [Safe Online Learning via Smooth Safety-Structured Policy Composition](https://mlsanity.com/paper/2606.31320/) (2026)
- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

The problem of dynamic locomotion over rough terrain requires both accurate foot placement together with an emphasis on dynamic stability. Existing approaches to this problem prioritize immediate safe foot placement over longer term dynamic stability considerations, or relegate the coordination of foot placement and dynamic stability to heuristic methods. We propose a multi-layered locomotion framework that unifies Control Barrier Functions (CBFs) with Model Predictive Control (MPC) to simultaneously achieve safe foot placement and dynamic stability. Our approach incorporates CBF based safety constraints both in a low frequency kino-dynamic MPC formulation and a high frequency inverse dynamics tracking controller. This ensures that safety-critical execution is considered when optimizing locomotion over a longer horizon. We validate the proposed method in a 3D stepping-stone scenario in simulation and experimentally on the ANYmal quadruped platform.