# Walking in Narrow Spaces: Safety-critical Locomotion Control for Quadrupedal Robots with Duality-based Optimization

arXiv: https://arxiv.org/abs/2212.14199 · HTML: https://mlsanity.com/paper/2212.14199/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2022.

## Built on by (most cited first, 10 of 10)

- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [DiffuseLoco: Real-Time Legged Locomotion Control with Diffusion from Offline Datasets](https://mlsanity.com/paper/2404.19264/) (2024)
- [DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectories](https://mlsanity.com/paper/2502.15043/) (2025)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments](https://mlsanity.com/paper/2412.09989/) (2024)
- [Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotion](https://mlsanity.com/paper/2602.00678/) (2026)
- [QuadWBG: Generalizable Quadrupedal Whole-Body Grasping](https://mlsanity.com/paper/2411.06782/) (2024)
- [TRANS: Terrain-aware Reinforcement Learning for Agile Navigation of Quadruped Robots under Social Interactions](https://mlsanity.com/paper/2602.12724/) (2026)
- [Discriminative Barrier Functions for Safe Adversarial Imitation Learning from Observation](https://mlsanity.com/paper/2607.13938/) (2026)
- [E2DRL: End-to-End Differentiable Reinforcement Learning for 3D Obstacle Avoidance in Quadruped Robots](https://mlsanity.com/paper/2610.19627/) (2026)

## Abstract (arXiv)

This paper presents a safety-critical locomotion control framework for quadrupedal robots. Our goal is to enable quadrupedal robots to safely navigate in cluttered environments. To tackle this, we introduce exponential Discrete Control Barrier Functions (exponential DCBFs) with duality-based obstacle avoidance constraints into a Nonlinear Model Predictive Control (NMPC) with Whole-Body Control (WBC) framework for quadrupedal locomotion control. This enables us to use polytopes to describe the shapes of the robot and obstacles for collision avoidance while doing locomotion control of quadrupedal robots. Compared to most prior work, especially using CBFs, that utilize spherical and conservative approximation for obstacle avoidance, this work demonstrates a quadrupedal robot autonomously and safely navigating through very tight spaces in the real world. (Our open-source code is available at github.com/HybridRobotics/quadruped_nmpc_dcbf_duality, and the video is available at youtu.be/p1gSQjwXm1Q.)