# Feasible Space Monitoring for Multiple Control Barrier Functions with application to Large Scale Indoor Navigation

arXiv: https://arxiv.org/abs/2312.07803 · HTML: https://mlsanity.com/paper/2312.07803/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2023.

## Built on by (most cited first, 1 of 1)

- [Differentiable Optimization Layered Safety-Critical Control for Risk-Aware Navigation via Conformal Prediction](https://mlsanity.com/paper/2605.16327/) (2026)

## Abstract (arXiv)

Quadratic programs (QP) subject to multiple time-dependent control barrier function (CBF) based constraints have been used to design safety-critical controllers. However, ensuring the existence of a solution at all times to the QP subject to multiple CBF constraints (hereby called compatibility) is non-trivial. We quantify the feasible control input space defined by multiple CBFs at a state in terms of its volume. We then introduce a novel feasible space (FS) CBF that prevents this volume from going to zero. FS-CBF is shown to be a sufficient condition for the compatibility of multiple CBFs. For high-dimensional systems though, finding a valid FS-CBF may be difficult due to the limitations of existing computational hardware or theoretical approaches. In such cases, we show empirically that imposing the feasible space volume as a candidate FS-CBF not only enhances feasibility but also exhibits reduced sensitivity to changes in the user-chosen parameters such as gains of the nominal controller. Finally, paired with a global planner, we evaluate our controller for navigation among other dynamically moving agents in the AWS Hospital gazebo environment. The proposed controller is demonstrated to outperform the standard CBF-QP controller in maintaining feasibility.