Feasibility and Singularity in High-Order Safety-Critical Control for Quadrotor UAVs
Abstract
We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.
Related
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- Diffusions with Critical Divergence-Free Drifts: Varadhan Asymptotics and Path-Law Singularity
BibTeX
@misc{nieto2026feasibility,
title = {{Feasibility and Singularity in High-Order Safety-Critical Control for Quadrotor UAVs}},
author = {Omayra Yago Nieto and Leonardo Colombo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19362},
eprint = {2609.19362},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19362},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feasibility and Singularity in High-Order Safety-Critical Control for Quadrotor UAVs
AU - Omayra Yago Nieto
AU - Leonardo Colombo
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19362
UR - https://arxiv.org/abs/2609.19362
AB - We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.
ER -