Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation
Abstract
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as ln(n/(n−m)) for symmetric designs. An explicit alignment ratio states when tracking can stay exact, otherwise the wrench error is bounded by 𝒪(ρ−1/2), and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision. Over $300$ randomized missions, greedy maximization violates the certified floor in up to 51% of authority-scarce missions, while the proposed filter never leaves the certified set and, in the hardest moment reversal, commits a 79× smaller wrench error. The robust variant holds the floor on all $150$ perturbed plants. A high-fidelity simulation with measured propeller and motor data shows that the floor holds under unmodeled aerodynamics, electrical limits, and delay, and where it stops applying.
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BibTeX
@misc{silano2026readiness,
title = {{Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation}},
author = {Giuseppe Silano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.16335},
eprint = {2608.16335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16335},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation
AU - Giuseppe Silano
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2608.16335
UR - https://arxiv.org/abs/2608.16335
AB - Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as ln(n/(n−m)) for symmetric designs. An explicit alignment ratio states when tracking can stay exact, otherwise the wrench error is bounded by 𝒪(ρ^−1/2), and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision. Over $300$ randomized missions, greedy maximization violates the certified floor in up to 51% of authority-scarce missions, while the proposed filter never leaves the certified set and, in the hardest moment reversal, commits a 79× smaller wrench error. The robust variant holds the floor on all $150$ perturbed plants. A high-fidelity simulation with measured propeller and motor data shows that the floor holds under unmodeled aerodynamics, electrical limits, and delay, and where it stops applying.
ER -