Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation

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 (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 times 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.