Delay-Certified Readiness Barriers for Overactuated Multirotor Allocation Without Lipschitz Constants

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 $\mathcal{O}(ρ^{-1/2})$, 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.

Fully-actuated multirotor aerial vehicles must not only track nominal wrenches but retain the "readiness" to modulate them rapidly under disturbances. Classical effort-minimizing allocators ignore this dynamic limit, whereas maximizing readiness leads to topologically disconnected optimal sheets demanding physically impossible actuator rates. Enforcing a readiness safety floor on fixed-geometry symmetric platforms further encounters a zero-sum degeneracy: motor-speed redistribution cannot improve authority without conceding wrench tracking. This paper uses active morphology to break the degeneracy, treating servo tilt as a geometric resource supplying authority-recovery directions unavailable to static rotors. We construct a configuration-dependent, motor-only readiness certificate - the log-volume of the reachable wrench-rate set - that explicitly excludes servo capacity, preventing a "ghost capacity fallacy" in which the certificate would falsely credit slow mechanical kinematic limits instead of collapsing accurately at motor saturation. The certificate is enforced as a Control Barrier Function (CBF) within a Unified Physical-Command Quadratic Program acting on motor torques and servo setpoints. Closed-loop simulations of an articulated octorotor under severe gust disturbances show classical allocators diverging and uncertified articulated allocators violating the safety floor, while the proposed CBF filter bounds the system state and preserves vehicle authority.

We develop a task-relative framework for certifying residual wrench authority after hover and contact loading in multirotors with bounded actuators. Using convex geometry, we derive signed margins for prescribed convex reserves, including Euclidean balls and weighted ellipsoids. We obtain computable reserve certificates from actuator-interiority bounds to support slack-maximizing allocation. To preserve the required reserve, we propose command projection onto a tightened feasible set. We then connect the available reserve to structured gain synthesis and certify a local tracking region that respects actuator limits. Within this region, we establish nominal exponential convergence and robust ultimate boundedness. For the prescribed task and morphology family, we show that the optimized octarotor attains a larger margin than the optimized hexarotor at equal total thrust. We evaluate the proposed framework in closed-loop simulations of sustained rigid-wall contact using a fixed-geometry octarotor and a variable-tilt quadrotor with matched installed thrust. The quadrotor's local certificate admits a higher normalized push limit for the prescribed task family. In tests beyond the realizability boundaries, we observe the predicted loss of authority through rotor-thrust limits for the octarotor and tilt-servo limits for the quadrotor.