Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation
2026-08-17 • Robotics
Robotics
AI summaryⓘ
The authors study how to control drones with more motors than needed (overactuated multirotors) to safely and smoothly use their motors without demanding impossible speeds. They propose a new method that keeps control authority (the drone's ability to respond to commands) within guaranteed limits by using a mathematical function that never decreases. This method balances between maximizing readiness and minimizing effort and maintains stable control even when motor parameters vary. Their tests show it works much better than greedy methods that can cause large control errors. Overall, the authors offer a reliable way to allocate control commands safely and efficiently.
overactuated multirotorcontrol allocationreadiness metriccontrol barrier functionquadratic programwrench authorityactuator constraintsrobust controlmotor parameter uncertaintynull space
Authors
Giuseppe Silano
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. Tracking is sacrificed only through an explicit alignment ratio, with wrench error 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; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.