CBF-Based Control Allocation for Omnidirectional Tiltrotor Aerial Robots

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.

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.

Aerial manipulation extends robotic operations to previously inaccessible aerial environments. Unlike arm-equipped aerial systems, tiltable-multirotors can directly generate six-degree-of-freedom wrenches through their flight bases, enabling both efficient movement and omnidirectional operation by tilting the thrust direction. This work presents a design analysis and a wrench-based control framework for tiltable-multirotors in aerial manipulation. We show that a four-rotor tiltable configuration provides a balance between interference-free propeller sizing and hovering efficiency across different attitudes, and its null-space redundancy is crucial for traversing singular configurations under physical constraints. We further show that an upward end-effector placement yields a favorable trade-off between geometric clearance and available wrench. To address disturbances, we propose a dual strategy consisting of a modified integral term for model error and an acceleration-based estimator for external wrenches. Building on these insights, we develop an effector-centric nonlinear model predictive control (NMPC) framework that integrates design choices, singularity handling, and disturbance compensation into a unified formulation. The proposed framework runs fully onboard at 100 Hz on a custom-built tiltable-quadrotor. Real-world experiments, including a 90-deg step cartwheel rotation, whiteboard pushing, and continuous 360-deg valve turning, demonstrate the feasibility of wrench-based omnidirectional manipulation with singularity traversal on a one-DoF-per-arm tiltable-quadrotor.