Aero-Promptness: Drag-Aware Aerodynamic Manipulability for Propeller-driven Vehicles

This work introduces the Drag-Aware Aerodynamic Manipulability (DAAM), a geometric framework for control allocation in redundant multirotors. By equipping the propeller spin-rate space with a Riemannian metric based on the remaining symmetric acceleration capacity of each motor, the formulation explicitly accounts for motor torque limits and aerodynamic drag. Mapping this metric through the nonlinear thrust law to the generalized force space yields a state-dependent manipulability volume. The log-determinant of this volume acts as a natural barrier function, strictly penalizing drag-induced saturation and low-spin thrust loss. Optimizing this volume along the allocation fibers provides a redundancy resolution strategy inherently invariant to arbitrary coordinate scaling in the generalized-force space. Analytically, we prove that the resulting optimal allocations locally form smooth embedded manifolds, and we geometrically characterize the global jump discontinuities that inevitably arise from physical actuator limits and spin-rate sign transitions.