Drag-Aware Aerodynamic Manipulability for Torque-Limited Redundant Multirotors: Aerodynamic Promptness based on the Symmetric Acceleration Capacity

Abstract

Aerodynamic promptness quantifies how rotor-speed variations generate multirotor wrench variations, but its Euclidean formulation assigns the same local cost to a given rotor acceleration at every operating speed. This work develops a capacity-aware extension for redundant multirotors with arbitrary numbers of heterogeneous rotors and wrench components. Under bounded motor torque and aerodynamic drag, each generally asymmetric instantaneous rotor-acceleration interval contains a largest zero-centered subset whose radius defines the symmetric acceleration capacity (SAC). The SAC induces a Riemannian metric on the positive-capacity rotor-speed region. Propagating its co-metric through the nonlinear rotor-speed-to-wrench differential yields a state-attached task-rate capability matrix and ellipsoid. The corresponding inverse quadratic form equals the minimum normalized rotor-acceleration effort required to realize a prescribed wrench rate, while the ellipsoid volume defines the drag-aware aerodynamic manipulability (DAAM) index. Fiberwise DAAM maximization provides a task-coordinate-invariant criterion for selecting task-equivalent actuator states; its maximizing set exists on compact regular domains and can be nonconvex and set valued. Low-dimensional two- and three-rotor studies make the resulting fiberwise geometry and parameter dependence directly visible. A complementary two-rotor use case shows how DAAM can inform a continuous allocation section subject to directional motor-torque feasibility. For two heterogeneous propulsion systems, the resulting sections reduce saturation-induced force-tracking degradation relative to the pseudoinverse in the faster command bands