Spinning Quadrotor: Hover Thrust Augmentation with Passive Lifting Surfaces

This work develops a geometric theory of aerodynamic promptness for multirotor platforms whose propeller directions depend on a smooth orientation-mechanism configuration. The actuator state consists of the actual signed propeller speeds and the mechanism configuration, and the nonlinear actuator map retains both the signed-quadratic propeller law and the configuration-dependent thrust directions. Constant direction maps represent fixed propellers, while shared dependence on mechanism coordinates represents mechanically coupled tilts. A Riemannian metric on the product actuator manifold compares propeller accelerations and orientation-mechanism rates through physically interpretable scales. Composing the actuator-map differential, the musical isomorphism induced by this metric, and the dual differential defines a task-rate authority map from wrench covectors to wrench-rate vectors. In fixed task coordinates, the square root of the determinant of its matrix defines aerodynamic promptness. Positive promptness is equivalent to local wrench-rate surjectivity, while the associated spectrum resolves directional authority and conditioning. The same construction yields the metric horizontal inverse, the orthogonal projector onto wrench-fiber directions, and task-preserving internal motions that regulate promptness without changing the instantaneous wrench. The construction is related intrinsically to dynamic feedback linearization and specialized to the independently tilting, radially arranged Holocopter and Voliro architectures, clarifying how their established allocation and rank constructions fit within the same actuator-manifold geometry.

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

Gust disturbances, dynamic vertical inflow and ground effect are key adverse aerodynamic phenomena that induce variations in the forces acting on a multirotor and complicate its flight control. Miniature rotorcraft typically rely on simplified modelling of such effects to compute adjustments in thrust to counteract these forces. In the most basic case, disturbance force estimations are derived from the aircraft's motion and the generated thrust is assumed to exactly match that requested by the controller. However, such systems rely on the aircraft's trajectory to be affected before disturbances can be sensed and compensated. Numerous approaches presented over the last 15-20 years aim to reject external disturbances more quickly, but challenges remain. This paper presents a new approach in this category by measuring the instantaneous force of the rotors directly at the point of generation using load-cells and implementing high-speed control to accurately track the desired thrust. Measurements from load-cells were previously considered too noisy to provide meaningful input, but the experiments presented in the paper using purpose-built hardware from low-cost commodity components in single- and dual rotor see-saw models and a flying aircraft demonstrate both the feasibility and the effectiveness of the approach in the presence of complex aerodynamic phenomena.