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Differential Realizability of Static Control Allocation in Multirotors: An Impossibility under Nonredundant Full Actuation and a Pseudoinverse Obstruction under Redundant Actuation

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

Control allocation for multirotors with bidirectional propellers is commonly formulated in signed-thrust variables, where the wrench map is linear. The signed-quadratic map from physical rotor speed to thrust, however, is not a local diffeomorphism at zero speed. This work derives two distinct consequences. Under nonredundant full actuation, a single-propeller reversal removes one instantaneous task direction; hence, no global continuously differentiable exact static allocator exists over the complete task space. Under redundant actuation, the physical task map may remain regular, yet a transv

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