Differential Realizability of Static Control Allocation in Multirotors: An Impossibility under Nonredundant Full Actuation and a Pseudoinverse Obstruction under Redundant Actuation
arXiv:2609.13588v1 Announce Type: new Abstract: 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 differe
Overview
arXiv:2609.13588v1 Announce Type: new Abstract: 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 transverse pseudoinverse zero crossing requires an unbounded rotor-speed derivative. We define differential realizability as regularity of the physical lift of an actuator-output section, derive exact and first-order validity conditions, and distinguish structural rank loss from an allocator- induced rate singularity. A local nullspace deformation repairs isolated pseudoinverse reversals, while a global fixed-orthant construction establishes existence of regular sections at the cost of persistent task-preserving internal actuation.
Source
Originally published at arxiv.org.
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Source: https://arxiv.org/abs/2609.13588