Multirotor control limits found in propeller speed reversals and redundancies

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

Robotics

Summary

Controlling multirotor drones involves adjusting propeller speeds to move as desired, but the relationship between propeller speed and generated force is tricky near zero speed. The authors found that when propellers are not redundant, changing a single propeller’s direction can cause a loss in the drone's ability to move instantly in some directions. With extra (redundant) propellers, the system can stay regular but controlling it smoothly requires difficult adjustments that can become infinitely fast. They also provide ways to fix or work around these control issues through mathematical methods.

What this means in practice

  • For drone control engineers: Identify and correct singularities in multirotor control allocation for drones with reversible propellers to improve control reliability.
  • For robotics system designers: Design drone actuation systems mindful of control limits imposed by propeller reversals to ensure stable and smooth dynamic performance.

A theory result. No direct application yet.

Authors

Antonio Franchi, Mirko Mizzoni

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.
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