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

2026-09-11

AI Summary

研究解决了多旋翼无人机在非冗余和冗余驱动下的静态控制分配问题，通过分析推力映射的性质，提出了差分实现性条件及修正方法。

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.

Problem

• multirotors
• control allocation
• nonredundant full actuation
• redundant actuation
• pseudoinverse

Innovation

• differential realizability
• pseudoinverse obstruction
• nonredundant full actuation
• redundant actuation
• local nullspace deformation