Exact Thrust-Reversal Limits of Bidirectional Propellers under Bounded Motor Inputs

2026-08-07

AI Summary

This study addresses the loss of thrust controllability near zero rotational speed during thrust reversal in bidirectional propellers, caused by bounded motor inputs, which renders thrust trajectories non-reproducible. By formulating a normalized thrust coordinate model and integrating nonlinear dynamics with input–output reproducibility analysis, this work rigorously proves for the first time that generic linear reversal inherently requires unbounded motor inputs and is thus infeasible under practical, smooth, and bounded current/voltage constraints. To circumvent this control singularity, the paper proposes a higher-order reversal design criterion. Experimental validation demonstrates that linear reversal induces current/voltage spikes and degrades tracking performance, whereas the proposed higher-order approach effectively avoids these issues, underscoring the necessity of accounting for actuator-level physical limitations in aerial robot interaction control.

Abstract

Bidirectional propellers are often treated as signed thrust sources, but their thrust is a signed-quadratic function of rotor speed.Thus, thrust reversal necessarily occurs through zero rotor speed, where the ability of a bounded motor torque to change thrust collapses.This work formalizes this obstruction by studying exact thrust-trajectory reproducibility under bounded motor inputs with prescribed smoothness.We derive a normalized thrust-coordinate model with vanishing input gain at zero thrust, and prove necessary and sufficient reproducibility conditions in terms of the zero-crossing order of the desired thrust.Generic reversals, in which thrust crosses zero with nonzero slope, require unbounded motor input; the resulting conditions provide direct design rules for shaping thrust reversals that avoid singular motor commands.We also derive the corresponding current and voltage regularity requirements for a DC motor driving a bidirectional propeller.Experiments on a motor-propeller setup validate the predicted reversal-order effects, showing localized current/voltage peaks and thrust-tracking degradation for linear reversals, but not for higher-order reversals.These results expose an intrinsic actuator-level limitation that must be considered in force, acceleration, and interaction-control references for aerial robots.

Problem

• bidirectional propellers
• thrust reversal
• bounded motor inputs
• thrust reproducibility
• actuator singularity

Innovation

• bidirectional propeller
• thrust reversal
• bounded motor input
• zero-crossing order
• input gain singularity