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

The paper 'Exact Thrust-Reversal Limits of Bidirectional Propellers under Bounded Motor Inputs' (arXiv:2608.06991v1) addresses the control problem of bidirectional propellers, which are often modeled as signed thrust sources. However, thrust is a signed-quadratic function of rotor speed, so thrust reversal requires passing through zero rotor speed, where the ability of bounded motor torque to change thrust collapses. The authors derive a normalized thrust-coordinate model with vanishing input gain at zero thrust and prove necessary and sufficient conditions for exact thrust-trajectory reproducibility based on the zero-crossing order of the desired thrust. They show that generic reversals (nonzero slope at zero crossing) require unbounded motor input, and provide design rules to shape reversals avoiding singular commands. They also derive current and voltage regularity requirements for DC motors. Experiments on a motor-propeller setup validate the predicted effects: linear reversals cause localized current/voltage peaks and thrust-tracking degradation, while higher-order reversals do not.

The key insight is that bidirectional propeller control must account for the vanishing input gain at zero thrust. For linear thrust reversals, bounded motor inputs cannot achieve exact tracking, leading to singular commands. Higher-order reversals (e.g., quadratic) avoid this issue. This suggests that control strategies should design thrust trajectories with higher-order zero crossings to maintain stability and avoid current/voltage spikes.