When an unmanned aerial vehicle learns from an experienced pilot, it memorizes not individual maneuvers but entire safe corridors — the trajectories along which the human mentor moved. This approach is called imitation learning: the machine mimics expert demonstrations. However, in real flight, factors absent from the training data inevitably arise: an unexpected gust of wind, camera vibrations, even aerodynamic turbulence from its own rotors. Under these changed conditions, directly copying the mentor's actions often leads to a crash — the so-called distribution shift kicks in. The data on which the drone learned in a simulator or in calm conditions no longer matches the real environment, and the learned patterns become erroneous.

The new algorithm tackles this problem by drawing invisible 'black holes' around all undesirable zones. Mathematically, these regions are described by a potential field where the repulsive force grows rapidly as danger approaches, like gravity working in reverse. The closer the drone gets to a forbidden boundary, the stronger the system corrects its course, smoothly guiding the aircraft into a safe area. This mechanism maintains stability even if sensors deliver noisy data or the communication link with the operator temporarily drops.

Experimental tests confirmed the approach's effectiveness: the aircraft never breached a safety boundary, successfully coping with strong crosswinds and sudden equipment failures. In other words, the algorithm figured out how to act in abnormal situations without relying on blind copying, instead continuously assessing the current risk level through the mathematical description of 'black holes'. This caution paves the way for reliable urban delivery in any weather or for rescue missions where a mistake could cost lives.