LNN-Fly: Continuous-Time UAV Navigation for Robust Obstacle Avoidance under Timing Mismatch

End-to-end unmanned aerial vehicle (UAV) navigation can achieve impressive agility in simulation, yet its obstacle-avoidance behavior often degrades after deployment because the policy must tolerate simulator mismatch, sensing irregularity, and variable-rate control. These effects are especially dangerous in cluttered environments, where stale observations or short control irregularities can directly lead to collisions. We present LNN-Fly, a deployment-oriented continuous-time navigation policy for LiDAR-based UAV obstacle avoidance. The policy combines a dynamic-programming-inspired structured recurrent update, explicit conditioning on the elapsed control interval {\Delta}t, and an input-driven adaptive forgetting gate that refreshes stale latent state near hazards while preserving consistency during sustained maneuvers. It is trained with differentiable rollouts that incorporate deployment-relevant sensing and timing perturbations. In simulation, LNN-Fly improves obstacle-avoidance performance in the tested settings and shows better tolerance to reduced control frequency, sparse observations, and control-period jitter. It also transfers zero-shot from a simplified differentiable simulator to a physical quadrotor. In indoor cross-frequency real-world tests, the system achieves 100% success over 20 flights, while policy inference has a median latency of 0.514 ms on a desktop graphics processing unit (GPU) and about 2.5 ms on the onboard central processing unit (CPU), with onboard P95 latency below 30 ms.