Differentiable End-to-End UAV Navigation Using Time-of-Arrival Fields and Control Barrier Functions

Abstract

Quadrotor UAVs are increasingly deployed in complex missions that demand reliable autonomous navigation and robust obstacle avoidance. Traditional modular pipelines suffer from cumulative latency, motivating a shift toward end-to-end learning-based methods. However, this paradigm still faces two fundamental challenges. First, Euclidean distance-based guidance is prone to local minima under large obstacles and lacks global planning capability. Second, safety mechanisms built on collision penalties alone cannot anticipate hazards, making them fragile at high speed. To address these issues, we propose an end-to-end differentiable physics framework that combines time-of-arrival fields and control barrier functions. During training, we generate a time-of-arrival (TOA) distance field online on the GPU via the jump flooding algorithm (JFA) as privileged information. A position-level geodesic objective is embedded into the differentiable pipeline through a straight-through gradient. A velocity-aligned yaw strategy keeps the depth camera pointed along the flight direction, mitigating blind spots caused by lateral motion. We further formulate the first-order control barrier function (CBF) as an analytic velocity constraint, driving the policy to learn anticipatory deceleration. At deployment, no privileged supervision is required. The policy operates using only onboard depth and inertial states, with no online map or solver. Extensive experiments show that our method outperforms existing baselines across all tested speeds, with zero-shot sim-to-real transfer reaching 7.8 m/s in outdoor forests.