Learning Geometry-Aware Planning Representations for Monocular Flight with Cross-Modal Supervision

Existing high-speed navigation systems for micro aerial vehicles (MAVs) commonly rely on depth cameras, stereo vision, or LiDAR to obtain explicit geometric information, while monocular cameras offer a lighter and lower-cost alternative. However, monocular flight remains challenging because RGB images offer no direct metric cues and visual appearance varies considerably across environments. We propose a geometry-aware monocular visual planning framework that predicts trajectories from two image frames, their relative pose, and the MAV state. Without explicitly reconstructing depth, the proposed method complements the downstream planning objective with feature-level geometric supervision by transferring the planning-relevant representation learned by a privileged depth expert to the RGB planner through cross-modal distillation. The framework first trains a depth-based geometric expert, then distills its planning features into a monocular branch using paired RGB-D observations, and finally adapts the planner to the downstream trajectory planning objective. This design encourages the policy to learn planning-relevant geometric features, enabling collision avoidance. We further use a 3D Gaussian Splatting (3DGS) simulator to render visual observations for data collection, paired RGB-D supervision, and simulation evaluation. The planner trained in simulation is then deployed in real-world environments without real-world fine-tuning, achieving obstacle avoidance at speeds of up to 6.5 m/s.