Hamilton--Jacobi Reachability for Spacecraft Collision Avoidance

This article presents a Hamilton--Jacobi (HJ) reachability framework for a two--satellite collision avoidance problem operating in the same circular orbit, where relative motion is modeled in the radial--tangential--normal (RTN) frame using planar Hill--Clohessy--Wiltshire (HCW) dynamics. We define the target state space as unsafe relative configurations in the orbit plane corresponding to minimum separation requirements consistent with Federal Communications Commission (FCC) orbital standards. The interaction between spacecraft is formulated as a zero--sum differential game, where Player 1 is the controlled satellite and Player 2 is modeled as a bounded adversarial disturbance with unknown intent. We present the HJ formulation and compute backward reachable sets that characterize relative states from which collision cannot be avoided under worst-case disturbances, while states outside this set admit provably collision-free trajectories. These reachable sets are integrated with supervisory hybrid control logic to determine when evasive maneuvers must be initiated, enabling mathematically grounded safety guarantees for scalability.

Towards Automated Air Traffic Safety Assessment Around Non-Towered Airports Using Large Language Models

We investigate frameworks for post-flight safety analysis at non-towered airports using large language models (LLMs). Non-towered airports rely on the Common Traffic Advisory Frequency (CTAF) for air traffic coordination and experience frequent near mid-air collisions due to the pilot self-announcement communication protocol. We propose a general vision-language model (VLM) approach to analyze the transcribed CTAF radio communications in natural language, METeorological Aerodrome Report (METAR) weather data, Automatic Dependent Surveillance-Broadcast (ADS-B) flight trajectories, and Visual Flight Rules sectional charts of the airfield. We provide a preliminary study at Half Moon Bay Airport, with a qualitative real world case study and a quantitative evaluation using a new synthetic dataset of communications and weather modalities. We qualitatively evaluate our framework on real flight data using Gemini 2.5 Pro, demonstrating accurate identification of a right-of-way violation. The synthetic dataset is derived from real examples and includes a 12-category hazard taxonomy, and is used to benchmark three open-source (Qwen 2.5-7B, Mistral-7B, Gemma-2-9B) and three closed-source (GPT-4o, GPT-5.4, Claude Sonnet 4.6) LLM models on the subset of inputs related to CTAF and METAR. Even limited to CTAF and METAR inputs and open source LLMs, instances of our framework typically achieve a macro F1 score above 0.85 on a binary nominal/danger classification task. Future work includes a quantitative evaluation across all modalities and a larger number of real world examples. Taken together, our results suggest that VLM analysis of safety at non-towered airports may be a valuable future capability.