Collision analysis for a UAV

Eva Crück, Anna Désilles and Hasnaa Zidani
Publication type:
International conference with proceedings
AIAA Guidance, Navigation and Control Conference, Minneapolis (USA), 13-16 August. Doi: 10.2514/6.2012-4526, vol. Chapt. 4526, pp. 23 pages
Keywords :
Reachability analysis, collision avoidance, HJB approach, numerical solution of HJB equations, viability algorithms
The Sense and Avoid capacity of Unmanned Aerial Vehicles (UAV) is one of the key elements to open the access to airspace for UAVs. In order to replace a pilot’s See and Avoid capacity such a system has to be certified "as safe as a human pilot on-board". The problem is to prove that an unmanned aircraft equipped with a See and Avoid system can comply with the actual air transportation regulations. This paper aims to provide mathematical and numerical tools to link together the safety objectives and sensors specifications. The proposed approach starts with the natural idea of a specified "safety volume" around the aircraft: the safety objective is to guarantee that no other aircraft can penetrate this volume. A general reachability and viability concepts are used to define nested sets which are meaningful to allocate sensor performances and manoeuvring capabilities necessary to protect the safety volume. Using the general framework of Hamilton-Jacobi equations for the optimal control and differential games, a rigorous mathematical characterization of these sets is given. This approach allows also to take into account some uncertainties in the measures of the parameters of the incoming traffic. Numerical tools are also provided to compute the defined sets, so that the technical specifications of a See and Avoid system can be derived in accordance with a small set of intuitive parameters. Several dynamical models was considered corresponding to the different choices of avoidance maneuvers (lateral, longitudinal and mixed).
title (translation) :
Analyse de collision pour un drone
    author={Eva Crück and Anna Désilles and Hasnaa Zidani },
    title={Collision analysis for a UAV },
    doi={10.2514/6.2012-4526 },
    booktitle={AIAA Guidance, Navigation and Control Conference, Minneapolis 
           (USA), 13-16 August. Doi: 10.2514/6.2012-4526 },
    year={2012 },
    volume={Chapt. 4526 },
    pages={23 pages},