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Journal Articles Fractional Calculus and Applied Analysis Year : 2022

Dynamical repulsive fractional potential fields in 3D environment


Unmanned Aerial Vehicle applications have highly increased in the last years, from surveillance, exploration, rescue to transport applications. UAVs are more and more autonomous, therefore real-time trajectory planning is necessary and can be achieved thanks to artificial potential fields. The classic Ge & Cui repulsive force solely allows taking into account the velocity of the obstacles without any distinction. The Weyl potential force associates a degree of danger with an obstacle and has enabled to distinguish between the obstacles but the obstacle velocity is no more considered. Therefore, a new dynamical fractional repulsive force has been proposed by combining both advantages. The new dynamical fractional repulsive potential field is usable in a 3D environment and takes into account both the obstacle dynamics (position and speed) and their degree of dangerousness. Obstacle avoidance robustness is guaranteed, both from a safety point of view and from a trajectory optimization point of view. The proposed repulsive potential fields are first of all dynamical as they are based on the relative position and speed of the UAV in relation to the obstacle positions and speeds. Moreover, the dangerousness of the obstacles is also considered by introducing a fractional degree in their definition. Simulations results are provided to compare different repulsive potential field method (Ge & Cui, Weyl methods) to the proposed dynamical fractional potential field both in static and dynamical environments.
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Dates and versions

hal-03722495 , version 1 (13-07-2022)



Stéphane Victor, Kendric Ruiz, Pierre Melchior, Serge Chaumette. Dynamical repulsive fractional potential fields in 3D environment. Fractional Calculus and Applied Analysis, 2022, 25 (2), pp.321-345. ⟨10.1007/s13540-022-00015-5⟩. ⟨hal-03722495⟩
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