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.

无人机应用在过去几年中大幅增加，从监视、探索、救援到运输应用。无人机越来越自主，因此实时轨迹规划是必要的，并且可以通过人工势场来实现。经典的葛崔斥力只考虑障碍物的速度，没有任何区别。Weyl 势力将一定程度的危险与障碍物联系起来，并能够区分障碍物，但不再考虑障碍物的速度。因此，结合这两个优点，提出了一种新的动态分数排斥力。新的动态分数排斥势场可用于 3D 环境，并考虑了障碍物动力学（位置和速度）及其危险程度。从安全的角度和轨迹优化的角度来看，都保证了避障鲁棒性。所提出的排斥势场首先是动态的，因为它们基于无人机相对于障碍物位置和速度的相对位置和速度。此外，还通过在定义中引入分数来考虑障碍物的危险性。提供了模拟结果以在静态和动态环境中比较不同的排斥势场方法（Ge & Cui, Weyl 方法）与所提出的动态分数势场。从安全的角度和轨迹优化的角度来看，都保证了避障鲁棒性。所提出的排斥势场首先是动态的，因为它们基于无人机相对于障碍物位置和速度的相对位置和速度。此外，还通过在定义中引入分数来考虑障碍物的危险性。提供了模拟结果以在静态和动态环境中比较不同的排斥势场方法（Ge & Cui, Weyl 方法）与所提出的动态分数势场。从安全的角度和轨迹优化的角度来看，都保证了避障鲁棒性。所提出的排斥势场首先是动态的，因为它们基于无人机相对于障碍物位置和速度的相对位置和速度。此外，还通过在定义中引入分数来考虑障碍物的危险性。提供了模拟结果以在静态和动态环境中比较不同的排斥势场方法（Ge & Cui, Weyl 方法）与所提出的动态分数势场。所提出的排斥势场首先是动态的，因为它们基于无人机相对于障碍物位置和速度的相对位置和速度。此外，还通过在定义中引入分数来考虑障碍物的危险性。提供了模拟结果以在静态和动态环境中比较不同的排斥势场方法（Ge & Cui, Weyl 方法）与所提出的动态分数势场。所提出的排斥势场首先是动态的，因为它们基于无人机相对于障碍物位置和速度的相对位置和速度。此外，还通过在定义中引入分数来考虑障碍物的危险性。提供了模拟结果以在静态和动态环境中比较不同的排斥势场方法（Ge & Cui, Weyl 方法）与所提出的动态分数势场。