Trajectory Planning for A Massive Number of UAVs in the Environment with Static and Dynamic Obstacles: A Mean Field Game Approach

Trajectory planning of massive unmanned aerial vehicles (UAVs) is very difficult in an environment with static and dynamic obstacles. This is mainly due to the huge number of UAVs, which pose challenges to their interaction and collision avoidance with companions and obstacles. In this paper, we propose a trajectory planning algorithm for a massive number of UAVs based on the mean field game (MFG). First, a differential game of N UAVs in a 3D environment is constructed, and the collision avoidance with static and dynamic obstacles is considered in the cost functional of each UAV. Then, when the number of UAVs is very large, the above differential game is transformed into a MFG using the mean field approximation. The existence and uniqueness of the equilibrium solution are proved. Finally, we derive the variational primal-dual formulation of the proposed MFG model and solve it with APAC-Net. The performance of the proposed algorithm is validated in an environment with multiple static obstacles and two different types of dynamic obstacles.

I. Introduction

Trajectory planning of a massive number of UAVs is very important and widely used in many fields, such as disaster rescue [1], warehouse management [2], and so on. However, the environment with static and dynamic obstacles has a sig-nificant impact on the flight safety of UAVs. In addition, UAVs need to avoid collisions with companions while successfully avoiding obstacles. When the number of UAVs is large, this poses high requirements to trajectory planning algorithms.