Energy-Efficient Velocity Control for Massive Numbers of UAVs: A Mean Field Game Approach

In this paper, we propose an energy-efficient velocity control algorithm for a large number of UAVs based on mean field games. In particular, we first formulate the velocity control problem for a large number of UAVs as a differential game, where we jointly consider the energy consumption, channel capacity, and obstacle avoidance in the cost function. Meanwhile, the state dynamics are used to describe the motion of UAVs under the influence of the wind. Then we derive the corresponding mean field game for a large number of UAVs and solve it with the G-prox primal dual hybrid gradient (PDHG) method using its underlying variational primal dual structure. Scalability analysis shows that the computational complexity of the proposed method is unrelated to the number of UAVs. Based on the PDHG method, we conduct a comprehensive experiment where we analytically show the fast convergence of our energy-efficient velocity control algorithm by the convergence of the residual errors of the Hamilton-Jacobi-Bellman equation and the Fokker-Planck-Kolmogorov equation. The experiment also shows that a large number of UAVs can avoid obstacles and provide communication services for the search and rescue team while minimizing their energy consumption.