A Constraint-Driven Approach to Line Flocking: The V Formation as an Energy-Saving Strategy

In this article, we present a constraint-driven control algorithm that minimizes the energy consumption of individual agents and yields an emergent V formation. As the formation emerges from the decentralized interaction between agents, our approach is robust to the spontaneous addition or removal of agents to the system. We start from an analytical model for the trailing upwash behind a fixed-wing uncrewed aerial vehicle (UAV), and we derive the optimal air speed for trailing UAVs to maximize their travel endurance. Next, we prove that simply flying at the optimal airspeed will never lead to emergent flocking behavior and propose a new decentralized “aneroid” behavior that yields emergent V formations. We encode these behaviors in a constraint-driven control algorithm that minimizes the locomotive power of each UAV. Finally, we prove that UAVs initialized in an approximate V or echelon formation will converge under our proposed control law, and we demonstrate that this emergence occurs in real time in simulation and in physical experiments with a fleet of Crazyflie quadrotors despite the noise and disturbances inherent in physical systems.