Reintroducing the Formation Flight Problem via Extremum Seeking Control

Flying in formation, as observed among migratory birds, has the potential to save significant amounts of energy when flying long distances. However, maintaining precise position control among a group of fixed-wing aircraft would require an accurate wake model available in real-time, which is impractical if not impossible. Extremum Seeking Control (ESC) operates in real-time and on a model-free basis, offering a potential solution which eliminates the need for an accurate real-time wake model. In this paper, we reintroduce the formation flight problem with direct application to a two aircraft leader-follower formation of Lockheed C-5 Galaxy aircraft consistent with the literature and in a sequence and clarity that we believe will be helpful to the aeronautical, aerospace, and applied control engineering communities. A formation hold controller was designed using classical methods to maintain a desired position of the follower relative to the leader. ESC was then wrapped around the formation hold controller to optimize the location of the follower in the wake for maximum upwash. A 6-DOF linear flight dynamics model of the C-5 Galaxy was simulated in conjunction with a nonlinear wake model to demonstrate that the proposed design indeed minimizes the pitch attitude of the follower. From these results, we emphasize the guarantees provided in the literature; ESC will drive the follower aircraft to the optimal location in the wake without the need for an accurate wake model a priori.