Cooperative Formation Flying with Hierarchical Control

*† In this paper, use of hierarchical control concepts is investigated for cooperative formation flying of aircrafts. T he airplanes are modeled as point mass and represented by double integrators. For demonstration of the concepts, a task of forming a square from arbitrary initial conditions is presented to four airplanes. The final position that each airplane has to reach is unknown to them. The goal for the team is abstracted in the top layer. The system is modeled as a hierarchical system in which the global information comes from the top level. Following this global information, each airplane positions itself from at le ast one other airplane such that a square is formed. Numerical results from this simulation show the effectiveness of the hierarchical concept . I. Introduction ormation Control has been a major area for control applications. Formation of robots has been con sidered in [Fax and Murray, 2002 ] where complex graph theory has been used to explain the information flow between the airplanes. It has been shown that by information flow the robots arrive at a consensus with respect to the formation center and thus prev ent the circuitous trajectories. Thus, when the robots have some knowledge about the global goal, they take smooth trajectories to reach the final destination. In this paper, a case where four airplanes are required to form a square is treated with a hiera rchical control framework [Dasgupta, Balakrishnan and Acar, 2002 ]. None of the airplanes in the formation is aware that a square is being formed. The upper level supplies the global goal required for the formation to form the square. The global goal is in terms of the separation distance between the two adjacent airplanes. The upper level dictates how the separation distance should change such that a square is formed. The airplanes at the lower level then cooperatively adjust their trajectories such that th ey track the global goal propagated from the top and form the square.