String instabilities in formation flight: Limitations due to integral constraints

Flying in formation improves aerodynamic efficiency and, consequently, leads to an energy savings. One strategy for formation control is to follow the preceding vehicle. Many researchers have shown through simulation results and analysis of specific control laws that this strategy leads to amplification of disturbances as they propagate through the formation. This effect is known as string instability. In this paper, we show that string instability is due to a fundamental constraint on coupled feedback loops. The tradeoffs imposed by this constraint imply that predecessor following is an inherently poor strategy for formation flight control. Finally, we present two examples that demonstrate the theoretical results.