Formation control as a classical decentralized multivariable problem: Performance, robustness, cross-coupling and perturbation rejection

Several control algorithms for vehicle-formation control have been proposed in recent years. Nonetheless, some aspects remain understudied in existing literature, such as the integration of the formation control with existing vehicle controllers, the formation cross-coupling and the distribution of single-agent perturbations across the formation. The main contribution of this article is the reformulation of the formation control problem as a decentralized control problem using classical multivariable theory. This novel reformulation enables the development of general theoretical results, which are also supported by numerical examples and extensive simulations. The following problems are studied: performance, robustness, cross-coupling and perturbation rejection. These general results are then used to analyze two issues: 1) the integration of the formation control with existing vehicle controllers and 2) the distribution of single-agent perturbations across the formation. The main concepts are first derived for a simple formation structure and later used to characterize more complex formations with ease. The results show that a naive formation control design can lead to troublesome cross-coupling issues, reducing performance, robustness and compromising the perturbation rejection capabilities of the formation. On the other hand, a better handling of the formation cross-coupling yields an improved formation behavior while maintaining the individual agent robustness and performance. Although the main objective of this article is to contribute to general formation theory (rather than presenting a vehicle-specific result), quad-rotor formations are used to illustrate the theoretical results with numerical examples.