Distributed Control of Spacecraft Formations

Significant interest in formation flying started to develop in the late 1990s, and today formation flying is a critical technology for many planned and future missions of NASA, the DoD, and ESA. Spacecraft formation algorithms can be divided into three main architectures: (i) Multiple-Input Multiple-Output (MIMO), in which the formation is treated as a single multiple-input, multiple-output plant, (ii) Leader-Follower, in which individual spacecraft controllers are connected hierarchically, and (iii) Cyclic, in which individual spacecraft controllers are connected non-hierarchically. Cyclic algorithms can distribute control effort more evenly, are generally more robust than MIMO algorithms, and can also be completely distributed. The two primary drawbacks of Cyclic algorithms are that the stability of these algorithms and their information requirements are poorly understood (a comprehensive and up-to-date survey on spacecraft formation flying can be found here). Motivated by the discussion above, we have developed a class of Cyclic algorithms for formation flying, for which (i) a rigorous stability analysis is possible, and (ii) the information requirements are minimal. In particular, we studied control policies that only rely on relative measurements, since in deep-space missions global measurements may not be available. Our control algorithms have been tested on the International Space Station in 2008/2009. Specifically, we tested balanced circular formation for three Spheres satellites (videos of the tests in space can be seen on the left). This is joint work with E. Frazzoli (MIT), J. Ramirez (MIT), and D. Miller (MIT)