Control of Spacecraft Formations Around the Libration Points Using Electric Motors with One Bit of Resolution
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Control of Spacecraft Formations Around the Libration Points Using Electric Motors with One Bit of Resolution Edoardo Serpelloni · Manfredi Maggiore · Christopher J. Damaren
© American Astronautical Society 2015
Abstract This paper investigates a formation control problem for two space vehicles in the vicinity of the L2 libration point of the Sun-Earth/Moon system. The objective is to accurately regulate the relative position vector between the vehicles to a desired configuration, under tight tolerances. It is shown that the formation control problem is solvable using six constant thrust electric actuators requiring only one bit of resolution, and bounded switching frequency. The proposed control law is hybrid, and it coordinates the sequence of on-off switches of the thrusters so as to achieve the control objective and, at the same time, avoid high-frequency switching. Keywords Formation control · Bang-bang control · Libration points
Introduction In recent years, several space agencies have proposed missions for the observation of the universe involving large spacecraft arrays flying in formation. The constraints imposed by the type of observations these missions must perform have led to the identification of trajectories in a neighborhood of the L2 Lagrangian point of the SunEarth/Moon system as an ideal location. NASA proposed, in the context of the Vision Program, the Stellar Imager (SI) mission, a large array of nearly 30 spacecraft flying in formation to form a large telescope, see [1]. The Terrestrial Planet Finder (TPF) Preliminary versions of parts of this material appeared in the conference proceedings [12, 13]. E. Serpelloni · M. Maggiore () Electrical and Computer Engineering Department, University of Toronto, Toronto, ON, M5S 2J7, Canada e-mail: [email protected] C. J. Damaren University of Toronto Institute for Aerospace Studies, Toronto, ON, M3H 5T6, Canada
J of Astronaut Sci
(see [2]) and the MAXIM mission concepts (see [3]) also involved large formations of spacecraft flying in the vicinity of the L2 libration point (small baselines for TPF, very large for MAXIM). These mission concepts share great challenges from the formation control perspective, as the relative position between spacecraft must be regulated with submillimetric error tolerances. In particular, SI requires the spacecraft to meet three different control specifications, classified as (see [1]): rough control, with accuracy up to a few meters; intermediate control, with accuracy of the order of a few centimeters; and, fine control, with submillimeter accuracy. Each of these control regimes is to be satisfied for an interval of time long enough to allow the scientific observation to be completed (for the SI mission, this would depend on the target star rotation period). The formation control problem has been intensively studied in recent years. Discrete control methods, such as the Equitime Targeting Method [4, 5] and the Tangential Targeting Method [6], implement impulsive maneuvers at various checkpoints along the r
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