Zero drift regions and control strategies to keep satellite in formation around triangular libration point in the restricted Sun–Earth–Moon scenario

In this work, we are interested in avoiding large variations in the mutual distances among multiple satellites and also in controlling their geometric configuration around an Earth–Moon triangular point. Previous studies about triangular libration points have determined the existence of zero drift regions with respect to the nominal trajectory, in which the expansion or contraction of the formation never take place. Our goal is to carry out two different control strategies for a formation near a given nominal trajectory around L4: a bang-off-bang control and a minimum weighted total ΔV consumption. A linearization relative to the reference trajectory around the triangular libration point is carried out, and different geometrical possibilities in the zero drift regions are studied. To investigate the influence of the gravitational force of the Sun, the BiCircular Four Body Problem is considered here. According to the results obtained, some meaningful insights to allow a proper design of the geometric configuration of the formation are drawn.