Natural formations at the Earth–Moon triangular point in perturbed restricted problems

Abstract

Previous studies for small formation flying dynamics about triangular libration points have determined the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory, that prevent from the expansion or contraction of the constellation. However, these studies only considered the gravitational force of the Earth and the Moon using the Circular Restricted Three Body Problem (CRTBP) scenario. Although the CRTBP model is a good approximation for the dynamics of spacecraft in the Earth-Moon system, the nominal trajectories around equilateral libration points are strongly affected when the primary orbit eccentricity and solar gravitational force are considered. In this manner, the goal of this work is the analysis of the best regions to place a formation that is flying close a bounded solution around L 4 , taking into account the Moon's eccentricity and Sun's gravity. This model is not only more realistic for practical engineering applications but permits to determine more accurately the fuel consumption to maintain the geometry of the formation.

Distributed adaptive synchronization for multiple spacecraft formation flying around Lagrange point orbits

“…In fact, since orbits around the collinear points are inherently unstable, a continuous active control is necessary to achieve long-term bounded relative motion. To that end, a number of formation control algorithms have been discussed, which can be roughly categorized into tight [10,11,12,13] and loose [14,15,16] strategies. The tight control method consists in stabilizing the spacecraft relative motion with respect to a specified nominal trajectory, using Lyapunov or eigenvalue stability theorem.…”