2D Necklace Flower Constellations

Abstract

The 2D Necklace Flower Constellation theory is a new design framework based on the 2D Lattice Flower Constellations that allows to expand the possibilities of design while maintaining the number of satellites in the configuration. The methodology presented is a generalization of the 2D Lattice design, where the concept of necklace is introduced in the formulation. This allows to assess the problem of building a constellation in orbit, or the study of the reconfiguration possibilities in a constellation. Moreover, this work includes three counting theorems that allow to know beforehand the number of possible configurations that the theory can provide. This new formulation is especially suited for design and optimization techniques.

Definition of Low Earth Orbit slotting architectures using 2D lattice flower constellations

“…Lattice Flower Constellations include, as a subset, the most widespread satellite constellation designs, including Walker Delta Pattern Constellations (Walker, 1984), Streets of Coverage (Luders, 1961), Draim Constellations (Draim, 1987, and Dufour Constellations (Dufour, 2003). In fact, the 2D-LFC methodology is able to generate all the possible uniform distributions performed in the right ascension of the ascending node and the mean anomaly (see Theorems 4, 5, 6 and 7 in Arnas (2018)). This provides a powerful tool to study all possible uniform distributions of satellites with a unified theory.…”

“…Therefore, among the single-inclination shell generation approaches considered in this paper, 2D-LFCs show the best packing. In particular, a single 2D-LFC is especially appropriate when actors have compatible mission requirements (Arnas, 2018) and the chief objective is to maximize capacity, or if a shell's primary user is a single large constellation. This shows that constellation design models based on the Flower Constellation Theory (Mortari et al, 2004;Avendañ o et al, 2013;Arnas et al, 2017a;Arnas et al, 2017b) are an adequate tool to study this problem.…”

4D Lattice Flower Constellations

“…This property makes this methodology of design interesting for many applications, especially global coverage, telecommunications and global positioning systems (Casanova et al, 2014a). Later, Lattice Flower Constellations were generalized with Necklace Flower Constellations (Arnas, 2018;Casanova et al, 2014b;Arnas et al, 2017a;Arnas et al, 2017c;Arnas et al, 2017d), which allowed to expand the number of possibilities of design by defining a fictitious constellation from where a subset of satellites were selected in such a way that the distribution properties of uniformity and symmetry were preserved.…”

“…The idea behind 4D-LFC is to define a periodic constellation dynamic in such a way that its resultant configuration presents the highest number of symmetries, both in time and geometrically, in a similar way as the 2D and 3D Lattice Flower Constellations were defined. That way, and based on the Lattice Theory, the 4D-LFC are able to provide all the uniformly distributed constellations that can be arranged with a given set of satellites (Arnas, 2018).…”

Seeking Optimal GNSS Radio Occultation Constellations Using Evolutionary Algorithms

“…Satellite constellation design is an essential sector of designing spacecraft missions such as global navigation, communication, remote sensing, and Earth and space observation. These satellite missions may consist of multiple spacecrafts which operate simultaneously in order to meet the optimal performance of the system and reduce the mission costs [1].…”