US Egypt Cooperative Research: Reliable Global Navigation System Using Flower Constellations

Texas A&M Engineering Experiment Station, College Station TX

Investigators

Abstract

The goal of this project is to design optimal global navigation systems using a novel constellation design framework, called Flower Constellations that include the Walker Constellation as a special case. In particular, two distinct approaches will be considered, a) the Lattice approach using circular orbits and b) the Juggling approach to explore elliptical orbits. The optimal design implies minimizing the Geometric Dilution Of Precision, quantifying the accuracy provided using the minimum number of satellites and the minimum cost to deploy them. The design includes the Earth oblateness perturbation. All the other orbit perturbations will be compensated using nonlinear feedback optimal control technique to simultaneously a) perform orbit maintenance and b) maintain the satellite relative phasing close to the optimal configuration. The project impact is of utmost importance as the proposed Flower Constellation Navigation System will provide us with better navigation performance than the American GPS and the European GalileoSat global navigation systems. The PI will be cooperating with Dr. Ashraf Hamdi Mohamed Owis of the Department of Astronomy at Cairo University, Egypt. Intellectual Merit. Despite decades of research, constellation design remains more an art than a science. Investigating Lattice Flower Constellations and the juggling of elliptical orbits broadens the knowledge base of constellation design. Walker constellations dominate the field, yet Lattice Flower Constellations provide a framework that includes both Walker constellations and the traditional Flower Constellations. Elliptical orbits are generally considered infeasible, yet the "juggling" method seeks to overcome those deficiencies, significantly expanding the design space. Optimal control of constellation maintenance, correcting for orbit perturbations, makes these constellation designs fully realizable. Broader Impact. This research is interdisciplinary in nature. It is based heavily on Number Theory to efficiently design Flower Constellations, on Combinatory to develop strategies for constellation deployment, on Engineering (Control systems and Orbital dynamics) to perform orbit station keeping and perturbation control. The inclusion of Lattice Flower Constellations and the "juggling" method for elliptic orbit constellation design add important tools to the constellation designer's toolbox. When considering global coverage for global navigation, communications, or reconnaissance, the Lattice Flower Constellations and the "juggling" method provide additional capabilities beyond typical streets-of-coverage or Walker constellations. Using these design techniques, constellations with fewer satellites and lower launch costs can be designed without sacrificing the performance objectives, making more global coverage missions feasible. The impact of this research for Global Navigation System is extremely important for the global community. Building Flower Navigation Systems characterized by higher accuracy will have strong impact not only in the standard navigation systems, but also in many other (side) activities, involving positioning systems, triangulation, moving detection and tracking, and so on. In fact, despite the strong relevance to and uniqueness of the proposed capability to design optimal global navigation systems, one could envision other follow-on applications of LFC/JFC designs, including regional or worldwide persistence surveillance. It may be the examination over time of crop growth, deforestation, mountain snow/ice melt, and other geological concerns would benefit by LFC/JFC design. One US postdoctoral student and one US graduate student will participate in the collaborative project and will travel to Egypt for an international research experience. The project is funded under the US-Egypt Joint Fund Program, which provides grants to scientists and engineers in both countries to undertake cooperative research.