Constellation optimization

In recent years, with the increasing number of missions to conduct human space exploration, the Moon is considered as an important milestone to evaluate new technologies, showing the need for navigation capabilities for low lunar orbiters, lunar landers, and human missions. In this scenario, the European Space Agency vision is represented by the Moonlight initiative, which aims to develop a European-led provision of communication and navigation services to support the next generations of institutional and private lunar exploration missions. In this context, the importance of developing a high-level definition of optimized constellation architectures is even more evident. Inspired by Moonlight, this research deals with the design of optimal constellations around the Moon, able to guarantee navigation and communication services for a local area on the lunar surface and to allow communication with the Earth. The problem consists in analysing the motion of a group of satellites around the Moon and to calculate the time intervals of visibility of each satellite with respect to the target points on the Moon and the Earth, respectively. This scenario considers a variable total number of satellites and a grid of target points on the lunar surface. The goal of the formulated algorithm is to minimize the global dilution of precision parameter (GDOP) related to the navigation performance, guaranteeing, at the same time, the visibility of at least four satellites from each single point (on the lunar surface). The implemented optimization method is based on a black-box approach, in combination with a global optimization algorithm. It is able to determine appropriate satellite configurations (corresponding to specific Keplerian orbital parameters) providing a minimum GDOP. All mathematical models and algorithms are implemented in the Matlab (MathWorks) environment and validated by the Ansys System Tool Kit (STK) software. A comparison with previous works from the specific literature, e.g., LCNS (Bhamidipati et al. 2023), has been carried out. Chapter 1 deals with an introduction about the Moonlight vision and the correspondent Lunar communication and navigation project proposed by ESA, while Chapter 2 proposes an overview of the existing Earth satellite navigation systems, their main features and parameters. The GDOP acts as a crucial factor for these kinds of applications to estimate the overall level of precision of the positioning system (GDOP, Langley 1999a, 1999b). Chapter 3 discusses the lunar constellation problem and the relevant physical/mathematical models. Chapter 4 summarize the most common optimization methods used in this context, pointing out their main features and advantages. Chapter 5 is dedicated to an extensive experimental analysis. The solutions obtained and validated with STK are reported in detail, showing the effectiveness of the approach adopted. Extensions and future developments will be described in Chapter 6. References Bhamidipati, S., Mina, T., Sanchez, A., & Gao, G. (2023). Satellite constellation design for a lunar navigation and communication system. NAVIGATION, 70(4). Langley R. B.: Dilution of Precision, GPS World, Vol. 10, No. 5, 1999, pp. 52-59. Langley R. B.: The Mathematics of GPS, GPS World, Vol. 10, No. 5, 1999, pp. 52-59.