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A Framework for Efficient Trajectory Comparisons in the Earth-Moon Design Space

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A Framework for Efficient Trajectory Comparisons in the Earth-Moon Design Space A Framework for Efficient Trajectory Comparisons in the Earth-Moon Design Space Davide Guzzetti,∗ Natasha Bosanac,∗ Kathleen C. Howelly Purdue University, Armstrong Hall of Engineering, 701 W. Stadium Ave., West Lafayette, IN 47907-2045 and David C. Folta z NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USA. The development of a blueprint for a long-term human presence in the Earth-Moon space, crewed and robotic, currently retains significant interest in orbital destinations that include the vicinity of the libration points, as well as other trajectories that exist within a multi-body dynamical environment. The concept of an interactive and \dynamic" catalog of potential solutions in the Earth-Moon system is explored and analyzed as an efficient framework to guide trajectory design. The catalog concept is practically implemented in the form of a graphical user interface. Examples demonstrating applications to preliminary mission design offer rapid and effective strategies for orbit comparison and selection within a multi-body regime. I. Introduction Despite some visionary missions that have extended robotic space exploration beyond the borders of the solar system, actual and stable human space settlements are currently and consistently active only in Low- Earth Orbits (LEO). For the development of a blueprint for a more permanent and long-term human presence in the Earth-Moon space, crewed and robotic, a more comprehensive and easily accessible \roadmap" of des- tinations and pathways throughout Earth-Moon neighborhood is a critical component. The regions near the libration points, as well as other trajectories that exist within a multi-body dynamical environment, retain significant interest. In fact, these types of dynamical structures prove to be a versatile framework for mission design. In recent years, many NASA-released studies have considered such alternative trajectory platforms for long-duration infrastructures to support science in the Earth-Moon region, to serve as gateways to other interplanetary destinations, to support lunar orbit and surface operations and to assist deep space telescopes.1,2,3 Most recently, both the 2013 Global Exploration Roadmap4 and the 2014 National Research Council report on human space exploration5 include additional mission concepts, e.g., travel to Mars and rendezvous with asteroids, that also leverage the dynamics associated with the equilibrium points of the Earth-Moon system. Altogether, this scenario suggests that broader knowledge of the dynamical accessibil- ity within the Earth-Moon system is warranted. Over the last few years, the success of many Sun-Earth libration point missions has positively contributed to the large rise in interest of the three-body problem. The Acceleration, Reconnection, Turbulence and Elec- trodynamics of the Moons Interaction with the Sun (ARTEMIS) mission also demonstrated that three-body analyses are viable options for trajectory design in the Earth-Moon neighborhood.6 Along with these ac- complishments, the mathematical foundations in the three-body problem are now better understood and more often exploited, frequently due to the dynamical systems approaches. Consequently, a large number of solutions and techniques have been developed and consolidated by the astrodynamics community that might be employed for orbit design and operation. Many software packages, for example, Satellite Tool Kit ∗Ph.D. Student, School of Aeronautics and Astronautics, Purdue University, Armstrong Hall of Engineering, 701 W. Stadium Ave., West Lafayette, IN 47907-2045. yHsu Lo Distinguished Professor, School of Aeronautics and Astronautics, Purdue University, Armstrong Hall of Engineering, 701 W. Stadium Ave., West Lafayette, IN 47907-2045. Fellow AAS; Fellow AIAA. zSenior Fellow, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USA. 1 of 26 American Institute of Aeronautics and Astronautics (STK) and NASA's General Mission Analysis Tool (GMAT), offer a graphical environment for trajectory design incorporating gravitational fields at various levels of fidelity.7,8 However, the focus of these packages is generally directed towards the delivery of trajectory designs and other actual mission support capabilities. Thus, they offer limited guidance and insight into the available dynamical structures throughout the region; a comprehensive design procedure to easily incorporate and leverage the three-body dynamical structures has not yet been completely established. The current effort is devoted to creating direct links between the problem understanding and its practical application by exploring the Earth-Moon design space. There exists a wide array of known orbits with significant potential for parking, staging and transfers within the Earth- Moon system. Software such as AUTO can supply a selection of these solutions as well as some insight into the local dynamics and the evolution of a set of orbits along any family.9 Nonetheless, mission designers currently lack a basic \blueprint" to support rapid, efficient and well-informed decisions regarding the use of these known periodic orbits for any mission prior to an end-to-end trajectory design. Typically, the most basic trade-offs in path planning are not intuitive and, yet, not easily accessible. The concept of a \dynamic" framework, as opposed to a static database, is explored to guide the pre- liminary selection of trajectories in a highly sensitive and rapidly evolving design space. A static database can not effectively encompass all the solutions available in the dynamical environment. First, the dynam- ical structure in the Earth-Moon system, which is represented in terms of the Circular Restricted Three Body Problem (CR3BP), is comprised of a pool of infinitely many solutions, currently without an analytical closed-form description. Second, it is unlikely that a trajectory or group of trajectories could be uniquely represented by a set of parameters that also retain intuitive physical meaning, as in the Keplerian regime. Third, the on-going investigation of the problem from the scientific community allows for the possibility of discovering new periodic orbits or updating the understanding of existing solutions. The capability to compute `on-demand' solutions and manipulate data through graphical interfaces is available with modern computational tools; accordingly, the concept of a \dynamic" catalog is introduced. Specifically, a \dy- namic" catalog is based upon an interactive environment and characterizes the design space also in terms of the trade-offs between various parameters of significance for mission design, rather than relying only on a static classification of solutions. In this way, the \dynamic" catalog may overcome some of the challenges associated with constructing a trade space to analyze the various characteristics of a large set of solutions and their neighboring dynamical behavior. The construction of a design framework to deliver the desired functional capabilities originates from the identification of parameters that may aid in trajectory design and selection. Quantities of interest may include size, period, energy, and stability. Representative operational costs, such as station-keeping maneu- ver ∆Vs, orbit insertion maneuver magnitude and flight time for transfers from LEO may also be useful. Then, known periodic and quasi-periodic orbits that are solutions in a circular restricted three-body model of the Earth-Moon system, and closely approximate the true dynamical structure, should be incorporated into the catalog. Such selections currently include two-dimensional and three-dimensional orbit families of libration point orbits, direct retrograde orbits about the Moon (DROs), direct prograde orbits about the Moon (DPOs), as well as resonant orbits. The catalog adopts a preliminary classification of orbits into groups, or families, that are well-established in the literature; however, such taxonomy is not definitive, as it must evolve to accommodate new solutions and/or better understanding of links between existing members. The families included in the catalog can also be statistically described in terms of the representative param- eters; the statistics are computed on a dataset of periodic orbits sampled along each family. The statistical description aims to create a concise tradeoff space. Moreover, compiling this information in an interactive environment, the orbits can be filtered and compared to identify candidate solutions that potentially satisfy a given set of mission requirements. Eventually, such a framework may offer faster and more efficient strate- gies for orbit design and operation, while also delivering innovative mission design parameters for further examination, for example, in GMAT or the Adaptive Trajectory Design (ATD) software created at Purdue University,10 or other end-to-end mission design tools. In this investigation, the CR3BP model is employed to approximate the dynamical structure of the Earth- Moon system. Based upon the understanding of the CR3BP, the essential concepts to construct a design framework in the Earth-Moon system are presented. As previously noted, the form proposed for the design framework is a \dynamic" catalog of reference solutions in the Earth-Moon system that is implemented as a graphical interactive interface. Accordingly, a catalog interface prototype is developed. To demonstrate that rapid and efficient trajectory comparisons are achievable through the catalog, the interactive interface prototype is applied to some representative scenarios within the context
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