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Mitigating the Impact of Momentum Unloads on Station Keeping Around Libration Point Orbits

The Space Weather Follow On (SWFO) observatory will observe the Sun from L1, collecting solar wind data and coronal imagery, while providing early warning for space weather events. SWFO is a ride-share mission on SpaceX Falcon9 that is carrying IMAP. The spacecraft will be operated by NOAA and is expected to launch in February 2025. In order to meet NOAA’s operational requirements SWFO must maintain a Sun-Earth-Vehicle (SEV) angle between 4 and 13 degrees for at least 5 years. This constraint drives the size of the Lissajous orbit. SWFO is required keep a Sun pointing attitude in order to perform the Sun observations. Frequent Momentum Unloads are required to desaturate its reaction wheals. Station-keeping maneuvers are required to stay in orbit around L1, they are planned to be performed every 30 days.

Libration Point Orbits

Formation Flying With Decentralized Control in Libration Point Orbits

A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.

Folta, David

Understanding the Sun-Earth Libration Point Orbit Formation Flying Challenges For WFIRST and Starshade

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

Sun-Earth-Moon

Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits

The purpose and direction of this document is to provide U.S. government agencies, specifically National Aeronautics and Space Administration (NASA) and Department of Defense (DoD) space related centers, with a foundational summary of astrodynamics concepts for trajectory design, navigation, and operations in the cislunar, lunar, and libration point regions. This document is provided in response to an Interagency Agreement (IAA) between NASA and the National Geospatial-Intelligence Agency (NGA). With applications to these regions of the Earth-Moon system, this document summarizes: the definitions of standard and unique coordinate systems for Positioning, Navigation, Timing and targeting (PNT), transformations between those coordinate frames, definitions of common time systems, a description of numerical integration, description of a widely-used and approximate dynamical model of a three-body system for preliminary analysis and nomenclature definition, description of higher-fidelity models of cislunar space, and the application of these concepts to sample scenarios with a focus on common steps in trajectory and maneuver design for a spacecraft in cislunar space. This information is critical to mission design and navigation far above the geosynchronous orbit region, where lunar perturbations are required to be modeled accurately and consistently but render trajectory design and analysis a complex procedure. Software tools such as the Goddard Space Flight Center (GSFC) open source General Mission Analysis Tool (GMAT) is used as a reference, along with a wide variety of resources constructed by NASA and other government agencies, academia, and industry, for mathematical specifications and practical considerations. This document has been prepared by and under the auspices of NASA. The GSFC Mission Engineering and Systems Analysis (MESA) Division (Code 590) and the Navigation and Mission Design Branch (Code 595) are part of NASA. Their engineers and scientists have expertise in lunar, cislunar, and libration point region trajectory guidance and navigation and timing. NASA GSFC has supported many successful lunar and cislunar missions over the past several decades. These missions include the Lunar Reconnaissance Orbiter (LRO), the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft, Transiting Exoplanet Survey Satellite (TESS), Lunar Prospector, Lunar Crater Observation and Sensing Satellite (LCROSS), Clementine, and several Sun-Earth libration point missions such as WIND and Deep Space Climate Observatory (DSCOVR), dating back four decades. NASA GSFC also supports the upcoming Gateway lunar mission, the Artemis Lunar Program and Human Landing Systems, and leads both the Lunar IceCube low thrust mission and concept design for the Lunar Communication Relay and Navigation System (LCRNS).

Lunar, CisLunar, Libration, trajectory dynamics, p

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell

Control of libration point orbits using lunar gravity-assisted transfer

The Interplanetary Physics Laboratory, WIND, will be placed in a small-amplitude halo orbit in late 1995. A lunar swingby is used to achieve the halo orbit. Using the lunar swingby reduces the fuel required to achieve the desired orbit. The spacecraft's position and velocity with respect to the Moon near the time of swingby are shown to determine the characteristics of the halo orbit. The shape of the halo orbit, its x-, y-, and z-amplitudes, must be designed to meet mission constraints. A convenient set of parameters for displaying the dependence of the halo orbit's shape upon the lunar swingby is formulated. The use of the lunar swingby adds additional constraints to the trajectory in terms of attainable swingby parameters. Strategies for obtaining the desired swingby parameters in view of these mission constraints are discussed. The limits on attainable halo orbit shapes using the lunar swingby technique are discussed in terms of minimum and maximum x-, y-, and z-amplitudes. The relevance of previous work on this topic is discussed.

Sharer, P.

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a traditional optimization formulation.

algorithm

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Christopher J. Sullivan

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification

Christopher John Sullivan

Multi-objective Reinforcement Learning for Low-thrust Transfer Design Between Libration Point Orbits

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective rein- forcement learning algorithm used to construct low-thrust transfers between pe- riodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Anderson, Rodney L.

Multi-objective Reinforcement Learning for Low-thrust Transfer Design Between Libration Point Orbits

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective rein- forcement learning algorithm used to construct low-thrust transfers between pe- riodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Anderson, Rodney L

ARTEMIS: The First Mission to the Lunar Libration Orbits

The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.

Woodward, Mark

Cislunar Near Rectilinear Halo Orbit for Human Space Exploration

In order to conduct sustained human exploration beyond Low Earth Orbit (LEO), spacecraft systems are designed to operate in a series of missions of increasing complexity. Regardless of the destination, Moon, Mars, asteroids or beyond, there is a substantial set of common objectives that must be met. Many orbit characterization studies have endeavored to evaluate the potential locations in cislunar space that are favorable for meeting common human exploration objectives in a stepwise approach. Multiple studies, by both NASA and other international space agencies, have indicated that Earth-­‐moon libration point orbits are attractive candidates for staging operations in the proving ground and beyond. In particular, the Near Rectilinear Orbit (NRO) has been demonstrated to meet multi-­‐mission and multi-­‐destination architectural constraints. However, a human mission to a selected NRO presents a variety of new challenges for mission planning. While a growing number of robotic missions have completed successful operations to various specific libration point orbits, human missions have never been conducted to orbits of this class. Human missions have unique challenges that differ significantly from robotic missions, including a lower tolerance for mission risk and additional operational constraints that are associated only with human spacecraft. In addition, neither robotic nor human missions have been operated in the NRO regime specifically, and NROs exhibit dynamical characteristics that can differ significantly as compared to other halo orbits. Finally, multi-­‐body orbits, such as libration point orbits, are identified to exist in a simplified orbit model known as the Circular Restricted Three Body Problem (CRTBP) and must then be re-­‐solved in the full ephemeris model. As a result, the behavior of multi-­‐body orbits cannot be effectively characterized within the classical two-­‐body orbit dynamics framework more familiar to the human spaceflight community. In fact, a given NRO is not identified by a set of Keplerian orbit parameters, and a valid epoch specific state vector must be first obtained from a multi-body dynamical model. In this paper, the significant performance and operational challenges of conducting human missions to the NRO are evaluated. First, a systematic process for generating full ephemeris based ballistic NROs of various families is outlined to demonstrate the relative ease in which a multi-­‐revolution orbit can be found for any epoch and for various orbit geometries. In the Earth-­‐Moon system, NROs, which are halo orbits with close passage over a lunar pole, can exist with respect to libration point 1 (L1) or libration point 2 (L2) and are either from a North or South family orbit class with respect to the ecliptic. Second, the ability to maintain the orbit over the lifetime of a habitat mission by applying a reliable station-keeping strategy is investigated. The NRO, while similar to the quasi-­‐halo orbits that the Artemis mission flew, requires an updated station keeping strategy. This is due to several dynamical differences such as the increased relative stability of the NRO compared to other halo orbits and the close passage over the lunar surface as shown in Figure 1. Multiple station-keeping strategies are being investigated to ensure a human spacecraft remains on a predictable path. As the NRO is not described in simple two-­‐body parameters, analysis must determine the best strategy for targeting a reference NRO as well as how closely a future state should be constrained. In addition, costs will be minimized by determining maneuver directionality based on an identified pattern in the optimal station-keeping solutions or an analytically derived relationship. The candidate station-keeping algorithm must be stable and robust to environmental and vehicle uncertainties as well to navigation estimation and flight control execution errors. To that end, navigation accuracies, the impact on the station-keeping execution errors as well as other vehicle uncertainties need to be assessed. Starting with Orion, current navigation accuracies are evaluated and then navigation requirements are derived assuming a desired station-keeping propellant budget. Third, the performance requirements to and from the NRO are evaluated. Important parameters for developing expected propellant costs include epoch of operation, size and type of NRO, Earth departure and return constraints, as well as abort or early-­‐return capability. Finally, rendezvous and proximity operations are vital aspects of multi-­‐mission human exploration endeavors. The ability to conduct rendezvous and the associated propellant costs are assessed as well as the impacts of various profile assumptions including the location within the NRO the rendezvous is performed. The results of these studies will influence plans for international cooperation on both nearer term proving ground missions and beyond.

Whitley, Ryan

Preliminary Design Considerations for Access and Operations in Earth-Moon L1/L2 Orbits

Within the context of manned spaceflight activities, Earth-Moon libration point orbits could support lunar surface operations and serve as staging areas for future missions to near-Earth asteroids and Mars. This investigation examines preliminary design considerations including Earth-Moon L1/L2 libration point orbit selection, transfers, and stationkeeping costs associated with maintaining a spacecraft in the vicinity of L1 or L2 for a specified duration. Existing tools in multi-body trajectory design, dynamical systems theory, and orbit maintenance are leveraged in this analysis to explore end-to-end concepts for manned missions to Earth-Moon libration points.

Folta, David C.

High Fidelity Modeling of SRP and Its Effect on the Relative Motion of Starshade and WFIRST

In this paper we perform a detailed analysis of how Solar Radiation Pressure (SRP) affects the relative motion of two spacecrafts, the Wide-Field Infrared Survey Telescope (WFIRST) and Starshade, orbiting in the vicinity of the Sun-Earth L2. While WFIRST orbits about its own Libration Point Orbit (LPO), Starshade will fly a specific trajectory to align with WFIRST and observe a Design Reference Mission of pre-determined target stars. In this analysis, we focus on the transfer orbit for Starshade from one observation to the other. We will describe how SRP affects the dynamics of the Starshade relative to WFIRSTand how relevant this effect is in order to get an accurate estimate of the total difference in velocity (delta v).

WFIRST

Orbital acrobatics in the Sun-Earth-Moon system

Unconventional trajectory techniques for space missions in the Sun-Earth-Moon system, including libration-point orbits, gravity-assist maneuvers, and Earth-return trajectories are reviewed. The ISEE-3/ICE flight experience is used to illustrate the utility of libration-point orbits called halo-orbits. Five lunar gravity-assist maneuvers used by the ISEE-3/ICE spacecraft are discussed. The final lunar swingby sent the spacecraft into a heliocentric trajectory that will eventually intercept Comet Giacobini-Zinner. As an example of the Earth-return trajectory concept, a proposed mission that includes flybys of three comets and two asteroids is described.

Farquhar, Robert W.

Stationkeeping of the First Earth-Moon Libration Orbiters: The ARTEMIS Mission

Libration point orbits near collinear locations are inherently unstable and must be controlled. For Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) Earth-Moon Lissajous orbit operations, stationkeeping is challenging because of short time scales, large orbital eccentricity of the secondary, and solar gravitational and radiation pressure perturbations. ARTEMIS is the first NASA mission continuously controlled at both Earth-Moon L1 and L2 locations and uses a balance of optimization, spacecraft implementation and constraints, and multi-body dynamics. Stationkeeping results are compared to pre-mission research including mode directions.

Folta, David