Multi-objective Reinforcement Learning for Low-thrust Transfer Design Between Libration Point Orbits
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Anderson, Rodney L↗
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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↗
Libration Orbit Selection Methods and Formulations to Meet Mission Requirements
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Ariadna Farres↗
Computing libration point isolated invariant sets using isolating blocks
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Rodney L. Anderson↗
Orbits of the Tethys Lagrangian bodies
Preliminary libration parameters are derived for the objects found in 1980 at the triangular libration points of Tethys. The parameters are obtained from an orbit analysis of ground-based and Voyager I data obtained in 1980 for the separation from Saturn along the ring major axis, the projected separations from the Tethys L4 and L5 points and the separations from Tethys in orbital longitude. The best fitting libration parameters indicate a small (approximately 2 deg) libration amplitude for the L4 body. Data for the object at the L5 point may be fit either by orbits with libration amplitudes greater than 50 deg, or with small libration amplitudes, which are in agreement with recent Voyager II observations.
Reitsema, H. J.↗
Conformational Dynamics of Bacteriochlorophyll c in Chlorosomes from the bchQ Mutant of Chlorobaculum tepidum
In contrast to the common viewpoint that bacteriochlorophyll (BChl) motion is largely absent within the chlorosome assembly, physics-based modeling points to a crucial role of the nanoscale librational motion of the macrocycle for the transfer of excitons. To elucidate this motion experimentally, compositional uniformity and high sensitivity are required. We focused on uniformly 13 C labeled chlorosome preparations from the bchQ mutant Chlorobaculum tepidum with significantly enhanced structural homogeneity. The librational motion is characterized using Rotational Echo DOuble Resonance (REDOR), and in addition, the impact of temperature on specific functionalities within BChl molecules is studied with 1-dimensional and 2-dimensional dipolar and scalar-based MAS NMR measurements. Results show the gradual freezing of the tails and side chains of the BChls with decreasing temperature. However, the librational motion analyzed by measuring the 5C–H dipolar coupling strength obtained from REDOR data sets persists at different temperatures. REDOR simulations show a close match to the experimental dephasing frequency of oscillation for a dipolar coupling strength of 17.5 ± 0.5 kHz which is considerably less than the dipolar coupling strength of 22.7 kHz in the rigid limit. Following a two-site jump model, we arrive at an estimate for BChl libration sampling at an angle of θ = 48 ± 4°, corroborating that the macrocycle indeed experiences significant librational motion on a time scale that is short compared to the NMR measurement time. This finding is in full quantitative support of the dominant rotational motion exhibited by the BChl macrocycle estimated from early MD simulations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
What do far-infrared spectra of solitary water in “water-in-solvent” systems reveal about water’s solvation and dynamics?
Classical molecular dynamics simulations of water in ionic and dipolar solvents were used to interpret the far-infrared (FIR) rotation/libration spectra of “solitary water” in terms of water’s rotational dynamics and interactions with solvents. Seven solvents represented by nonpolarizable all-atom force fields and a series of idealized variable-charge solvents were used to span the range of solvent polarities (hydrogen bonding) studied experimentally. Simulated spectra capture the solvent dependence observed, as well as the relationship between the frequencies of water libration (νL) and OH stretching bands (νOH). In more strongly interacting solvents, simulated νL are ∼20% higher than those of experiment. In all solvents, the simulated spectra are composites of rotational motions about the two axes perpendicular to water’s dipole moment, and the different frequencies of these two motions are responsible for the breadth of the libration band and the bimodal shape observed in halide ionic liquids. Simulations overestimate the separation of these two components in most solvents. The character of water rotational motions changes markedly with solvent polarity, from quasi-free rotation in nonpolar and weakly polar solvents to highly constrained libration in strongly hydrogen bonding environments. The changeover to librational motions dominating the spectrum occurs between solvents such as benzene (νL ∼ 250 cm−1) and acetonitrile (νL ∼ 400 cm−1). For solvents in the latter category, the mean frequency of the experimental FIR band provides a direct measure of mean-squared torques and, therefore, force constants associated with interactions constraining water’s librational motion.
Chemistry↗
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↗
Ferromagnetic gyroscopes for tests of fundamental physics
Abstract A ferromagnetic gyroscope (FG) is a ferromagnet whose angular momentum is dominated by electron spin polarization and that will process under the action of an external torque, such as that due to a magnetic field. Here we model and analyze FG dynamics and sensitivity, focusing on practical schemes for experimental realization. In the case of a freely floating FG, we model the transition from dynamics dominated by libration in relatively high externally applied magnetic fields, to those dominated by precession at relatively low applied fields. Measurement of the libration frequency enables in situ determination of the magnetic field and a technique to reduce the field below the threshold for which precession dominates the FG dynamics. We note that evidence of gyroscopic behavior is present even at magnetic fields much larger than the threshold field below which precession dominates. We also model the dynamics of an FG levitated above a type-I superconductor via the Meissner effect, and find that for FGs with dimensions larger than about 100 nm the observed precession frequency is reduced compared to that of a freely floating FG. This is due to an effect akin to negative feedback that arises from the distortion of the field from the FG by the superconductor. Finally we assess the sensitivity of an FG levitated above a type-I superconductor to exotic spin-dependent interactions under practical experimental conditions, demonstrating the potential of FGs for tests of fundamental physics.
Physics↗
Linking NH$^+_4$ motion to magnetism in molecular multiferroic (NH 4 ) 2 [FeCl 5 (H 2 O)]: A neutron vibrational spectroscopy study
Here, we present a neutron vibrational spectroscopy study to investigate the influence of NH$^+_4$ motion on the magnetism in [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)]. The parent compounds, (NH 4 ) 2 [FeCl 5 (H 2 O)] (x = 0) and K 2 [FeCl 5 (H 2 O)](x = 1) are isostructural at room temperature, yet displaying drastically different magnetic and multiferroic behavior. K 2 [FeCl 5 (H 2 O)] is nonmultiferroic with type-A collinear antiferromagnetic structure below T N ≈ 14.06 K, whereas (NH 4 ) 2 [FeCl 5 (H 2 O)] is a type-II multiferroic with incommensurate cycloidal spin structure below T FE ≈ 6.8 K. A recent study of the dielectric, structure, and magnetic properties in the mixed [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)] shows that a small amount of potassium substitution to replace NH$^+_4$ transforms the spin structure from incommensurate cycloidal (x ≤ 0.06) into commensurate collinear antiferromagnetic (x ≥ 0.15), indicating NH$^+_4$ is essential to the emergent phenomena observed in this molecular multiferroic compound. Our vibrational spectroscopy study reveals that NH$^+_4$ libration and torsion motion exhibit substantial temperature dependence at low temperatures. The intensity of NH$^+_4$ libration and torsion modes increases slightly at 5 K in comparison with data at 25 K behaving like a magnon, indicating that they are coupled to the magnetism in (NH 4 ) 2 [FeCl 5 (H 2 O)]. Comparing data of x=0, 0.06, 0.09, and 0.15 samples further illustrates that the strength of the increased signal in NH$^+_4$ libration mode is very sensitive to potassium concentration. The signal diminishes quickly with increasing potassium concentration and vanishes in the x = 0.15 sample corresponding to the magnetic structure change for x ≥ 0.15. The results directly link the anomalous behavior in NH$^+_4$ libration motion to the magnetism in [(NH 4 ) 1–x K x ] 2 [FeCl 5 (H 2 O)], providing new insights into the crucial role NH$^+_4$ plays in the coupled phenomena in (NH 4 ) 2 [FeCl 5 (H 2 O)]. The unique information opens a new door to go through in searching for new multifunctional materials by incorporation of NH 4 via a material-by-design approach.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Dynamical consequences of meteorite impacts on the moon
The magnitudes of the excitation of free precession of the lunar spin axis about the position defined by Cassini's laws, free libration in longitude, and free wobble are determined as a function of meteorite angular momentum relative to the lunar center of mass and the position of impact on the lunar surface. Angular-momentum conservation suffices for the estimates of precession and libration excitation, but a cratering model for the ejecta distribution is necessary for the estimate of the wobble excitation. The simultaneous excitation of free wobble is always associated with the excitation of precession, and the angular amplitude is at least comparable to, but may exceed, that of the induced precession by a factor of 3 or 4. It is possible to excite a free libration in longitude with no first-order excitation of free wobble, but generally, all three free motions are excited simultaneously. The induced libration will nearly always have the largest amplitude. For crater sizes scaled as powers of impact energy, impacts leaving craters as small as a few kilometers in diameter can excite free motions which will ultimately be observable by the lunar laser-ranging experiment.
Peale, S. J.↗
Mission design for a halo orbiter of the earth
The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.
Farquhar, R. W.↗
Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2
The following topics related to the dynamics of the 4-mass tethered system are addressed: (1) the development of damping algorithms for damping the out-of-plane libration of the system and the interaction of the out-of-plane control with the other degrees of freedom; and (2) the development of environmental models to be added to the dynamics simulation computer code. The environmental models are specifically a new drag routine based on the Jacchia's 1977 model, a J(2) model and an accurate thermal model of the wire. Regarding topic (1) a survey of various out-of-plane libration control laws was carried out. Consequently a yo-yo control law with amplitude of the tether length variation proportional to the amplitude of the out-of-game libration has been selected. This control law provides good damping when applied to a (theoretical) two-dimensional system. In the actual 3-dimensional 4-mass tethered system, however, energy is transferred to the least damped degrees of freedom (the out-of-plane lateral deflections are still undamped in the present simulations) in such a way as to decrease the effectiveness of the algorithm for out-of-plane libration control. The addition of damping algorithms for the out-of-plane lateral deflections is therefore necessary.
Lorenzini, E. C.↗
User and technical documentation
The program LIBRATE calculates velocities for trajectories from low earth orbit (LEO) to four of the five libration points (L2, L3, L4, and L5), and from low lunar orbit (LLO) to libration points L1 and L2. The flight to be analyzed departs from a circular orbit of any altitude and inclination about the Earth or Moon and finishes in a circular orbit about the Earth at the desired libration point within a specified flight time. This program produces a matrix of the delta V's needed to complete the desired flight. The user specifies the departure orbit, and the maximum flight time. A matrix is then developed with 10 inclinations, ranging from 0 to 90 degrees, forming the columns, and 19 possible flight times, ranging from the flight time (input) to 36 hours less than the input value, in decrements of 2 hours, forming the rows. This matrix is presented in three different reports including the total delta V's, and both of the delta V components discussed. The input required from the user to define the flight is discussed. The contents of the three reports that are produced as outputs are also described. The instructions are also included which are needed to execute the program.
Source record↗
Human Exploration of Earth's Neighborhood and Mars
The presentation examines Mars landing scenarios, Earth to Moon transfers comparing direct vs. via libration points. Lunar transfer/orbit diagrams, comparison of opposition class and conjunction class missions, and artificial gravity for human exploration missions. Slides related to Mars landing scenarios include: mission scenario; direct entry landing locations; 2005 opportunity - Type 1; Earth-mars superior conjunction; Lander latitude accessibility; Low thrust - Earth return phase; SEP Earth return sequence; Missions - 200, 2007, 2009; and Mission map. Slides related to Earth to Moon transfers (direct vs. via libration points (L1, L2) include libration point missions, expeditionary vs. evolutionary, Earth-Moon L1 - gateway for lunar surface operations, and Lunar mission libration point vs. lunar orbit rendezvous (LOR). Slides related to lunar transfer/orbit diagrams include: trans-lunar trajectory from ISS parking orbit, trans-Earth trajectories, parking orbit considerations, and landing latitude restrictions. Slides related to comparison of opposition class (short-stay) and conjunction class (long-stay) missions for human exploration of Mars include: Mars mission planning, Earth-Mars orbital characteristics, delta-V variations, and Mars mission duration comparison. Slides related to artificial gravity for human exploration missions include: current configuration, NEP thruster location trades, minor axis rotation, and example load paths.
Condon, Gerald↗
Time and Energy, Exploring Trajectory Options Between Nodes in Earth-Moon Space
The Global Exploration Roadmap (GER) was released by the International Space Exploration Coordination Group (ISECG) in September of 2011. It describes mission scenarios that begin with the International Space Station and utilize it to demonstrate necessary technologies and capabilities prior to deployment of systems into Earth-Moon space. Deployment of these systems is an intermediate step in preparation for more complex deep space missions to near-Earth asteroids and eventually Mars. In one of the scenarios described in the GER, "Asteroid Next", there are activities that occur in Earth-Moon space at one of the Earth-Moon Lagrange (libration) points. In this regard, the authors examine the possible role of an intermediate staging point in an effort to illuminate potential trajectory options for conducting missions in Earth-Moon space of increasing duration, ultimately leading to deep space missions. This paper will describe several options for transits between Low Earth Orbit (LEO) and the libration points, transits between libration points, and transits between the libration points and interplanetary trajectories. The solution space provided will be constrained by selected orbital mechanics design techniques and physical characteristics of hardware to be used in both crewed missions and uncrewed missions. The relationships between time and energy required to transfer hardware between these locations will provide a better understanding of the potential trade-offs mission planners could consider in the development of capabilities, individual missions, and mission series in the context of the ISECG GER.
Martinez, Roland↗
Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS
In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.
Folta, D. C.↗