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Anderson, Rodney L.

Publications and source records attributed to Anderson, Rodney L..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Exploring the Low-Thrust Transfer Design Space in an Ephemeris Model via Multi-Objective Reinforcement Learning

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to train multiple policies to uncover solutions within a multi-objective solution space. MRPPO is used in this paper to train policies to construct low-thrust transfers for a SmallSat from the vicinity of ๐ฟ2 to an ๐ฟ5 short period orbit in the Sun-Earth-Moon system. First, the policies are trained in this scenario in the circular restricted three-body problem. This information is used to initialize the policies before training in a higher-fidelity ephemeris model; a process known as transfer learning. The recovered segments of the solution space will be compared to fundamental dynamical structures to both examine the results of MRPPO in this complex design scenario and explore the effectiveness of transfer learning.

Mashiku, Alinda K.โ†—
NASA NTRS2021

Exploration of Spatial Chaotic Orbits Using Isolating Neighborhoods

Isolating blocks and isolating neighborhoods have previously been used to compute periodic and quasiperiodic orbits around the collinear libration points in the circular restricted three-body problem. Isolating neighborhoods may be used to further explore the boundary between the Lissajous and quasihalo orbits at en- ergies where the halo orbits have bifurcated from the Lyapunov orbits. A method to compute trajectories that are forward and backward asymptotic to the libration point invariant set using very small velocity corrections is developed here. The method is then used to compute representative trajectories within this region and characterize their behavior.

Lo, Martin W.โ†—
NASA NTRS2021

Two-Spacecraft Orbiting in Opposition to Enable Bistatic Radar Observations Around an Asteroid

Fundamental answers about the origin and evolution of the Solar System hinge on our ability to image in detail the 3D interior structure of small bodies at highresolution. By collecting radar measurements we can ultimately create 3D maps of the interior structure. In this study we focus our attention on a specific mission scenario which consists of a carrier spacecraft and two daughter spacecraft sent to orbit the asteroid Apophis. The orbits of the spacecraft are optimized to maximize radar measurements by dynamically modeling the harmonics and solar radiation pressure. For long mission durations, orbital correction maneuvers maintain the spacecraft in formation.

Anderson, Rodney L.โ†—
NASA NTRS2021

Investigations of Relations Between Jupiter-Europa and Jupiter-Ganymede Resonant Tori in the Planar Bicircular Restricted 4-Body Problem

Most unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. Among the persisting orbits are unstable resonant periodic or- bits. In this study, we first compute invariant tori in the planar concentric cir- cular restricted 4-body problem corresponding to exterior Jupiter-Europa and in- terior Jupiter-Ganymede PCRTBP resonant periodic orbits. Motivated by the 2:1 Laplace resonance between the orbits of Europa and Ganymede around Jupiter, we then use the computed tori to characterize relations between m:n Jupiter-Ganymede and m:2n Jupiter-Europa PCRTBP resonant orbits.

de la Llave, Rafaelโ†—
NASA NTRS2021

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 โ€˜moving referenceโ€™, 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.โ†—
NASA NTRS2020

Rapid and Accurate Computation of Invariant Tori, Manifolds, and Connections Near Mean Motion Resonances in the Periodically Perturbed Planar Circular Restricted 3-Body Problem Models

When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, most unstable resonant periodic orbits become invariant tori. In this study, we 1) develop a quasi-Newton method which simultaneously solves for the tori and their center, stable, and unstable directions; 2) implement continuation by both perturbation as well as rotation numbers; 3) compute Fourier-Taylor parameterizations of the stable and unstable manifolds; 4) globalize these manifolds; 5) compute homoclinic and heteroclinic connections. Our methodology improves on efficiency and accuracy compared to prior studies, and applies to a variety of periodic perturbations. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafaelโ†—
NASA NTRS2020

Direct Exploration of the L2 Isolated Invariant Set Using Isolating Neighborhoods

Previous studies have used isolating blocks to explore the isolated invariant set around the L2 Lagrange point in the circular restricted three-body problem by computing trajectories on the asymptotic set and using them to track particular orbits. Once an initial map of the location of the orbits within the isolated invariant set projected into configuration space has been found, it is possible to further explore these orbits more directly by starting from appropriately chosen points within the mapped space. Here, we develop a method that uses these points to explore the periodic and quasiperiodic orbits within the isolated invariant set.

Lo, Martin W.โ†—
NASA NTRS2019

Trajectory design for small-satellite missions to near-earth objects

This paper describes new techniques for use in designing possible trajectories to near-Earth objects (NEOs) given the constraints imposed by the limited propulsive capabilities of small satellites and by being launched as a secondary with larger spacecraft. It illustrates the use of these techniques with the design of a trajectory that achieves rendezvous with the NEO 2007 UN12.

Sims, Jon A.โ†—
NASA NTRS2019

Connecting resonant trajectories to a Europa capture through Lissajous staging orbits

The current interest in studying the surface of Europa in search of biosignatures demands efficient strategies in mission design to reach this distant world. An affordable strategy is to use a low energy moon tour, which has natural access to the moon via the L2 gateway. Staging around this libration point allows to decouple the approaching moon tour and the landing trajectory, which enables the option of designing each phase separately. Furthermore, a staging step frees the landing time from the capture phase, adding an additional degree of freedom. Lissajous orbits are the dynamical structures used for these staging orbits. In this paper, the possible ballistic connections between the resonances from the moon tour and Lissajous orbits are studied, including the different geometries that allow for time phasing control.

Anderson, Rodney L.โ†—
NASA NTRS2018

Magnetour: Surfing Planetary Systems on Electromagnetic and Multi-Body Gravity Fields

In this NIAC Phase One study, we propose a new mission concept, named Magnetour, to facilitate the exploration of outer planet systems and address both power and propulsion challenges. Our approach would enable a single spacecraft to orbit and travel between multiple moons of an outer planet, with no propellant required. Our approach would enable a single spacecraft to orbit and travel between multiple moons of an outer planet, with no propellant nor onboard power source required. To achieve this free-lunch _Grand Tour', we exploit the unexplored combination of magnetic and multi-body gravitational fields of planetary systems, with a unique focus on using a bare tether for power and propulsion. The main objective of the study is to develop this conceptually novel mission architecture, explore its design space, and investigate its feasibility and applicability to enhance the exploration of planetary systems within a 10-year timeframe. Propellantless propulsion technology offers enormous potential to transform the way NASA conducts outer planet missions. We hope to demonstrate that our free-lunch tour concept can replace heavy, costly, traditional chemical-based missions and can open up a new variety of trajectories around outer planets. Leveraging the powerful magnetic and multi-body gravity fields of planetary systems to travel freely among planetary moons would allow for long-term missions and provide unique scientific capabilities and flagship-class science for a fraction of the mass and cost of traditional concepts. New mission design techniques are needed to fully exploit the potential of this new concept.This final report contains the results and findings of the Phase One study, and is organized as follows. First, an overview of the Magnetour mission concept is presented. Then, the research methodology adopted for this Phase One study is described, followed by a brief outline of the main findings and their correspondence with the original Phase One task plan. Next, an overview of the environment of outer planets is provided, including magnetosphere, radiation belt and planetary moons. Then performance of electrodynamic tethers is assessed, as well as other electromagnetic systems. A method to exploit multi-body dynamics is given next. These analyses allow us to carry out a Jovian mission design to gain insight in the benefits of Magnetour. In addition, a spacecraft configuration is presented that fully incorporates the tether in the design. Finally technology roadmap considerations are discussed.

Gravity Fieldsโ†—
NASA NTRS2016

Periodic Orbit-Attitude Solutions in the Planar Elliptic Restricted Three-Body Problem

The pitch motion of a spacecraft in the planar elliptic restricted three-body system is studied. Previous studies laid the foundation for spacecraft stability analysis with a small perturbation to the zero pitch motion. In this study, a cell mapping approach that combines analytical and numerical techniques is used to study the global behavior of the full nonlinear spacecraft attitude in which coupling between orbital dynamics and attitude occurs. The effect of gravity gradient torques, orbital eccentricity, and the spacecraft configuration at different Lagrangian points is analyzed. Multiple-period periodic solutions and invariant surfaces are presented for different cases. Reference trajectories around the Lagrangian points are also considered to study coupled dynamics.

Koh, Dayungโ†—
NASA NTRS2016

MAGNETOUR: Surfing Planetary Systems on Electromagnetic and Multi-Body Gravity Fields

A comprehensive visit of the complex outer planet systems is a central goal in space science. However, orbiting multiple moons of the same planet would be extremely prohibitive using traditional propulsion and power technologies. In this paper, a new mission concept, named Magnetour, is presented to facilitate the exploration of outer planet systems and address both power and propulsion challenges. This approach would enable a single spacecraft to orbit and travel between multiple moons of an outer planet, without significant propellant or onboard power source. To achieve this free-lunch โ€˜Grand Tourโ€™, Magnetour exploits the unexplored combination of magnetic and multi-body gravitational fields of planetary systems, with a unique focus on using a bare electrodynamic tether for power and propulsion. Preliminary results indicate that the Magnetour concept is sound and is potentially highly promising at Jupiter.

Lantoine, Gregoryโ†—
NASA NTRS2014

Analysis of Petal Rotation Trajectory Characteristics

In this study, the characteristics of petal rotation trajectories are explored in both the two-body and circular restricted three-body problem (CRTBP) models. Petal rotation trajectories alternate long and short resonances of different kinds to rotate the line of apsides. They are typically computed using the patched conic model, and they are used in a number of different missions and mission concepts including Cassini, JUICE, and Europa mission concepts. Petal rotation trajectories are first analyzed here using the patched conic model to quantify their characteristics and search for cases with fast rotation of the line of apsides. When they are computed in the CRTBP, they are unstable periodic orbits with corresponding stable and unstable manifolds. The characteristics of these orbits are explored from a dynamical systems perspective in the second phase of the study.

Resonanceโ†—
NASA NTRS2013

Trajectory Design for MoonRise: A Proposed Lunar South Pole-Aitken Basin Sample Return Mission

This paper presents the mission design for the proposed MoonRise New Frontiers mission: a lunar far side lander and return vehicle, with an accompanying communication satellite. Both vehicles are launched together, but fly separate low-energy transfers to the Moon. The communication satellite enters lunar orbit immediately upon arrival at the Moon, whereas the lander enters a staging orbit about the lunar Lagrange points. The lander descends and touches down on the surface 17 days after the communication satellite enters orbit. The lander remains on the surface for nearly two weeks before lifting off and returning to Earth via a low-energy return.

NASA's New Frontieโ†—