Engineering topics

Englander, Jacob A.

Publications and source records attributed to Englander, Jacob A..

At least 19 records

NASA NTRS2019

Trajectory Design of the Lucy Mission to Explore the Diversity of the Jupiter Trojans

Lucy, NASA’s next Discovery-class mission, will explore the diversity of the Jupiter Trojan asteroids. The Jupiter Trojans are thought to be remnants of the early solar system that were scattered inward when the gas giants migrated to their current positions as described in the Nice model. There are two stable subpopulations, or “swarms,” captured at the Sun-Jupiter L4 and L5 regions. These objects are the most accessible samples of what the outer solar system may have originally looked like. Lucy will launch in 2021 and will visit five Trojans, including one binary system. This paper discusses the target selection process, including a description of “alternate Lucys” that were ultimately passed over in favor of the final design. The mathematics of the trajectory optimization are also discussed.

Lucy↗

NASA NTRS2019

High-Fidelity Multiple-Flyby Trajectory Optimization Using Multiple-Shooting

Rendering a complex spacecraft trajectory in high fidelity can be an expensive endeavor, both computationally and from a human time/cost standpoint. However, in many cases, a low-fidelity trajectory that reasonably approximates a high-fidelity counterpart is much easier to obtain. Thus, it is important to have an efficient process for converting a trajectory from lower-fidelity model to high fidelity. We present a method for converting low-fidelity trajectories into high fidelity that relies on multiple shooting, nonlinear programming, and numerical integration. The procedure converts any zero-radius sphere-of-influence gravity-assist events to fully integrated flyby events. Several numerical examples are presented that showcase the flexibility of the high-fidelity rendering process across multiple mission types and flight regimes.

high-fidelity↗

NASA NTRS2019

Interplanetary Low-Thrust Design Using Proximal Policy Optimization

This paper aims to demonstrate a reinforcement learning technique for developing complex, decision-making policies capable of planning interplanetary transfers.Using Proximal Policy Optimization (PPO), a neural network agent is trained to produce a closed-loop controller capable of transfers between Earth and Mars.The agent is trained in an environment that utilizes a medium fidelity solar electric propulsion model and a real ephemeris model of the Earth and Mars. The results are compared against those generated by the Evolutionary Mission Trajectory Generator (EMTG) tool.

proximal policy optimization↗

NASA NTRS2019

Refining Lucy Mission Delta-V During Spacecraft Design Using Trajectory Optimization Within High-Fidelity Monte Carlo Maneuver Analysis

Recent advances linking medium-fidelity trajectory optimization and high-fidelity trajectory propagation/maneuver design software with Monte Carlo maneuver analysis and parallel processing enabled realistic statistical delta-V estimation well before launch. Completing this high-confidence, refined statistical maneuver analysis early enabled release of excess delta-V margin for increased dry mass margin for the Lucy Jupiter Trojan flyby mission. By 3.3 years before launch, 16 of 34 TCMs had 1000 re-optimized trajectory design samples, yielding tens of m/s lower 99%-probability delta-V versus targeting maneuvers to one optimal trajectory. One year later, 1000 re-optimized samples of all deterministic maneuvers and subsequent flybys further lowered estimated delta-V.

Trojan↗

NASA NTRS2019

Optimization of the Lucy Interplanetary Trajectory via Two-Point Direct Shooting

Lucy is NASA’s next Discovery-class mission and will explore the Trojan asteroids in the Sun-Jupiter L4 and L5 regions. This paper details the design of Lucy’s interplanetary trajectory using a two-point direct shooting transcription, nonlinear programming, and monotonic basin hopping. These techniques are implemented in the Evolutionary Mission Trajectory Generator (EMTG), a trajectory optimization tool developed at NASA Goddard Space Flight Center. We present applications to the baseline trajectory design, Monte Carlo analysis, and operations.

Lucy↗

NASA NTRS2017

Mission Design and Optimal Asteroid Deflection for Planetary Defense

Planetary defense is a topic of increasing interest for many reasons, which has been mentioned in "Vision and Voyages for Planetary Science in the Decade 2013-2022''. However, perhaps one of the most significant rationales for asteroid studies is the number of close approaches that have been documented recently. A space mission with a planetary defense objective aims to deflect the threatening body as far as possible from Earth. The design of a mission that optimally deflects an asteroid has different challenges: speed, precision, and system trade-off. This work addresses such issues and develops a fast transcription of the problem that can be implemented into an optimization tool, which allows for a broader trade study of different mission concepts with a medium fidelity. Such work is suitable for a mission?s preliminary study. It is shown, using the fictitious asteroid impact scenario 2017 PDC, that the complete tool is able to account for the orbit sensitivity to small perturbations and quickly optimize a deflection trajectory. The speed in which the tool operates allows for a trade study between the available hardware. As a result, key deflection dates and mission strategies are identified for the 2017 PDC.

Planetary defense↗

NASA NTRS2017

Mission Design and Optimal Asteroid Deflection for Planetary Defense

Planetary defense is a topic of increasing interest for many reasons, which has been mentioned in "Vision and Voyages for Planetary Science in the Decade 2013-2022". However, perhaps one of the most significant rationales for asteroid studies is the number of close approaches that have been documented recently. A space mission with a planetary defense objective aims to deflect the threatening body as far as possible from Earth. The design of a mission that optimally deflects an asteroid has different challenges: speed, precision, and system trade-off. This work addresses such issues and develops a fast transcription of the problem that can be implemented into an optimization tool, which allows for a broader trade study of different mission concepts with a medium fidelity. Such work is suitable for a mission's preliminary study. It is shown, using the fictitious asteroid impact scenario 2017 PDC, that the complete tool is able to account for the orbit sensitivity to small perturbations and quickly optimize a deflection trajectory. The speed in which the tool operates allows for a trade study between the available hardware. As a result, key deflection dates and mission strategies are identified for the 2017 PDC.

Trajectory optimization↗

NASA NTRS2017

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

Interplanetary trajectory optimization problems are highly complex and are characterized by a large number of decision variables and equality and inequality constraints as well as many locally optimal solutions. Stochastic global search techniques, coupled with a large-scale NLP solver, have been shown to solve such problems but are inadequately robust when the problem constraints become very complex. In this work, we present a novel search algorithm that takes advantage of the fact that equality constraints effectively collapse the solution space to lower dimensionality. This new approach walks the filament'' of feasibility to efficiently find the global optimal solution.

Englander, Arnold C.↗

NASA NTRS2017

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass-or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

NASA NTRS2017

Global, Multi-Objective Trajectory Optimization With Parametric Spreading

Mission design problems are often characterized by multiple, competing trajectory optimization objectives. Recent multi-objective trajectory optimization formulations enable generation of globally-optimal, Pareto solutions via a multi-objective genetic algorithm. A byproduct of these formulations is that clustering in design space can occur in evolving the population towards the Pareto front. This clustering can be a drawback, however, if parametric evaluations of design variables are desired. This effort addresses clustering by incorporating operators that encourage a uniform spread over specified design variables while maintaining Pareto front representation. The algorithm is demonstrated on a Neptune orbiter mission, and enhanced multidimensional visualization strategies are presented.

trajectory design↗

NASA NTRS2017

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

Englander, Arnold C.↗

NASA NTRS2017

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass- Or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood-allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

NASA NTRS2017

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

trajectory design↗

NASA NTRS2017

Spacecraft Mission Design for the Mitigation of the 2017 PDC Hypothetical Asteroid Threat

This paper presents a detailed mission design analysis results for the 2017 Planetary Defense Conference (PDC) Hypothetical Asteroid Impact Scenario, documented at https:cneos.jpl.nasa.govpdcspdc17. The mission design includes campaigns for both reconnaissance (flyby or rendezvous) of the asteroid (to characterize it and the nature of the threat it poses to Earth) and mitigation of the asteroid, via kinetic impactor deflection, nuclear explosive device (NED) deflection, or NED disruption. Relevant scenario parameters are varied to assess the sensitivity of the design outcome, such as asteroid bulk density, asteroid diameter, momentum enhancement factor, spacecraft launch vehicle, and mitigation system type. Different trajectory types are evaluated in the mission design process from purely ballistic to those involving optimal midcourse maneuvers, planetary gravity assists, and/or low-thrust solar electric propulsion. The trajectory optimization is targeted around peak deflection points that were found through a novel linear numerical technique method. The optimization process includes constrain parameters, such as Earth departure date, launch declination, spacecraft, asteroid relative velocity and solar phase angle, spacecraft dry mass, minimum/maximum spacecraft distances from Sun and Earth, and Earth-spacecraft communications line of sight. Results show that one of the best options for the 2017 PDC deflection is solar electric propelled rendezvous mission with a single spacecraft using NED for the deflection.

Barbee, Brent W.↗

NASA NTRS2017

Spacecraft Mission Design for the Mitigation of the 2017 PDC Hypothetical Asteroid Threat

This paper presents a detailed mission design analysis results for the 2017 Planetary Defense Conference (PDC) Hypothetical Asteroid Impact Scenario, documented at https://cneos.jpl.nasa.gov/ pd/cs/pdc17/. The mission design includes campaigns for both reconnaissance (flyby or rendezvous) of the asteroid (to characterize it and the nature of the threat it poses to Earth) and mitigation of the asteroid, via kinetic impactor deflection, nuclear explosive device (NED) deflection, or NED disruption. Relevant scenario parameters are varied to assess the sensitivity of the design outcome, such as asteroid bulk density, asteroid diameter, momentum enhancement factor, spacecraft launch vehicle, and mitigation system type. Different trajectory types are evaluated in the mission design process from purely ballistic to those involving optimal midcourse maneuvers, planetary gravity assists, and/or lowthrust solar electric propulsion. The trajectory optimization is targeted around peak deflection points that were found through a novel linear numerical technique method. The optimization process includes constrain parameters, such as Earth departure date, launch declination, spacecraft/asteroid relative velocity and solar phase angle, spacecraft dry mass, minimum/maximum spacecraft distances from Sun and Earth, and Earth/spacecraft communications line of sight. Results show that one of the best options for the 2017 PDC deflection is solar electric propelled rendezvous mission with a single spacecraft using NED for the deflection

Barbee, Brent W.↗

NASA NTRS2017

Validation of a Low-Thrust Mission Design Tool Using Operational Navigation Software

Design of flight trajectories for missions employing solar electric propulsion requires a suitably high-fidelity design tool. In this work, the Evolutionary Mission Trajectory Generator (EMTG) is presented as a medium-high fidelity design tool that is suitable for mission proposals. EMTG is validated against the high-heritage deep-space navigation tool MIRAGE, demonstrating both the accuracy of EMTG's model and an operational mission design and navigation procedure using both tools. The validation is performed using a benchmark mission to the Jupiter Trojans.

Englander, Jacob A.↗

NASA NTRS2017

A Time-Regularized, Multiple Gravity-Assist Low-Thrust, Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Keplers equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Keplers equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization↗

NASA NTRS2017

A Time-Regularized Multiple Gravity-Assist Low-Thrust Bounded-Impulse Model for Trajectory Optimization

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Kepler's equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight-suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Kepler's equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

Optimization↗