Search NASASearch

SEARCH · Search NASA

Results for “Trajectory Optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

Computation of Optimal Interplanetary Low-Thrust Trajectories With Bounded Thrust Magnitude By Means of the Generalized Newton-Raphson Method

The generalized Newton-Raphson method, an iterative procedure for solving nonlinear operator equations, has been extended in application to variational problems with bounded control variables. A minimum fuel interplanetary low thrust orbital transfer problem is worked out in detail to demonstrate the practical aspects of the algorithm as well as its computational effectiveness. The control variables are the thrust magnitude, limited from zero to some prescribed maximum value, and the thrust steering angle.

Computation

Mission Design Considerations for a Low-Thrust Spacecraft

Developing an executable low-thrust trajectory for use in a spaceflight mission requires the design and optimization of a deterministic trajectory as well as the validation that the selected architecture is robust to some set of uncertainties, execution errors, and potential contingencies. Uncertainty in the ability of the spacecraft and its launch vehicle to execute a trajectory as well as potential deviations such as in-flight anomalies combine with design-to constraints and requirements to complicate the optimization problem. The approach by which robust mission design was accomplished for the initial capability of NASA’s Gateway is presented as well as associated results.

NRHO

Mission Design Considerations for a Low-Thrust Spacecraft

Developing an executable low-thrust trajectory for use in a spaceflight mission requires the design and optimization of a deterministic trajectory as well as the validation that the selected architecture is robust to some set of uncertainties, execution errors, and potential contingencies. Uncertainty in the ability of the spacecraft and its launch vehicle to execute a trajectory as well as potential deviations such as in-flight anomalies combine with design-to constraints and requirements to complicate the optimization problem. The approach by which robust mission design was accomplished for the initial capability of NASA’s Gateway is presented as well as associated results.

mission design

A Missed Thrust Framework for Low-Thrust Spiral Trajectories to the NRHO

A framework is developed by which end-to-end optimization of many-revolution low-thrust spiral trajectories can be completed in the presence of missed thrust events. This framework is applied to the Lunar Transit trajectory by which the initial capability of NASA’s Gateway lunar space station will be delivered to a Near Rectilinear Halo Orbit. This low-thrust mission consists of three subphases, each designed according to the specific objectives and dynamical regimes encountered as the mission progresses from a medium Earth insertion orbit to cislunar space. The presented framework accounts for the unique considerations demanded by each mission phase and incorporates appropriate capabilities into a novel mission analysis tool. This methodology enables large scale and reliable analyses of missed thrust events across the end-to-end Lunar Transit to verify the robustness of flight trajectories across the full range of considered launch dates.

missed thrust

Parameterization of Nuclear Electric Propulsion Trajectories for Outer Solar System Science Missions Methodology

This manuscript addresses the methodology used to create a database of low thrust missions to outer planets. This database utilizes previous work modeling NEP systems to determine the maximum delivered mass to outer planets based on a range of mission parameters, such as time of flight, launch vehicle, and power system mass. Trajectories were selected which best utilized NEP benefits. Additionally, a discussion on the database outputs for missions to Saturn is included, such as time of flight based on trajectory type and maximum payload, given a specific launch vehicle. The purpose of this work was to create a basis for future mission design, and a tool to investigate general trends across mission options.

Outer Planets

Minimum Heating Re-Entry Trajectories for Advanced Hypersonic Launch Vehicles

Optimal re-entry trajectories are generated for reusable launch vehicles which minimize: (1) the heat absorbed at the vehicle surface, (2) the lower surface temperature, and (3) the heat absorbed by the internal structure. The approach uses the energy state approximation technique and a finite control volume heat transfer code coupled to a flight path integration code. These trajectories are compared to the optimal re-entry trajectory minimizing the integrated convective heat rate to determine which trajectory produces the minimum internal structural temperatures for a given thermal protection system. Three different thermal protection systems are considered: tile, blanket, and metallic.

Robert Windhorst

Advances in Design Capabilities for Planetary Missions from the NASA Entry Systems Modeling and Instrumentation Portfolio

The Entry Systems Modeling project (ESM) is supported by both the NASA Space Technology and the Science Mission Directorates and focuses on developing simulation tools and validated models for characterizing the performance of entry systems tailored to planetary destinations across the Solar System. ESM is organized into six technical capability areas that together address all relevant factors related to spacecraft entry, as well as some aspects of descent: Thermal Protection System (TPS) Materials; Aerothermodynamics; Entry & Descent Vehicle Dynamics; Guidance, Navigation, and Control; Vehicle Systems Analysis; and Advanced Tools and Numerical Methods. Development within the capability areas is undertaken explicitly with a focus on transition and infusion to science missions, human exploration missions, and commercial space activities. The present talk details developments that specifically impact science missions, including simulation tool capabilities that aid in mission design and model development to understand entry system performance at a given destination. Examples of the successful infusion and transition of such project outcomes to science missions also are provided. Several simulation tool development efforts within ESM have resulted in new design capabilities for missions. One such outcome is improved toolsets for mission trajectory and concept of operations design. Specifically, an initiative to couple a leading tool for entry, ascent/descent, and orbital trajectory optimization (Program to Optimize Simulated Trajectories II or POST2) to those used within the Agency for interplanetary trajectory optimization (Copernicus and Monte) has made substantial progress, with the outcomes to date promising to allow efficient trajectory optimization across mission phases. Additionally, toolchains for the evaluation of vehicle performance during entry and descent have been developed that allow assessment of multi-dimensional aeroheating on detailed vehicle geometries, characterization of deployment and inflation of parachutes, and assessment of vehicle dynamic stability during descent. These capabilities are achieved by coupling diverse sets of physics together – material response, computational fluid dynamics, radiation, and vehicle dynamics – to suitably describe complex entry and descent phenomena. Several model development and validation efforts for specific destinations and entry regimes also are underway within the ESM project. For instance, new experimental capabilities to validate radiation models at low densities/high altitudes recently have been established with project support, specifically the Low-Density Shock Tube (LDST) at the NASA Ames Research Center Electric Arc Shock Tube (EAST) facility. The LDST is being leveraged to develop improved models of shock layer kinetics and radiation in Titan atmospheres, while future studies will be conducted in the LDST and the existing high velocity shock tube to provide validation data for radiation models of Venus, Ice Giants, and Mars atmospheres. Models describing the aerothermal and thermo-structural performance of Thermal Protection System (TPS) materials has been another focus, with multiscale modeling activities on-going for the two leading TPS materials applicable to a range of entry conditions and science missions: the Phenolic-Impregnated Carbon Ablator (PICA) and woven materials like 3D Mid-Density Carbon Phenolic (3MDCP). A continual effort is made to infuse and transition outcomes from ESM simulation tool and model development activities into relevant science missions. Significant progress has been made on this front, with missions such as Dragonfly, DAVINCI, and Mars Missions benefitting from project outcomes. The groundwork also is being laid to provide insights into forward looking missions to Gas/Ice Giants as well as for potential sample returns.

Justin Haskins

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. The transient finite-element analysis is done using TACS, and the cell-discharge battery model uses OpenMDAO and dymos. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

The Trajectory of Recent Solid State Fusion Results

Both NASA and Google have explored and funded Low Energy Nuclear Reaction (LENR) aka Solid-State Fusion or Lattice Confinement Fusion (LCF) research. NASA has funded efforts since 1989, and Google Research began in 2014. Google, and researchers initially-funded by Google, published significant scientific papers in Nature, Nature Communications and the Journal of Applied Physics. NASA began a significant set of LENR-triggering programs in 2012 resulting in papers in Physical Review C, the Journal of Electroanalytical Chemistry and the Journal of Condensed Matter Nuclear Science. Both NASA and Google engaged researchers across fields of nuclear physics, chemistry, electrochemistry, material science and more. NASA built upon early novel gas pumping experiments then followed the patented work of the US Navy SPAWAR (US8,419,919, “System and Method to Generate Particles”) and experiments with the Naval Surface Warfare Centers. Google supported researchers at Lawrence Berkeley National Laboratory (LBNL), the University of British Columbia (UBC), MIT and others. This resulted in patent applications and two granted patents (US10264661B2, “Target structure for enhanced electron screening” and US10566094B2 “Enhanced electron screening through plasmon oscillations”). These separate efforts, unknown to the researchers at the time, provided the impetus for the DoE ARPA-E LENR program followed by the DARPA DSO “Mechanisms for Amplification of Fusion Reaction Rates in Solids” (MARRS) program. This document briefly describes the overlapping NASA and Google Research efforts in plasma loading and electron screening emphasizing the results of the latest paper in Nature Communications. The papers and patents cited are listed.

electron screening

Research Summary No. 36-8 for the Period February 1, 1961 to April 1, 1961

The Research Summary is a report of supporting research and development activities at the Jet Propulsion Laboratory, California Institute of Technology. This bimonthly periodical is usually published in two volumes. However, for this issue, all the material has been combined into one volume. To foster a more rapid interchange of original ideas and information throughout the scientific and technical community, all authors' names have been added as bylines to the material they contributed.

Telecommunication

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump

NASA Space Launch System Artemis I & II Post Flight Ascent Aerothermal Environments Overview

Since 2011 the Aerosciences Branch/EV33 at NASA Marshall Space Flight Center has been involved with the development of ascent external aerothermal environments for the NASA Space Launch System (SLS) Block 1 launch vehicle for the purposes of supporting thermal analysis and the design of thermal protection systems. The SLS Block 1 Artemis I and II launch vehicles successfully launched from Pad39B at NASA Kennedy Space Center on November 16th, 2022 and April 1st, 2026, respectively. Over 70 aerothermal islands, consisting of over 265 operational instruments captured aerodynamic heating and plume induced environments throughout the launch vehicles. Gauges consisted of calorimeters, radiometers, gas temperature probes, pressure transducers, bi-directional pressure probes and thermocouples. Prior to launch, aerothermal design environment models were generated to predict ascent aerodynamic heating and plume induced environments over a design space that covered a range of vehicle trajectories that varied atmospheric, vehicle performance, and off-nominal, engine-out conditions. Post flight reconstruction models were developed for each flight island using the Day-of-Launch (DOL) Best Equivalent Trajectory (BET) that provided freestream conditions and propulsion system boundary conditions. This paper discusses a summary of the ascent aerothermal environments observed during the flights and the respective modelling approaches and the performance of them through comparisons of flight data and predictions.

aerothermodynamics

From Exploration Flight Test-1 to Artemis II--A NASA Langley's Orion Aerosciences Overview

The Orion Aerosciences program at NASA Langley has played a central role in advancing the aerodynamic and aeroheating prediction capabilities required for the Orion crew vehicle’s return from deep space. This presentation provides a technical overview of aerosciences contributions spanning Exploration Flight Test-1 (EFT-1), Artemis I, and the ongoing post-flight analysis of Artemis II. EFT-1 provided the first high-energy entry dataset for Orion, enabling critical validation of aerodynamic force and moment predictions, static and dynamic stability characteristics, and aeroheating environments at relevant flight Mach and Reynolds numbers. Flight-derived pressure data were used to refine the Flush Air Data System (FADS) methodology for atmospheric density reconstruction and to improve Best Estimated Trajectory (BET) solutions. The EFT-1 data also offered key insights into heat shield performance, including char layer recession, in-depth thermal response, and material retention behavior under flight conditions, informing updates to both thermal response models and uncertainty quantification practices. Building on EFT-1, Artemis I extended the database to true lunar-return conditions. Observations of heat shield performance, including localized char loss, bondline response, and recession variability, provided an unprecedented opportunity to reassess Thermal Protection System (TPS) and aeroheating modeling assumptions. Aerodynamic reconstruction efforts incorporated improved FADS calibration, enhanced atmospheric modeling, and refined force and moment databases to reduce trajectory and load uncertainties. Aeroheating comparisons between pre-flight predictions and flight data enabled targeted model updates, particularly in transitional flow environments and wake heating regions. For Artemis II, these lessons were systematically incorporated into the pre-flight prediction process. Updates included refined aerodynamic databases anchored to flight-validated corrections, improved density estimation and BET methodologies using enhanced database interpolation algorithm and FADS modeling, and revised aeroheating design environments informed by Artemis I material response observations. By the time of the workshop, Artemis II post-flight analysis will be underway, and preliminary findings will be presented where available, including early comparisons of aerodynamic reconstruction, atmospheric density estimation, and thermal protection system performance relative to updated predictions. Collectively, this body of work is a testament to the dedicated and multidisciplinary team whose sustained efforts have contributed to the program’s success and to the progressive maturation of Orion aerosciences modeling through numerical modeling, ground and flight data assimilation. The integrated advancement of aerodynamics, trajectory reconstruction, FADS-based density estimation, and aeroheating analysis has reduced predictive uncertainty and strengthened confidence for future crewed lunar and deep-space missions.

Orion

Uranus Orbiter and Probe: Mission Challenges and Concept Updates Since the Origins, Worlds, and Life Decadal Survey

Origins, Worlds, and Life: Planetary Science and Astrobiology in the Next Decade identified a Uranus Orbiter and Probe as the highest-priority strategic mission for the decade 2023–2032, as it enables broad cross-disciplinary science in the largely unexplored Uranian system. The mission architecture evaluated by the Decadal Survey was a singular proof of concept demonstrating that a moderately instrumented mission could deliver Decadal-priority science with a reduced cost and risk posture by leveraging existing technologies to the maximum extent possible. With revised assumptions since the Decadal, we have explored a large trade space including launch vehicles, propulsion options, cruise trajectories, available power sources, viable concept of operations, and science data return for later launch dates without a Jupiter gravity assist. The most repeatable trajectory solutions employ either a commercially derived solar electric propulsion (SEP) transfer stage or the availability of a more capable launch vehicle under development, such as the SpaceX Starship. Orbit insertion has been moved farther from Uranus to acknowledge the remaining uncertainty in Uranian ring structure. A streamlined, SEP-adaptable, orbiter design was developed using two Next Gen Radioisotope Thermoelectric Generators, and the probe design was matured, reducing the entry gravitational acceleration, and assuming the largest Decadal-recommended payload to provide margin for future instrument selections. With this updated design, we also constructed a detailed concept of operations for three representative science cases, returning 13–15 Gbit of science data and spacecraft telemetry per ∼34 day orbit.

Amy A Simon

Manned Mars Systems Study

A study is underway to determine attractive system options, perform trade studies, and provide comparative data for astronaut missions to Mars. Because of an emphasis in this work on deriving requirements and candidates for the transportation and facility infrastructure for such missions, all relevant technologies and mission constraints are also being considered. These include on-orbit assembly, trajectory type, launch opportunities, propellant storage, crew size, cabin pressure, artificial gravity, life-support systems, radiation hazards, power/energy storage, thermal control, human factors, communications, abort scenarios, landing techniques, exploration strategies and science activities. It is planned to scope several example missions and to identify enabling and significantly enhancing technologies for accomplishing the goals of the human exploration of Mars.

Benton C Clark

PROBABALISTIC RISK ANALYSIS AND THERMAL MARGIN PROCESS FOR AN INFLATABLE AEROSHELL

Atmospheric entry vehicle thermal protection systems (TPS) are margined due to the uncertainties that exist in entry aeroheating environments and the thermal response of the materials and structures. Traditional approaches typically over-margin TPS and offer very little insight into the risk of over-temperature during flight. A probabilistic margin process can be used to apply thermal margin to an aeroshell based on a rigorously calculated risk of failure. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory modifications, and risk trades while preventing excessive margin from being applied. This methodology can also be applied to other TPS applications, hot structures, and other engineering disciplines.

Steven A Tobin