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NASA NTRS2025

Mission-Maps For Outbound Cislunar Transfer Trajectories

This study quantifies the robustness and sensitivity of an outbound cislunar trajectory for a lunar lander in the form of mission-maps, or topological maps that allows either a computer program or mission designer to intuitively optimize the placement of critical outbound correction burns from the derived sensitivity data. The non-linear multi-body dynamics are applied to generate an outbound cislunar reference profile used by a linear covariance analysis (LinCov) tool to compute the expected Δv and trajectory dispersions due to the initial state uncertainty, sensor errors, maneuver execution errors, and disturbance accelerations along the outbound cislunar profile. The rapid performance analysis capabilities of LinCov are complimented with parallel processing techniques to evaluate hundreds and thousands of different translational burn locations, placements, and targeting constraints to identify the combination that minimizes the total Δv usage (nominal plus 3σ Δv) and trajectory dispersions at lunar orbit insertion. This study utilizes a generalized reference targeting algorithm to quickly assess the integrated closed-loop GN&C system performance due to different targeting configurations and constraints. The resulting mission maps provide an intuitive insight to ascertain each trajectory correction maneuver’s (TCM) sensitivity to different burn times along an outbound cislunar trajectory and quickly identify desirable engineering tradeoffs when performing analysis on the number and placement of these burns that nominally zero. Multiple mission maps are generated for a variety of different performance parameters that allow engineers to visually identify optimal solutions for trajectory correction maneuver placements, the number of correction burns, and the targeting constraints for each burn.

GN&C↗

DOE OSTI2024

Extracting Vehicle Trajectories from Partially Overlapping Roadside Radar

This work presents a methodology for extracting vehicle trajectories from six partially-overlapping roadside radars through a signalized corridor. The methodology incorporates radar calibration, transformation to the Frenet space, Kalman filtering, short-term prediction, lane-classification, trajectory association, and a covariance intersection-based approach to track fusion. The resulting dataset contains 79,000 fused radar trajectories over a 26-h period, capturing diverse driving scenarios including signalized intersections, merging behavior, and a wide range of speeds. Compared to popular trajectory datasets such as NGSIM and highD, this dataset offers extended temporal coverage, a large number of vehicles, and varied driving conditions. The filtered leader–follower pairs from the dataset provide a substantial number of trajectories suitable for car-following model calibration. The framework and dataset presented in this work has the potential to be leveraged broadly in the study of advanced traffic management systems, autonomous vehicle decision-making, and traffic research.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Automated Classification of Vehicle Movements at Signalized Intersections Using Vehicle Trajectories

Accurate vehicle movement classification through signalized intersections is of paramount importance to the analysis of intersection performance and the optimization of traffic control strategies. Conventional techniques for tracking vehicle turning movements depend on infrastructure-based strategies like human counts, loop detectors, and video analytics, all of which are costly, prone to errors, and spatially constrained. High-frequency trajectory data can be utilized to determine vehicle movement patterns in a scalable and infrastructure-independent method due to the adoption of connected vehicles (CVs). In recent years, several studies have utilized connected vehicle data to generate performance measures. Most of the trajectory-based performance measures approaches, however, require map matching-i.e., extracting geospatial references from maps to identify the movements that individual vehicles make at a signalized intersection. These approaches are often time-consuming and hinder scalability since geographic features need to be provided for an analysis to be conducted. Map matching methods are prone to errors as different map versions change these geographic features. This research presents a novel automatic classification pipeline that uses CV trajectory data to classify vehicle movements at signalized crossings, specifically pass-through left-turn and right-turn maneuvers. The process starts by filtering trips that cross a spatial bounding box that has been defined at the target intersection. Approach and departure headings for each trajectory crossing the boundary are computed and are clustered together to identify dominant movements. The proposed algorithm is used to classify the movement of vehicles at 10 intersections in the state of California, and the results indicate that the algorithm can classify movements at these intersections with varying traffic volumes and road network configurations, all in a map-less framework with no need for conflation of vehicle trajectories to a digital base map.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2012

EUROPA Multiple-Flyby Trajectory Design

As reinforced by the 2011 NRC Decadal Survey, Europa remains one of the most scientifically intriguing targets in planetary science due to its potential suitability for life. However, based on JEO cost estimates and current budgetary constraints, the Decadal Survey recommended-and later directed by NASA Headquarters-a more affordable pathway to Europa exploration be derived. In response, a flyby-only proof-of-concept trajectory has been developed to investigate Europa. The trajectory, enabled by employing a novel combination of new mission design techniques, successfully fulfills a set of Science Definition Team derived scientific objectives carried out by a notional payload including ice penetrating radar, topographic imaging, and short wavelength infrared observations, and ion neutral mass spectrometry in-situ measurements. The current baseline trajectory, referred to as 11-F5, consists of 34 Europa and 9 Ganymede flybys executed over the course of 2.4 years, reached a maximum inclination of 15 degrees, has a deterministic delta v of 157 m/s (post-PJR), and has a total ionizing dose of 2.06 Mrad (Si behind 100 mil Al, spherical shell). The 11-F5 trajectory and more generally speaking, flyby-only trajectories-exhibit a number of potential advantages over an Europa orbiter mission.

Europa↗

NASA NTRS2016

Computational Approaches to Simulation and Optimization of Global Aircraft Trajectories

This study examines three possible approaches to improving the speed in generating wind-optimal routes for air traffic at the national or global level. They are: (a) using the resources of a supercomputer, (b) running the computations on multiple commercially available computers and (c) implementing those same algorithms into NASAs Future ATM Concepts Evaluation Tool (FACET) and compares those to a standard implementation run on a single CPU. Wind-optimal aircraft trajectories are computed using global air traffic schedules. The run time and wait time on the supercomputer for trajectory optimization using various numbers of CPUs ranging from 80 to 10,240 units are compared with the total computational time for running the same computation on a single desktop computer and on multiple commercially available computers for potential computational enhancement through parallel processing on the computer clusters. This study also re-implements the trajectory optimization algorithm for further reduction of computational time through algorithm modifications and integrates that with FACET to facilitate the use of the new features which calculate time-optimal routes between worldwide airport pairs in a wind field for use with existing FACET applications. The implementations of trajectory optimization algorithms use MATLAB, Python, and Java programming languages. The performance evaluations are done by comparing their computational efficiencies and based on the potential application of optimized trajectories. The paper shows that in the absence of special privileges on a supercomputer, a cluster of commercially available computers provides a feasible approach for national and global air traffic system studies.

global air traffic optimization↗

NASA NTRS2016

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

aircraft↗

NASA NTRS2017

Improved Propulsion Modeling for Low-Thrust Trajectory Optimization

Low-thrust trajectory design is tightly coupled with spacecraft systems design. In particular, the propulsion and power characteristics of a low-thrust spacecraft are major drivers in the design of the optimal trajectory. Accurate modeling of the power and propulsion behavior is essential for meaningful low-thrust trajectory optimization. In this work, we discuss new techniques to improve the accuracy of propulsion modeling in low-thrust trajectory optimization while maintaining the smooth derivatives that are necessary for a gradient-based optimizer. The resulting model is significantly more realistic than the industry standard and performs well inside an optimizer. A variety of deep-space trajectory examples are presented.

trajectory↗

NASA NTRS2018

Performance Evaluation of Conflict-Free Trajectory Taxiing in Airport Ramp Area Using Fast-Time Simulations

The German Aerospace Center (DLR) and the National Aeronautics and Space Administration (NASA) have been collaborating to conduct joint research addressing future surface traffic management challenges. The surface management tool from DLR, called Taxi Routing for Aircraft: Creation and Controlling (TRACC), was adapted to be integrated in NASA's fast-time simulation environment called Surface Operations Simulator and Scheduler (SOSS). The research described in this paper 1) applied TRACC to trajectory-based ramp traffic management, where TRACC generates conflict-free aircraft trajectories in a congested ramp area, 2) investigated the feasibility of the concept through the integrated TRACC-SOSS fast-time simulation, and 3) evaluated the performance of the integrated system. For this activity, TRACC was adapted for ramp operations at Charlotte Douglas International Airport, called TRACC_PB (TRACC for pushback optimization). TRACC_PB provides four-dimensional taxi trajectories with a command speed profile for each aircraft following standard taxi routes within the ramp area. In this study, departures are given the Target Movement Area entry Times (TMATs) provided by the baseline surface metering scheduler based on NASA's Spot and Runway Departure Advisor (SARDA). TRACC_PB also calculates optimal pushback times for departures, as well as the times when arrivals shall enter the ramp, the Target Movement area Exit Times (TMETs). The initial results showed that the TRACC_PB successfully generated conflict-free trajectories for the ramp area taxi operations and improved taxiing efficiency compared to the baseline results. TRACC_PB aimed to provide conflict-free taxi routes avoiding any stops while taxiing. This resulted in longer gate hold times for departures and postponed throughput values compared to the baseline simulation without trajectory optimization. Having conflict-free routes without stoppage also created shorter taxi times but required renegotiation of the given TMATs. TRACC_PB also achieved reductions in both fuel consumption and engine emissions (17% for departures and 10% for arrivals), which correlate with the ramp taxi time reduction.

trajectory-based taxi operations↗

NASA NTRSDate not supplied

Trajectory Generation for Distributed Electric Propulsion Vehicles with Propeller Synchronization

In this paper, we propose a method for generating dynamically feasible trajectories for an acoustically aware vehicle with propeller phase control. The trajectory generation procedure allows both propeller phase control and navigation objectives to be considered simultaneously. The presented method is demonstrated where the mission objectives are given as a desired position and phase trajectory. From these trajectories, the full desired state of the vehicle is calculated. Furthermore, the control inputs that realize the desired mission objectives are computed. The acoustic performance for the given trajectory is estimated in terms of sound pressure level as a function of tracking performance. The method is demonstrated in simulation, where the vehicle must navigate through an urban environment with both spatial and acoustic constraints. In the presented scenario, the vehicle must follow a given flight path, and can only reduce sound pressure level by changing the propeller phase targets.

acoustically-aware vehicle↗

NASA NTRSDate not supplied

Trajectory Generation for Distributed Electric Propulsion Vehicles with Propeller Synchronization

Acoustically-aware vehicle↗

NASA NTRS2022

Reconstruction of the Apollo 11 Moon Landing Final Descent Trajectory

Relatively limited data on the Apollo 11 pre-planned and as-flown trajectories are available in the open literature and in the NASA archives. Furthermore, a single report appears to be the only source containing plots comparing the pre-planned and as-flown final approach and landing trajectories. The plots in that report, however, are small and difficult to read, and contain data that are insufficient for directly reconstructing the final landing trajectory. In this report, several published graphics are digitized, and then a variety of least-squares and Kalman filter estimators are applied using kinematic equations and simplified dynamic equations to reconstruct the final descent trajectory. The reconstructed trajectory is important in the crew training effort for program Artemis, which intends to send humans back to the moon, as well as other studies focusing on landing on extraterrestrial worlds.

Apollo 11↗

NASA NTRS2022

Wind-Optimal Lateral Trajectories for a Multirotor Aircraft in Urban Air Mobility

The primary motivation for this paper is to quantify the operational benefits (energy consumption and flight duration) of flying wind-optimal lateral trajectories for short flights (less than 60 miles) anticipated in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the lateral trajectory. The optimal control problem is numerically solved using the direct collocation method. Energy consumption and flight duration flying wind-optimal lateral trajectories are compared with corresponding values obtained flying great-circle paths between the same origin and destination pairs to determine the operational benefits of wind-optimal routing for short flights. The flight duration results for different scenarios are validated using a simulation tool designed and developed at NASA for exploring advanced air traffic management concepts. This research study suggests that for short flights in an urban environment, operational benefits of the wind-optimal lateral trajectories over the corresponding great-circle trajectories in terms of energy consumption and flight duration per flight are dependent on: i) wind field’s spatial variability, ii) wind magnitude, iii) the direction of route relative to the wind field, and iv) cruise segment length. The operational benefits observed in realistic flyable wind scenarios are less than 2.5%; these could be translated to an equivalent of a maximum of 2 min of cruise flight duration savings in the urban air mobility environment. As expected, headwinds and tailwinds along the flight route most significantly impact energy consumption and flight duration.

Wind-Optimal Trajectory, Lateral Path, Urban Air M↗

NASA NTRSDate not supplied

Optimized Trajectory Correction Burn Placement for the NASA Artemis II Mission

The NASA Artemis II mission represents the first time humans plan to return to the lunar vicinity in over 50 years with a crew traveling to the Moon in the Orion spacecraft on a free return trajectory. This first crewed mission of the Artemis program will evaluate human-rated elements of Orion in preparation to sending astronauts to the lunar surface. The selected free-return cislunar trajectory profile that is reminiscent of the Apollo 8 mission that nominally requires no additional translational burns following the trans-lunar injection (TLI) burn. Due to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations; periodic trajectory corrections burns are necessary to ensure proper entry interface (EI) conditions are satisfied for a safe return to Earth. Robust trajectory optimization techniques are utilized to determine the optimized placements for the Artemis II trajectory correction burns that accounts for the crew schedule, both the primary and backup navigation systems, targeting strategies and burn plan configurations, spacecraft venting, thruster selection, and the integrated GN&C performance.

Linear Covariance Analysis↗

NASA NTRSDate not supplied

Design of Safe Separation Bounds for Temporally Deconflicted Trajectories Under Bounded Uncertainties

This paper explores the derivation of safe separation bounds for a heterogeneous group of~$n$ Uncrewed Aerial Systems (UAS) that are assigned temporally deconflicted trajectories. Compared to spatially deconflicted trajectories, temporal deconfliction can lead to higher traffic capacities and a more efficient use of the available airspace. One challenge with this type of deconfliction is that collisions can occur if some cooperating UAS are behind or ahead of schedule. To overcome this risk, this paper derives a lower bound on the safety distance between two heterogeneous UAS in the presence of bounded uncertainties. This safety distance can be leveraged to inform trajectory generation algorithms. The proposed bound establishes a rigorous safety margin when the fleet deviates from the planned trajectories, both temporally and spatially. For its derivation the paper assumes the UAS implement a distributed coordination algorithm that allows the fleet to maintain their schedules synchronized within a bounded temporal error, and a path-following algorithm that lets the vehicles track a target that moves along the planned trajectory with a bounded spatial error.

autonomy↗

NASA NTRSDate not supplied

Angles-Only Robust Trajectory Optimization for NRHO Rendezvous

This study demonstrates a robust trajectory optimization approach for rendezvous and proximity operations with angles-only navigation measurements. Often, sensors that directly measure relative range and velocity require communication or coordination between the chaser and target vehicle and can have limiting pointing accuracy, mass, or power requirements compared to angle measurement sensors. Thus, the capability to perform a rendezvous with only angle measurements can be advantageous for vehicle design and to improve robustness to failures. However, the well studied limitation of angles-only navigation in measuring range results in large uncertainties in the navigation system that must be reduced with chaser vehicle thrust maneuvers to induce observability in range for the navigation filter. This analysis presents a trajectory optimization problem for a lunar ascent rendezvous during a crewed lunar mission in a Near-Rectilinear Halo Orbit (NRHO) that is limited to only angle measurements. The objective of this study is to show that an angles-only rendezvous is feasible in an NRHO and to present the sensitivity to an assortment of constraints generated from a systematic optimization process using linear covariance analysis and particle swarm optimization. Linearized NRHO dynamics and linearized relative targeting are applied to use linear covariance analysis to determine the expected delta-v and trajectory dispersions due to initial state uncertainty, sensor errors, maneuver execution errors, and unmodeled dynamics. The delta-v and trajectory dispersions are passed into a particle swarm optimization algorithm to find the optimized maneuver profile that minimizes fuel use while satisfying constraints such as free drift and underburn to 3-sigma certainty. The trajectory constraints including time available, desired final uncertainty, and initial uncertainty are varied to ascertain sensitivity and desirable engineering trades.

Linear Covariance Analysis↗

NASA NTRSDate not supplied

Ballistic Leverage for Conjunction Avoidance During the Lunar Transit Trajectory of NASA's Co-Manifested Vehicle

Analysis is completed to investigate the sensitivity of the Lunar Transit Trajectory of NASA’s Co-Manifested Vehicle (CMV) to the insertion of intentional coasting into an otherwise nearly continuous low thrust maneuver. A reference trajectory is developed which explicitly models low altitude thruster shutdowns in a level of detail not included in previous Design Reference Missions. This reference trajectory is used to investigate the sensitivity of the Lunar Transit to additional inserted coasting, presented in the form of separation of the perturbed trajectory from the reference as a function of mission elapsed time and duration and location of the coast segment. These results are shown to inform potential conjunction avoidance strategies during the CMV’s long low thrust spiral from a highly elliptic Earth parking orbit to the target Gateway Near Rectilinear HALO Orbit (NRHO).

low thrust↗

NASA NTRSDate not supplied

Ballistic Leverage for Conjunction Avoidance During the Lunar Transit Trajectory of NASA's Co-Manifested Vehicle

low thrust↗

NASA NTRS1963

Lunar Flight Study Series: Volume 7. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program: Principles for Reducing Earth-Moon Trajectory Analysis to Fundamentals - 2

This report presents an empirical investigation of earth-to-moon trajectories. The primary objective is to uncover relationships that result in the reduction of mission analysis or trajectory analysis problems to fundamentals. It is considered imperative that the results be accurate to the extent that any relationships that are uncovered are not brought about by simplifying or unrealistic assumptions. Consequently, the model used is as accurate as is presently available for use and the computations are performed under strict error controls. Procedures are reasonable from the engineering viewpoint. Some very helpful principles are uncovered. These may be briefly stated as follows: 1) Trajectories of constant flight time to the moon (in the 66 hour to 90 hour range), and arriving within a few minutes of the same time pass over a common point on the moon regardless of the arrival altitude and inclination, This common point of passage for such a family of trajectories is arbitrarily referred to as a VERTEX point; 2) These VERTEX points lie within a bounded region on the lunar surface as arrival time varies throughout the years, for a given flight time or flight time spread; 3) Increasing flight time results primarily in a longitude shift of the VERTEX point for a given arrival time; 4) Launch azimuth should be treated as a strong parameter regarding its influence on the vertex. Launch azimuth variations up to +/- 20 degrees about 90 degrees can shift the vertex as much as 3 degrees in latitude even when one is free to pick launch time, coast time, and S-IVB burn time appropriately with launch azimuth; and 5) The locus of periselenum, as arrival inclination takes on all possible values, is nearly circular about the vertex point for a given arrival altitude. A publication is now in preparation that applies these principles to much advantage in the solution of various trajectory analysis problems.

LUNAR FLIGHT↗