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NASA NTRS2008

Development of a Smooth Trajectory Maneuver Method to Accommodate the Ares I Flight Control Constraints

Six degree-of-freedom (DOF) launch vehicle trajectories are designed to follow an optimized 3-DOF reference trajectory. A vehicle has a finite amount of control power that it can allocate to performing maneuvers. Therefore, the 3-DOF trajectory must be designed to refrain from using 100% of the allowable control capability to perform maneuvers, saving control power for handling off-nominal conditions, wind gusts and other perturbations. During the Ares I trajectory analysis, two maneuvers were found to be hard for the control system to implement; a roll maneuver prior to the gravity turn and an angle of attack maneuver immediately after the J-2X engine start-up. It was decided to develop an approach for creating smooth maneuvers in the optimized reference trajectories that accounts for the thrust available from the engines. A feature of this method is that no additional angular velocity in the direction of the maneuver has been added to the vehicle after the maneuver completion. This paper discusses the equations behind these new maneuvers and their implementation into the Ares I trajectory design cycle. Also discussed is a possible extension to adjusting closed-loop guidance.

Pinson, Robin M.↗

NASA NTRS2009

Survey and Method for Determination of Trajectory Predictor Requirements

A survey of air-traffic-management researchers, representing a broad range of automation applications, was conducted to document trajectory-predictor requirements for future decision-support systems. Results indicated that the researchers were unable to articulate a basic set of trajectory-prediction requirements for their automation concepts. Survey responses showed the need to establish a process to help developers determine the trajectory-predictor-performance requirements for their concepts. Two methods for determining trajectory-predictor requirements are introduced. A fast-time simulation method is discussed that captures the sensitivity of a concept to the performance of its trajectory-prediction capability. A characterization method is proposed to provide quicker, yet less precise results, based on analysis and simulation to characterize the trajectory-prediction errors associated with key modeling options for a specific concept. Concept developers can then identify the relative sizes of errors associated with key modeling options, and qualitatively determine which options lead to significant errors. The characterization method is demonstrated for a case study involving future airport surface traffic management automation. Of the top four sources of error, results indicated that the error associated with accelerations to and from turn speeds was unacceptable, the error associated with the turn path model was acceptable, and the error associated with taxi-speed estimation was of concern and needed a higher fidelity concept simulation to obtain a more precise result

Rentas, Tamika L.↗

NASA NTRS2010

IRVE-II Post-Flight Trajectory Reconstruction

NASA s Inflatable Re-entry Vehicle Experiment (IRVE) II successfully demonstrated an inflatable aerodynamic decelerator after being launched aboard a sounding rocket from Wallops Flight Facility (WFF). Preliminary day of flight data compared well with pre-flight Monte Carlo analysis, and a more complete trajectory reconstruction performed with an Extended Kalman Filter (EKF) approach followed. The reconstructed trajectory and comparisons to an attitude solution provided by NASA Sounding Rocket Operations Contract (NSROC) personnel at WFF are presented. Additional comparisons are made between the reconstructed trajectory and pre and post-flight Monte Carlo trajectory predictions. Alternative observations of the trajectory are summarized which leverage flight accelerometer measurements, the pre-flight aerodynamic database, and on-board flight video. Finally, analysis of the payload separation and aeroshell deployment events are presented. The flight trajectory is reconstructed to fidelity sufficient to assess overall project objectives related to flight dynamics and overall, IRVE-II flight dynamics are in line with expectations

O'Keefe, Stephen A.↗

NASA NTRS2010

A Final Approach Trajectory Model for Current Operations

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Gong, Chester↗

NASA NTRS2010

A Near-Term Concept for Trajectory Based Operations with Air/Ground Data Link Communication

An operating concept and required system components for trajectory-based operations with air/ground data link for today's en route and transition airspace is proposed. Controllers are fully responsible for separation as they are today, and no new aircraft equipage is required. Trajectory automation computes integrated solutions to problems like metering, weather avoidance, traffic conflicts and the desire to find and fly more time/fuel efficient flight trajectories. A common ground-based system supports all levels of aircraft equipage and performance including those equipped and not equipped for data link. User interface functions for the radar controller's display make trajectory-based clearance advisories easy to visualize, modify if necessary, and implement. Laboratory simulations (without human operators) were conducted to test integrated operation of selected system components with uncertainty modeling. Results are based on 102 hours of Fort Worth Center traffic recordings involving over 37,000 individual flights. The presence of uncertainty had a marginal effect (5%) on minimum-delay conflict resolution performance, and windfavorable routes had no effect on detection and resolution metrics. Flight plan amendments and clearances were substantially reduced compared to today s operations. Top-of-descent prediction errors are the largest cause of failure indicating that better descent predictions are needed to reliably achieve fuel-efficient descent profiles in medium to heavy traffic. Improved conflict detections for climbing flights could enable substantially more continuous climbs to cruise altitude. Unlike today s Conflict Alert, tactical automation must alert when an altitude amendment is entered, but before the aircraft starts the maneuver. In every other failure case tactical automation prevented losses of separation. A real-time prototype trajectory trajectory-automation system is running now and could be made ready for operational testing at an en route Center in 1-2 years.

McNally, David↗

NASA NTRS2011

Orbiter Trajectory Analysis for a Two-Stage Reusable Launch Vehicle

Trajectory analysis performed on NASA's reference two-stage-to-orbit launch vehicle upper stage will be presented. The work was completed in support of the Hypersonics Multidisciplinary Analysis and Optimization effort for the NASA-Air Force Joint System Study. Three degree-of-freedom (3-DOF) untrimmed trajectory analysis was performed for the orbiter ascent, closure and re-entry. An iterative closure process resulted in a 333,000 lb initial mass for the orbiter. The re-entry trajectory satisfied heating constraints for all payload out cases and met the constraints with reduced margins for payload in cases. Abort trajectories for engine out at staging, engine out during ascent, and failure to circularize in orbit, gave insight to the robustness of the orbiter. A trimmed ascent trajectory defined an engine gimbal location and the body flap angle best suited for maximizing injected mass. A trimmed re-entry trajectory revealed a need to update the trim routine to accommodate full flap aerodynamic data.

Cowling, Adam L.↗

NASA NTRS2015

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

Narkawicz, Anthony↗

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

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 NTRS2016

The Viability of Trajectory Analysis for Diagnosing Dynamical and Chemical Influences on Ozone Concentrations in the UTLS

The viability of trajectory analysis for diagnosing the interplay between chemistry and dynamics is investigated by comparing ozone mixing ratios modelled using air-parcel pathways to values observed along flight tracks during ATTREX (Airborne Tropical TRopopause EXperiment). Trajectories are initiated at the locations of ozone observations and tracked backward in time to their sources at termini of backward trajectories. The modelled values of ozone utilize 3-dimensional analysis fields from WACCM (Whole Atmosphere Community Climate Model) (a chemical-climate model with dynamical fields nudged towards MERRA (Modern-Era Retrospective Analysis and Research Applications) reanalysis) and ERA-interim (product of ECMWF - the European Centre for Medium-Range Weather Forecasts) to determine source mixing ratios with chemical production and loss terms derived from the ozone chemistry used in WACCM. A statistical base of modelled ozone is constructed with 6 trajectory platforms (adiabatic, diabatic, and kinematic forced by ERA-interim and MERRA), two chemical models (WACCM chemistry and no chemistry), and 4 trajectory lengths (5, 10, 20, and 30 days). Linear regression is employed to separate systematic errors from random errors and to characterize the impact of source mixing ratios, path length, vertical motion, and chemistry on modelled ozone errors. Errors in the analysis ozone fields are large, if not dominant, contributors to model error. Random errors are particularly large for point-by-point comparisons, however averaging over 800 km (75 minutes) flight segments substantially reduces random error and exposes systematic errors. Of the two analysis ozone data sets, WACCM, which incorporates detailed chemistry, provides the smaller systematic errors while ERA-interim, which has crude chemistry but assimilates observational data, has the smaller random errors. Of the different trajectory platforms, adiabatic calculations produce the smaller random errors (irrespective of the use of chemistry) but both vertical motion and chemistry are required to optimally reduce systematic errors. These results suggest that meaningful analysis of dynamical and chemical interactions that control ozone mixing ratios are viable on spatial scales larger than a few reanalysis grid spaces, that errors in the analyzed ozone data sets are large but not prohibitively so, and that vertical velocities and heating rates from reanalysis data, while problematic, contain useful information [on the ozone concentrations in the UTLS (Upper Troposphere/Lower Stratosphere)].

ozone↗

NASA NTRS2015

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 NASA’s 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 good option for computing wind-optimal trajectories for national and global air traffic system studies.

Ng, Hok K.↗

NASA NTRS2018

Understanding Extended Projected Profile (EPP) Trajectory Error Using a Medium-Fidelity Aircraft Simulation

A critical component of Trajectory-Based Operations is the ability for a consistent and accurate 4-dimensional trajectory to be shared and synchronized between airborne and ground systems as well as amongst various ground automation systems. The Aeronautical Telecommunication Network—Baseline 2 standard defines the Extended Projected Profile (EPP) trajectory that can be sent via Automatic Dependent Surveillance-Contract from an aircraft to ground automation. The EPP trajectory message contains a representation of the reference trajectory from an aircraft’s Flight Management System (FMS). In this work, a set of scenarios were run in a medium-fidelity aircraft and FMS simulation to perform an initial characterization of EPP trajectory errors under a given set of conditions. The parameters investigated were the route length, route type, wind magnitude error, wind direction error, and with and without a required time-of-arrival constraint.

Guerreiro, Nelson M.↗

NASA NTRSDate not supplied

Keplerian Analysis for Versatile Evaluation of Arbitrary Trajectories

Designing interplanetary missions is an iterative process, with a tight coupling between mission analysis and vehicle design. The ability to simultaneously process both analyses early on can provide significant benefits in both the concept formulation and in overall mission feasibility. To implement such a simultaneous analysis process, there is a need to model interplanetary trajectories rapidly while maintaining an acceptable level of fidelity. Many simple patched conics tools make too many assumptions to satisfactorily address all relevant constraints and objectives, while full-fidelity trajectory design tools often require more time and expertise than is available in early conceptual studies. Hence, some form of middle-ground modeling tool would provide value. This paper introduces the development of such a tool using Python. This tool, Keplerian Analysis for Versatile Evaluation of Arbitrary Trajectories (KAVEAT), implements a patched conics method that enforces continuity of state (time, mass, position, velocity) through all transitions between various spheres of influence on the trajectory. The trajectory is constructed in an object-oriented manner, dynamically assembling unique maneuvers such as departure burns, heliocentric transfers (ballistic or with electric propulsion), and planetary flybys (powered or unpowered). Each maneuver has its own specific set of basic inputs needed to define it. The tool then takes these defined maneuvers, strings them together creating all the interdependencies required, and solves for the ideal trajectory using a gradient-based optimizer.

Katherine T McBrayer↗

NASA NTRS2018

An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation

Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–eﬀector motion. The Jacobian matrix maps incremental joint motion to incremental end–eﬀector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not eﬃcient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–eﬀector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–eﬀector motion, from which a linear combination of joints that projects fully onto the desired end–eﬀector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–eﬀector trajectory accommodating the ability of each joint in terms of its motion transmission.

Ravani, Bahram↗

NASA NTRS2020

Designing Trajectories Resilient to Missed Thrust Events Using Expected Thrust Fraction

With the adoption of efficient low-thrust propulsion methods, the probability of a missed thrust event occurring has become a significant concern for short and long- duration missions. If the missed thrust events take place during a critical portion of the trajectory, the mission can be compromised. Therefore, it is essential to de- velop trajectories that are resilient to missed thrust events. This paper investigates the use of expected thrust fraction, which embeds the stochastic nature of missed thrust events into a deterministic optimal control problem. The performance of trajectories designed using expected thrust fraction is compared with traditionally designed trajectories to measure changes in resiliency to missed thrust events. In this investigation, trajectories designed using expected thrust fraction arrive with a median lateness half that of traditionally designed trajectories. Using expected thrust fraction can help astrodynamicists mitigate risks posed by the use of low- thrust propulsion.

Laipert, Frank E.↗

NASA NTRSDate not supplied

Trajectory Optimization Methods and Applications at NASA Goddard

The process of spacecraft trajectory design frequently incorporates an optimization step in which one or more objectives, such as propellant consumption or time of flight, is minimized. Optimization is especially crucial for low-thrust mission design, due to the need to specify a thrust vector at every instant in time along a trajectory. At NASA's Goddard Space Flight Center (GSFC) a number of open-source tools have been developed for spacecraft trajectory optimization that utilize direct shooting and collocation methods. These tools have been effectively applied to cislunar, libration point, and interplanetary mission design for the Lunar IceCube, SWFO, and DAVINCI missions, among others. This presentation outlines the theory underlying these optimization tools along with the details of their application to several trajectory design problems, with a focus on the Lunar IceCube (LIC) mission. The LIC mission required a low-thrust trajectory from a high-energy deployment state to a lunar orbit, and its limited control authority necessitated the use of optimization tools and low-energy trajectory design techniques. The tools discussed demonstrate how the use of optimization methods expands mission capabilities and enables transformational science.

Robert Pritchett↗

NASA NTRSDate not supplied

Trajectory Reconstruction of the Low-Earth Orbit Flight Test of an Inflatable Decelerator

The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) project conducted a flight test of a 6m inflatable aeroshell. The LOFTID test article was a secondary payload on an Atlas V launcher that carried the Joint Polar Satellite System-2 (JPSS-2) as its primary payload. The vehicle launched on November 10th, 2022. After reaching orbit, the LOFTID test article inflated the aeroshell, separated from the upper stage on an entry trajectory, and entered the atmosphere to splash down in the Pacific Ocean under parachutes. The test concept of operations is shown in Figure 1. The test article was instrumented with a variety of sensors to be used for post-flight evaluation of vehicle performance. Data from one of the key sensors for trajectory reconstruction, the Inertial Measurement Unit (IMU), was not captured in the data recorder due to a malfunction. Data from the nose cone mounted Flush Air Data Sensing (FADS) system were successfully acquired. The layout of the FADS sensors and the measured pressures during atmospheric entry are shown in Figure 2. The FADS data were combined with a Newtonian flow pressure model [1, 2] to produce estimates of the atmospheric relative trajectory. A Mach number anchoring technique given in [2] was used to stabilize estimates in high speed flight conditions. Since no IMU data were available, a trajectory simulation was used to provide the Mach number time history. The resulting estimates of the atmospheric-relative trajectory are shown in Figures 3. Given the loss of the IMU data, alternate methods for trajectory reconstruction are being explored. One approach under investigation is the use of the on-board video recorder data to be analyzed to reconstruct attitude motion. This approach is currently under investigation and will be reported on in the final paper. The Newtonian flow pressure model for the FADS analysis will also be updated with a CFD-based pressure model.

Christopher D Karlgaard↗

NASA NTRSDate not supplied

Trajectory Reconstruction of the Low-Earth Orbit Flight Test of an Inflatable Decelerator

Christopher D. Karlgaard↗