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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
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

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 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

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 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↗
NASA NTRS1972

An analytic guidance technique for planetary and lunar approach trajectories.

An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.

Carlson, N. A.↗
NASA NTRS1972

Encounter trajectory design for SEP rendezvous with low mass celestial bodies.

This paper shows the considerations which precede and affect encounter trajectory design and the impact of this design on propulsion system performance requirements and interplanetary trajectory design. Representative missions selected to illustrate the problems and characteristics of encounter trajectory design are a Mercury Orbiter, Eros Rendezvous, Encke Rendezvous, and Ceres Orbiter. The paper shows that for SEP missions, particularly for low mass celestial bodies, the encounter trajectory may be freely specified to a large extent to satisfy mission goals rather than being dictated by a rigid interplanetary trajectory design.

Driver, J. M.↗
NASA NTRS1974

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 2: Programmer's manual

The six month effort was responsible for the development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs. The program NOMNAL targets a transfer trajectory from earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty.

Byrnes, D. V.↗
NASA NTRS1974

Four-body trajectory optimization

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

Pu, C. L.↗
NASA NTRS1975

Fixed-range optimum trajectories for short-haul aircraft

An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum.

Erzberger, H.↗
NASA NTRS1977

Space shuttle engineering and operations support. ALT separation reference trajectories for tailcone on orbiter forward and aft CG configurations. Mission planning, mission analysis and software formulation

A preflight analysis of the ALT separation reference trajectories for the tailcone on, forward, and aft cg orbiter configurations is documented. The ALT separation reference trajectories encompass the time from physical separation of the orbiter from the carrier to orbiter attainment of the maximum ALT interface airspeed. The trajectories include post separation roll maneuvers by both vehicles and are generated using the final preflight data base. The trajectories so generated satisfy all known separation design criteria and violate no known constraints. The requirement for this analysis is given along with the specifications, assumptions, and analytical approach used to generate the separation trajectories. The results of the analytical approach are evaluated, and conclusions and recommendations are summarized.

Glenn, G. M.↗
NASA NTRS1977

Optimal solar sail planetocentric trajectories

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Sackett, L. L.↗
NASA NTRS1978

Trajectory module of the NASA Ames Research Center aircraft synthesis program ACSYNT

A program was developed to calculate trajectories for both military and commercial aircraft for use in the aircraft synthesis program, ACSYNT. The function of the trajectory module was to calculate the changes in the vehicle's flight conditions and weight, as fuel is consumed, during the flying of one or more missions. The trajectory calculations started with a takeoff, followed by up to 12 phases chosen from among the following: climb, cruise, acceleration, combat, loiter, descent, and paths. In addition, a balanced field length was computed. The emphasis was on relatively simple formulations and analytic expressions suitable for rapid computation since a prescribed trajectory had to be calculated many times in the process of converging an aircraft design, or finding an optimum configuration. The trajectory module consists of about 2500 cards and operational on a CDC 7600 computer.

Tauber, M. E.↗