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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Phase-Free Orbital Element Model Designed to Enable Rapid Assessment of Eclipse and Radiation Profiles for Low-Thrust Spiral Transfers Around the Earth

The Gateway Power and Propulsion Element (PPE) will be the first low-thrust solar electric ion propulsion mission to transfer from a highly elliptical Earth-bound orbit to a southern near-rectilinear halo orbit (NRHO) at the Earth-Moon L2 point. Due to the low thrust nature of the transfer orbit, it is desirable to locate viable trajectories that minimize the time spent in the Van Allen radiation belts to reduce solar array degradation and keep radiation dosages below design limits. In addition to radiation, low thrust trajectories which spiral around the Earth will pass through at least one or more seasons of Earth eclipses. The solar electric propulsion system relies on sunlight to generate the power necessary to operate the ion thrusters. Therefore, it is advantageous to find trajectories which also minimize the amount of time spent in eclipse and avoid excessive battery draw-down periods. We present an analytical method which rapidly approximates low-thrust spiral trajectories, fit to high-fidelity simulated data and parameterized to allow for changes in vehicle thrust characteristics, that is post-processed to determine eclipse profiles and time spent in the belts using a novel approach that estimates the geometry of the belts using a first-order dipole approximation of the Earth’s magnetic field. This method can be used to find satisfactory launch dates and orbit orientations that can serve as initial guesses when optimizing such missions in high-fidelity software.

low thrust trajectory design↗
NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗
NASA NTRS2016

Rapid Preliminary Design of Interplanetary Trajectories Using the Evolutionary Mission Trajectory Generator

Preliminary design of interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on notional high-thrust chemical and low-thrust electric propulsion missions. In the low-thrust case, the hybrid optimal control problem is augmented to include systems design optimization.

Design↗
NASA NTRS2016

Global Optimization of N-Maneuver, High-Thrust Trajectories Using Direct Multiple Shooting

The performance of impulsive, gravity-assist trajectories often improves with the inclusion of one or more maneuvers between flybys. However, grid-based scans over the entire design space can become computationally intractable for even one deep-space maneuver, and few global search routines are capable of an arbitrary number of maneuvers. To address this difficulty a trajectory transcription allowing for any number of maneuvers is developed within a multi-objective, global optimization framework for constrained, multiple gravity-assist trajectories. The formulation exploits a robust shooting scheme and analytic derivatives for computational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess.

optimization↗
NASA NTRS2015

Global Optimization of N-Maneuver, High-Thrust Trajectories Using Direct Multiple Shooting

The performance of impulsive, gravity-assist trajectories often improves with the inclusion of one or more maneuvers between flybys. However, grid-based scans over the entire design space can become computationally intractable for even one deep-space maneuver, and few global search routines are capable of an arbitrary number of maneuvers. To address this difficulty a trajectory transcription allow-ing for any number of maneuvers is developed within a multi-objective, global optimization framework for constrained, multiple gravity-assist trajectories. The formulation exploits a robust shooting scheme and analytic derivatives for com-putational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess.

trajectory design↗
NASA NTRS1994

(abstract) Optimal Low Thrust Trajectories Using Differential Inclusion Concepts

Low thrust propulsion systems typically have their greatest benefit for high energy missions or missions with large post-launch maneuver requirements. Missions which have been examined include main belt asteroid rendezvous, comet rendezvous, outer planet and Mercury orbiters, Pluto flyby, and solar probe missions. Low thrust mission design software used to determine these trajectories is based on two distinct formulations of the optimal control problem: the indirect and direct methods. The traditional approach (indirect) is to use the calculus of variations to obtain first order necessary conditions on the states and costates. In contrast, direct methods are conceptually different in that no explicit integration takes place. A direct method based on differential inclusion concepts has been developed and successfully used to compute low thrust trajectories. This new approach removes explicit control dependence from the problem thereby reducing the dimension of the parameter space for the nonlinear programming problem. Also when compared to other direct methods, fewer nonlinear constraints are required to represent the dynamics of the problem.

low↗
NASA NTRSDate not supplied

Static and Forced Oscillation Wind Tunnel Tests of A Tandem Propeller Configuration

A series of static and forced oscillation tests were conducted using a tandem propeller configuration in the NASA Langley 12-Foot Low-Speed Tunnel. The primary objectives were to quantify the effect of aerodynamic interactions on propeller thrust and identify conditions where the effect is most significant. A secondary objective was to obtain a preliminary data set from dynamic testing to assess the impact of angular rate on thrust performance. This paper presents analysis of the experimental data, which includes propeller performance measurements and qualitative flow visualization. The static results show that the rear propeller in the tandem configuration can experience thrust degradations greater than 30%. The extent of the wake interaction is a function of the hub separation distance and the advance ratio of the front propeller. Forced oscillation results showed that the front propeller exhibited primarily linear behavior across the conditions tested, whereas the rear propeller exhibited dynamic nonlinearity in the region of significant thrust degradation. These results are intended to support high-fidelity modeling research, particularly for flight dynamics simulation development to aid trajectory prediction, control design, and identification of hazardous conditions for multirotor vehicles.

Aerodynamic Interactions↗
NASA NTRSDate not supplied

Overview of the Lunar Transit Trajectory Performed by the Power and Propulsion Element of NASA’s Gateway

NASA has committed to returning to the moon, landing the first woman and the next man on its surface. To support a sustained lunar presence, NASA is designing an orbital platform to be assembled in an orbit near the moon called the Near Rectilinear Halo Orbit (NRHO). This platform is known as the Gateway and its purpose it to support missions primarily to the lunar south pole. As NASA continues to study ways to reduce the cost of lunar exploration, a simplification implemented in 2020combinedthe first two elements of the Gateway, the Power and Propulsion Element (PPE) and NASA’s Habitation and Logistics Outpost (HALO), onto a single commercial launch vehicle (CLV). When launched together, the PPE and HALO make up the first two elements of NASA’s Gateway and exceed the performance capacity of commercially available launch vehicles to deliver directly to the moon. The delivery of the Gateway is enabled by and takes advantage of the high efficiency of the PPEs high-power Solar Electric Propulsion (SEP) system to transfer a significant starting mass from an initial Earth orbit to final insertion into the NRHO. The PPE is a 50-kW class high power solar electric propulsion stage comprised of two different types of electric thruster strings. The SEP system is operated in two different modes, a high thrust and high Isp (specific impulse), to both maximize the final delivered mass and attempt to minimize the time spent in the Van Allen Belts early in the transit trajectory. Additionally, this SEP system brings the capability to the assembled Gateway for transfer between orbits in cislunar space. This paper captures the preliminary low thrust lunar transfer reference trajectory to be flown by the PPE it delivers itself and HALO via a spiral trajectory from launch vehicle insertion to insertion into the NRHO as well as a preliminary reference round trip transfer of the Gateway from the NRHO to a Distant Retrograde Orbit (DRO) using the PPE. Once in its final NRHO, the Gateway is being designed to enable long duration human and robotic exploration of the lunar south pole as a precursor to Mars. The Gateway’s low thrust lunar transit trajectory is envisioned to prove out the application of and flight of a high-power SEP system as a demonstration of technologies applicable to the enabling of future human space exploration.

human exploration↗
NASA NTRS1978

Foil bearings for axial and radial support of high speed rotors: Design, development, and determination of operating characteristics

Flexible surface thrust and journal foil bearings were fabricated, and their performance was demonstrated, both individually and jointly as a unified rotor support system. Experimental results are documented with graphs and oscilloscopic data of trajectories, waveforms, and scans of amplitude response. At speeds of 40,000 to 45,000 rpm and a mean clearance of the order of 15 to 20 micrometers (600 to 800 micrometers, the resilient, air lubricated, spiral groove thrust bearings support a load of 127 N (29 lb; 13 kgf), equivalent to 3.0 N/sq cm (4.5 lb/sq in 0.31 kgf sq cm). Journal bearings with polygonal sections provided stable and highly damped supports at speeds up to 50,000 rpm.

Licht, L.↗
NASA NTRS2006

Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design

A tool developed for the preliminary design of low-thrust trajectories is described. The trajectory is discretized into segments and a nonlinear programming method is used for optimization. The tool is easy to use, has robust convergence, and can handle many intermediate encounters. In addition, the tool has a wide variety of features, including several options for objective function and different low-thrust propulsion models (e.g., solar electric propulsion, nuclear electric propulsion, and solar sail). High-thrust, impulsive trajectories can also be optimized.

optimization↗
NASA NTRS1991

Disposal modes for Mars transfer nuclear propulsion

A managed disposal approach is proposed that would place the nuclear stage or vehicle in a highly stable orbit at modest cost to mission performance. The approach requires only a small increase in initial mass in LEO, but should be included in preliminary trajectory design and performance calculations. The mass penalty is expected to be larger for all-up flight profiles, or in cases of high-thrust propulsion systems for the cargo vehicle.

Stancati, Michael L.↗
NASA NTRS2016

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.

Design↗
NASA NTRS2008

Chasing a Comet with a Solar Sail

Solar sail propulsion systems enable a wide range of missions that require constant thrust or high delta-V over long mission times. One particularly challenging mission type is a comet rendezvous mission. This paper presents optimal low-thrust trajectory designs for a range of sailcraft performance metrics and mission transit times that enables a comet rendezvous mission. These optimal trajectory results provide a trade space which can be parameterized in terms of mission duration and sailcraft performance parameters such that a design space for a small satellite comet chaser mission is identified. These results show that a feasible space exists for a small satellite to perform a comet chaser mission in a reasonable mission time.

Stough, Robert W.↗
NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Pinson, Robin M.↗
NASA NTRS2006

The Development of NASA's Low Thrust Trajectory Tool Set

Highly efficient electric propulsion systems can enable interesting classes of missions; unfortunately, they provide only a limited amount of thrust. Low-thrust (LT) trajectories are much more difficult to design than impulsive-type (chemical propulsion) trajectories. Previous low-thrust (LT) trajectory optimization software was often difficult to use, often had difficulties converging, and was somewhat limited in the types of missions it could support. A new state-of-the-art suite (toolbox) of low-thrust (LT) tools along with improved algorithms and methods was developed by NASA's MSFC, JPL, JSC, and GRC to address the needs of our customers to help foster technology development in the areas of advanced LT propulsion systems, and to facilitate generation of similar results by different analysts.

Sims, Jon↗
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 NTRS2014

Lunar Cube Transfer Trajectory Options

Contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these designs can be restricted by the selection of the Cubesat subsystem design such as propulsion or communication. Nonetheless, many trajectory options can be designed with have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several design options including deployment into low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfer orbits. In addition to direct transfer options from these initial orbits, we also investigate the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory. In this article we examine several design options that meet the above limited deployment and subsystem drivers. We study ways that both impulsive and low-thrust Solar Electric Propulsion (SEP) engines can be used to place the Cubesat first into a highly eccentric Earth orbit, enter the Moon's Sphere of Influence, and finally achieve a highly eccentric lunar orbit. We show that such low-thrust transfers are feasible with a realistic micro-thruster model, assuming that the Cubesat can generate sufficient power for the SEP. Two examples are shown here: (1) A Cubestat injected by Exploration Mission 1 (EM-1) then employing low thrust; and (2) a CubSat deployed in a GTO, then employing impulsive maneuvers. For the EM-1 injected initial design, we increase the EM-1 targeted lunar flyby distance to reduce the energy of the lunar flyby to match that of a typical lMoon system heteroclinic manifold. Figure 1 presents an option that encompasses the similar dynamics as that of the ARTEMIS mission design. Low-thrust maneuvers are used along the manifold trajectory to raise perigee to that of a lunar orbit, adjust the timing with respect to the Moon, rotate the line of apsides, and target a ballistic lunar encounter. In this design a second flyby decreases the orbital energy with respect to the Moon, so that C3 -0.1 km2s2. Another design, shown in Figure 2 emanates from a GTO then uses impulsive maneuvers to phase onto a local Earth-Moon manifold, which then transfers the CubeSat to a lunar encounter.

Dynamical System↗
NASA NTRS1998

The Strutjet Rocket Based Combined Cycle Engine

The multi stage chemical rocket has been established over many years as the propulsion System for space transportation vehicles, while, at the same time, there is increasing concern about its continued affordability and rather involved reusability. Two broad approaches to addressing this overall launch cost problem consist in one, the further development of the rocket motor, and two, the use of airbreathing propulsion to the maximum extent possible as a complement to the limited use of a conventional rocket. In both cases, a single-stage-to-orbit (SSTO) vehicle is considered a desirable goal. However, neither the "all-rocket" nor the "all-airbreathing" approach seems realizable and workable in practice without appreciable advances in materials and manufacturing. An affordable system must be reusable with minimal refurbishing on-ground, and large mean time between overhauls, and thus with high margins in design. It has been suggested that one may use different engine cycles, some rocket and others airbreathing, in a combination over a flight trajectory, but this approach does not lead to a converged solution with thrust-to-mass, specific impulse, and other performance and operational characteristics that can be obtained in the different engines. The reason is this type of engine is simply a combination of different engines with no commonality of gas flowpath or components, and therefore tends to have the deficiencies of each of the combined engines. A further development in this approach is a truly combined cycle that incorporates a series of cycles for different modes of propulsion along a flight path with multiple use of a set of components and an essentially single gas flowpath through the engine. This integrated approach is based on realizing the benefits of both a rocket engine and airbreathing engine in various combinations by a systematic functional integration of components in an engine class usually referred to as a rocket-based combined cycle (RBCC) engine. RBCC engines exhibit a high potential for lowering the operating cost of launching payloads into orbit. Two sources of cost reductions can be identified. First, RBCC powered vehicles require only 20% takeoff thrust compared to conventional rockets, thereby lowering the thrust requirements and the replacement cost of the engines. Second, due to the higher structural and thermal margins achievable with RBCC engines coupled with a higher degree of subsystem redundance lower maintenance and operating cost are obtainable.

Siebenhaar, A.↗