Search NASA⌕ Search

SEARCH · Search NASA

Results for “initial guess”

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

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

At least 19 records

Kappa Group: The initial guess. A proposal in response to a commercial air transportation study

Kappa Aerospace presents their Aeroworld Aircraft, the Initial Guess (IG). This aircraft is designed to generate profit in the market which is currently controlled by the train and boat industry. The main priority of the design team was to develop an extremely efficient aircraft that could be sold at a reasonable price. The IG offers a quick and safe alternative to the existing means of transportation at a competitive price. The cruise velocity of 28 ft/sec. allows all flights to be between 20 and 45 minutes, which is a remarkable savings in time compared to travel by boat or train. The IG is propelled by a single Astro-05 engine with a Zinger 10-6 propeller. The Astro-05 is not an extremely powerful engine; however, it provides enough thrust to meet the design and safety requirements. The major advantage of the Astro-05 is that it is the most efficient engine available. The fuel efficiency of the Astro-05 is what puts the aircraft ahead of the competition. The money saved on an efficient engine can be passed on as lower ticket prices or increased revenue. The IG has a payload of 56 passengers and a wingspan of 7 ft. The 7 ft. wingspan allows the aircraft to fit into the gates of all of the cities that are targeted. Future endeavors of Kappa Aerospace will include fitting a stretch version of the IG with a larger propulsion system. This derivative aircraft will be able to carry more passengers and will be placed on the routes which have the greatest demand for travel. The fuselage and empennage are made of a wooden truss configuration, while the wing is made of a rib/spare configuration. The stress carrying elements are made of spruce, the nonstress carrying elements are made of balsa. The wing is removable for easy access into the fuselage. The easy access to the batteries will keep maintenance costs down.

Source record↗

Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools

Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.

design process↗

An Optimal Initial Guess Generator for Entry Interface Targeters

If a pure numerical iterative approach is used, targeting entry interface (EI) conditions for nominal and abort return trajectories or for correction maneuvers can be computationally expensive. This paper describes an algorithm to obtain an optimal impulsive maneuver that generates a trajectory satisfying a set of EI targets: inequality constraints on longitude, latitude and azimuth and a fixed flight-path angle. Most of the calculations require no iterations, making it suitable for real-time applications or large trade studies. This algorithm has been used to generate initial guesses for abort trajectories during Earth-Moon transfers.

Senent, Juan S.↗

End-to-End Mission Design & Trajectory Optimization

Need: A need exists for a generalized, robust, user-friendly and accessible end-to-end mission design optimization tool. Solution: Our solution to developing this capability was to interface two JSC tools—Copernicus and Genesis. Each of these tools has a specific area of the mission design process that it excels at. By utilizing them both, we can gain performance benefits not seen by either on their own. - Copernicus is a trajectory design and optimization software used for in-space trajectories around multiple bodies. - Genesis is a flight mechanics tool used to model ascent, entry, descent, and landing trajectories around a single planetary body. Year 1 was focused on combining these 2 software packages—allowing Copernicus to incorporate the ascent/descent capabilities of Genesis into the optimization problem—and developing this end-to-end mission design capability. Year 2 we focused on increasing the robustness of this capability by building the initial guess generator (IGG), which produces initial guesses based on simplifying assumptions and the physics of the problem. Year 3 of our project focused on utilizing the end-to-end mission design and optimization capabilities developed in the previous 2 years to analyze specific mission scenarios—scaling up from proof of concept to real analyses—capturing any resulting performance benefits, as well as addressing the Big Data challenges we’re faced with—namely, how we’re going to manage and interpret all the data that’s generated.

Kristin Nichols↗

Objective analysis of pseudostress over the Indian Ocean using a direct-minimization approach

A technique not previously used in objective analysis of meteorological data is used here to produce monthly average surface pseudostress data over the Indian Ocean. An initial guess field is derived and a cost functional is constructed with five terms: approximation to initial guess, approximation to climatology, a smoothness parameter, and two kinematic terms. The functional is minimized using a conjugate-gradient technique, and the weight for the climatology term controls the overall balance of influence between the climatology and the initial guess. Results from various weight combinations are presented for January and July 1984. Quantitative and qualitative comparisons to the subject analysis are made to find which weight combination provides the best results. The weight on the approximation to climatology is found to balance the influence of the original field and climatology.

Legler, David M.↗

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.↗

Conversion of Osculating Orbital Elements to Mean Orbital Elements

Orbit determination and ephemeris generation or prediction over relatively long elapsed times can be accomplished with mean elements. The most simple and efficient method for orbit determination, which is also known as epoch point conversion, performs the conversion of osculating elements to mean elements by iterative procedures. Previous epoch point conversion methods are restricted to shorter elapsed times with linear convergence. The new method presented in this paper calculates an analytic initial guess of the unknown mean elements from a first order theory of secular perturbations and computes a transition matrix with accurate numerical partials. It thereby eliminates the problem of an inaccurate initial guess and an identity transition matrix employed by previous methods. With a good initial guess of the unknown mean elements and an accurate transition matrix, converging osculating elements to mean elements can be accomplished over long elapsed times with quadratic convergence.

Der, Gim J.↗

Tests of a procedure for inserting satellite radiance measurements into a numerical circulation model.

Description of experiments designed to test the sensitivity of a new method for retrieving vertical temperature profiles from satellite radiance measurements to the initial guess of temperature distribution. Emphasis is placed on initial guesses of the kind that would be provided by a numerical model of the atmospheric circulation, with the objective of developing a procedure for direct use of satellite radiation measurements as input to a numerical forecasting scheme.

Hogan, J. S.↗

Multiple steady states in atmospheric chemistry

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

Stewart, Richard W.↗

Deriving mesoscale temperature and moisture fields from satellite radiance measurements over the United States

The ability to provide mesoscale temperature and moisture fields from operational satellite infrared sounding radiances over the United States is explored. High-resolution sounding information for mesoscale analysis and forecasting is shown to be obtainable in mostly clear areas. An iterative retrieval algorithm applied to NOAA-VTPR radiances uses a mean radiosonde sounding as a best initial-guess profile. Temperature soundings are then retrieved at a horizontal resolution of about 70 km, as is an indication of the precipitable water content of the vertical sounding columns. Derived temperature values may be biased in general by the initial-guess sounding or in certain areas by the cloud correction technique, but the resulting relative temperature changes across the field when not contaminated by clouds will be useful for mesoscale forecasting and models. The derived moisture, affected only by high clouds, proves to be reliable to within 0.5 cm of precipitable water and contains valuable horizontal information. Present-day applications from polar-orbiting satellites as well as possibilities from upcoming temperature and moisture sounders on geostationary satellites are noted.

Hillger, D. W.↗

Constructing a Database from Multiple 2D Images for Camera Pose Estimation and Robot Localization

The LMDB (Landmark Database) Builder software identifies persistent image features (landmarks) in a scene viewed multiple times and precisely estimates the landmarks 3D world positions. The software receives as input multiple 2D images of approximately the same scene, along with an initial guess of the camera poses for each image, and a table of features matched pair-wise in each frame. LMDB Builder aggregates landmarks across an arbitrarily large collection of frames with matched features. Range data from stereo vision processing can also be passed to improve the initial guess of the 3D point estimates. The LMDB Builder aggregates feature lists across all frames, manages the process to promote selected features to landmarks, and iteratively calculates the 3D landmark positions using the current camera pose estimations (via an optimal ray projection method), and then improves the camera pose estimates using the 3D landmark positions. Finally, it extracts image patches for each landmark from auto-selected key frames and constructs the landmark database. The landmark database can then be used to estimate future camera poses (and therefore localize a robotic vehicle that may be carrying the cameras) by matching current imagery to landmark database image patches and using the known 3D landmark positions to estimate the current pose.

Wolf, Michael↗

Larger Convergence Zones for Newton's Method

Iterative technique applies over wider range of initial guesses. New theorem describes convergence zone of Newton's iterative method for finding zeros of real function. Involves two points, Xp and Xp*, called primary conjugate points. If exact solution lies between these points (Xp is less than Xz is less than Xp*) and no other conjugate points in interval, then according to theorem, subsequent iterations will converge upon exact solution if initial guess lies in interval.

Campbell, C. W.↗

Predictor-Corrector Entry Guidance for Reusable Launch Vehicles

An online entry guidance algorithm has been developed using a predictor-corrector approach. The algorithm is designed for the Reusable Launch Vehicle (RLV) and is demonstrated by using, the X-33 model. The objective of the design is to handle widely dispersed entry conditions and deliver the vehicle at the Terminal Area Energy Management (TAEM) interface box within an acceptable tolerance and without violating any of the vehicle physical constraints. Combination of several control variables is used in testing the performance and computational requirement of the algorithm. The control variables are the bank angle, angle-of-attack and the time for roll reversal. The bank angle and angle-of-attack profiles are the nominal profiles plus the perturbations in each direction. The initial guess of the bank profile is a 45 degrees bank angle with reversal at 360 seconds from liftoff. A six-element state vector is propagated to the TAEM interface box through the integration of the equations of motion (EOM). Altitude, heading and range errors are computed between the desired and the achieved state at the TAEM interface. These errors are used to correct the initial guess of the control variables. This process is repeated until the errors meet an acceptable level at the TAEM interface. Several numerical optimization methods are used to evaluate the convergent property of the predictor-predictor methodology. Successful results are demonstrated using the X-33 model.

Youssef, Hussein↗

Low-Thrust Trajectory Design via Direct Transcription Leveraging Structure from the Low-Thrust Restricted Problem

A primary challenge of low-thrust mission design is the development of an initial guess for the state and control history of a trajectory. To address this challenge, one technique assembles dynamical structures, such as periodic orbits and their associated manifolds, into discontinuous chains that are corrected to locally optimal transfer solutions via direct transcription. In this investigation, dynamical structures that leverage low-thrust in a multi-body regime are incorporated into the orbit chain approach to expand the options available for construction of an initial guess and to guide the direct transcription algorithm toward different categories of locally optimal solutions. The properties and structures of the low-thrust model which facilitate orbit chain construction are demonstrated in representative transfer scenarios. Direct transcription is applied to converge upon locally optimal transfer trajectories in both simplified and ephemeris models. Results indicate that low-thrust dynamical structures offer a promising new catalog of options for use in the orbit chain approach to designing optimal low-thrust trajectories.

Grebow, Daniel↗

Mesoscale temperature and moisture fields from satellite infrared soundings

The combined use of radiosonde and satellite infrared soundings can provide mesoscale temperature and moisture fields at the time of satellite coverage. Radiance data from the vertical temperature profile radiometer on NOAA polar-orbiting satellites can be used along with a radiosonde sounding as an initial guess in an iterative retrieval algorithm. The mesoscale temperature and moisture fields at local 9 - 10 a.m., which are produced by retrieving temperature profiles at each scan spot for the BTPR (every 70 km), can be used for analysis or as a forecasting tool for subsequent weather events during the day. The advantage of better horizontal resolution of satellite soundings can be coupled with the radiosonde temperature and moisture profile both as a best initial guess profile and as a means of eliminating problems due to the limited vertical resolution of satellite soundings.

Hillger, D. W.↗

Semi-analytic preliminary design of low-thrust missions

Using generalized logarithmic spirals to approximate low-thrust trajectories, a new strategy for the design of low-thrust gravity-assist transfers has been developed. Each transfer leg is defined by a semi-analytic model, and its solution is equivalent to a hybrid Lambert’s problem. The method is suitable for approximating both flyby and rendezvous transfer legs. A branch and prune algorithm is used to generate a collection of initial guesses for further optimization. The analytic nature of the low-thrust model simplifies the pruning step, since dynamical and operational constraints (like maximum thrust or total v) can be imposed easily. The solutions obtained with the global search algorithm can be post-processed, filtered, and ranked according to various criteria. This is where the versatility of the method resides, because changing the selection criteria does not require a new search. Selected candidates are then optimized further, in order to generate actual low-thrust orbits. Two mission design examples are presented: an asteroid deflection mission using a kinetic impactor, and a rendezvous mission to Jupiter. These examples are used to analyze the convergence of the optimization stage, in particular how far from the optimal solution the initial guesses are.

Park, Ryan S.↗