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NASA NTRS1982

Singular perturbation techniques for real time aircraft trajectory optimization and control

The usefulness of singular perturbation methods for developing real time computer algorithms to control and optimize aircraft flight trajectories is examined. A minimum time intercept problem using F-8 aerodynamic and propulsion data is used as a baseline. This provides a framework within which issues relating to problem formulation, solution methodology and real time implementation are examined. Theoretical questions relating to separability of dynamics are addressed. With respect to implementation, situations leading to numerical singularities are identified, and procedures for dealing with them are outlined. Also, particular attention is given to identifying quantities that can be precomputed and stored, thus greatly reducing the on-board computational load. Numerical results are given to illustrate the minimum time algorithm, and the resulting flight paths. An estimate is given for execution time and storage requirements.

Calise, A. J.↗

NASA NTRS1981

Modification to Scott's method for direct integration of gaseous transmission to improve speed and accuracy

Two limitations to the method of Scott for rapid direct integration of gaseous transmission in a finite spectral interval over an inhomogeneous optical path are discussed. One of these is the inability to use a precomputed form of the Voigt line shape, which can be parameterized via the linewidth alone. This is rectified using the Voigt shape approximation of Kielkopf, which involves a linear combination of three functions which can be pre-computed: the Lorentz shape, the Doppler shape and a correction function. The other limitation involves situations where lines must be treated individually, either line positions must be known with great precision or a uniform value for the widths of all lines in the spectral interval does not describe the transmission adequately. In this case, the strongest lines are treated individually, while the remainder are treated assuming uniform line widths and line positions coincident with positions on the frequency grid, i.e. following Scott's method directly.

Orton, G. S.↗

NASA NTRS1983

Accelerometer-enhanced orbit control near the sun-earth L1 libration point

Because the halo-orbit about the sun-earth L(1) libration point in which the satellite ISEE-3 was maintained for nearly four years is unstable, a loose control scheme about a precomputed nominal path was implemented which required orbit maneuvers approximately every three months. Execution errors were minimized by processing on-board accelerometer telemetry data in real time, and adjusting the maneuvers. Because spacecraft vibrations caused oscillations in the accelerometer data, smoothing techniques were applied to provide accurate estimates of the performance of pulse mode thrusters employed in the spin stabilization of the spacecraft. It has been found that the processed accelerometer data has an average error of only + or - 1.3 per cent.

Muhonen, D. P.↗

NASA NTRS1984

Feedback laws for fuel minimization for transport aircraft

The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

Price, D. B.↗

NASA NTRS1984

Method and apparatus for self-calibration and phasing of array antenna

A technique for self-calibrating and phasing a lens-feed array antenna, while normal operation is stopped, utilizes reflected energy of a continuous and coherent wave broadcast by a transmitter through a central feed while a phase controller advances the phase angles of reciprocal phase shifters in radiation electronics of the array elements at different rates to provide a distinct frequency modulation of electromagnetic wave energy returned by reflection in one mode and leakage in another mode from the radiation electronics of each array element. The composite return signal received by a synchronous receiver goes through a Fourier transform processing system and produces a response function for each antenna element. Compensation of the phase angles for the antenna elements required to conform the antenna response to a precomputed array pattern is derived from the reciprocal square root of the response functions for the antenna elements which, for a rectangular array of NXM elements, is a response function T(n,m). A third mode of calibration uses an external pilot tone from a separate antenna element. Respective responses are thus obtained from the three modes of calibration.

Wu, C.↗

NASA NTRS1985

Method and apparatus for transfer function simulator for testing complex systems

A method and apparatus for testing the operation of a complex stabilization circuit in a closed loop system is presented. The method is comprised of a programmed analog or digital computing system for implementing the transfer function of a load thereby providing a predictable load. The digital computing system employs a table stored in a microprocessor in which precomputed values of the load transfer function are stored for values of input signal from the stabilization circuit over the range of interest. This technique may be used not only for isolating faults in the stabilization circuit, but also for analyzing a fault in a faulty load by so varying parameters of the computing system as to simulate operation of the actual load with the fault.

Kavaya, M. J.↗

NASA NTRS1983

Broadband transmission functions for atmospheric IR flux computations and climate studies

In order to reduce the size of precomputed tables which are used in the emissivity approach to computing IR radiation in a climate model, the three-dimensional transmission function in the water vapor bands is defined in this study by a simple regression equation consisting of three two-dimensional parameters. The transmittances in the 9.6 and 15 micron bands are individually parameterized as functions of the amount of scaled absorber. This approach can thus be applied to atmospheres with a variable CO2 concentration.

Chou, M.-D.↗

NASA NTRS1984

Region-based modeling algorithms for remotely-sensed data

Five algorithms being developed for performing region-based modeling operations on classified remotely-sensed images are described. The first algorithm converts images from standard grid structure into topological grid structure, while the remaining algorithms act upon topologically grid-structured images to perform region-based relabelling, overlaying, distance searching, and neighborhood scanning operations. The use of precomputed topological information, through the use of topological grid structure, makes region-based algorithms highly accessible to earth scientists.

Goldberg, M.↗

NASA NTRS1986

Discrete-time Markovian-jump linear quadratic optimal control

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.↗

NASA NTRS1988

Real time pipelined system for forming the sum of products in the processing of video data

A 3-by-3 convolver utilizes 9 binary arithmetic units connected in cascade for multiplying 12-bit binary pixel values P sub i which are positive or two's complement binary numbers by 5-bit magnitide (plus sign) weights W sub i which may be positive or negative. The weights are stored in registers including the sign bits. For a negative weight, the one's complement of the pixel value to be multiplied is formed at each unit by a bank of 17 exclusive or gates G sub i under control of the sign of the corresponding weight W sub i, and a correction is made by adding the sum of the absolute values of all the negative weights for each 3-by-3 kernel. Since this correction value remains constant as long as the weights are constant, it can be precomputed and stored in a register as a value to be added to the product PW of the first arithmetic unit.

Wilcox, Brian↗

NASA NTRS1989

A few modeling and rendering techniques for computer graphics and their implementation on ultra hardware

Ultra network is a recently installed very high speed graphic hardware at NASA Langley Research Center. The Ultra Network interfaced to Voyager through its HSX channel is capable of transmitting up to 800 million bits of information per second. It is capable of displaying fifteen to twenty frames of precomputed images of size 1024 x 2368 with 24 bits of color information per pixel per second. Modeling and rendering techniques are being developed in computer graphics and implemented on Ultra hardware. A ray tracer is being developed for use at the Flight Software and Graphic branch. Changes were made to make the ray tracer compatible with Voyager.

Bidasaria, Hari↗

NASA NTRS1988

Interactive grid generation for fighter aircraft geometries

An interactive procedure to construct grids about fighter aircraft configurations using a 'state-of-the-art' workstation is described. A multiple-block grid topology is used to minimize grid skewness. Grid points on the surface of a configuration are precomputed and stored on the faces of appropriate blocks. Grid points at intermediate and far field boundary surfaces are computed with analytical functions and stored on appropriate faces. Grid points in the interior of blocks are computed using transfinite interpolation with Lagrangian and exponential blending functions. Interactive software has been written for the IRIS 3030 graphics workstation to control the shape and spacing of grid points on intermediate and far field boundaries, and to control the interior interpolation.

Smith, Robert E.↗

NASA NTRS1989

Digital filter design for radar image formation

Novel weighted-least-squares approaches to the design of digital filters for SAR applications are presented. The filters belong to three different categories according to their combinations of minimax passband, least-squares stopband, minimax stopband, and maximally-flat passband. For real-time applications, it is important to design the sets of digital filter coefficient tables in an offline environment; the appropriate precomputed filter is then selected for each SAR signal-processing function, as a function of both mode and mapping geometry during real-time processing.

Adams, John W.↗

NASA NTRS1989

An optimal recursive filter for the attitude determination of the Spacelab instrument pointing subsystem

The instrument pointing subsystem (IPS) is a three-axis stabilized platform developed to point various astronomical observation instruments aboard NASA's Shuttle. In order to compensate for system drifts and attitude errors, the IPS utilizes a linearized Kalman filter (LKF) with precomputed gains. Since the a priori gains are generated for an expected system configuration, any system variations result in a suboptimal estimation process. The performance of two real-time estimation filters is compared with that of the current LKF implementation. It is shown that a real-time estimation filter that reduces sensitivity to system variations and preflight computations is feasible.

West, Mark E.↗

NASA NTRS1990

Programmable remapper with single flow architecture

The invention relates to image processing systems and methods and in particular to a machine which accepts a real time video image in the form of a matrix of picture elements (pixels) and remaps such image according to a selectable one of a plurality of mapping functions to create an output matrix of pixels. Such mapping functions, or transformations, may be any one of a number of different transformations depending on the objective of the user of the system. The system remaps input images from one coordinate system to another using a set of look-up tables for the data necessary for the transform. The transforms, which are operator selectable, are precomputed and loaded into massive look-up tables. Input pixels, via the look-up tables of any particular transform selected, are mapped into output pixels with the radiance information of the input pixels being appropriately weighted. An earlier embodiment of the system included two parallel processors: a collective processor which mapped multiple input pixels into a single output pixel and an interpolative processor. The interpolative processor performed an interpolation among pixels in the input image where a given input pixel may affect the value of many output pixels. Several advantages are provided over previous embodiments in that the two distinct processors are replaced by a single processor capable of performing both types of operations (collective and interpolative) with no more complexity. Previously, there has existed no image processor or 'remapper' that can operate with sufficient speed and flexibility to permit investigating different transformation patterns in real time.

Fisher, Timothy E.↗

NASA NTRS1991

Planning and executing motions for multibody systems in free-fall

The purpose of this research is to develop an end-to-end system that can be applied to a multibody system in free-fall to analyze its possible motions, save those motions in a database, and design a controller that can execute those motions. A goal is for the process to be highly automated and involve little human intervention. Ideally, the output of the system would be data and algorithms that could be put in ROM to control the multibody system in free-fall. The research applies to more than just robots in space. It applies to any multibody system in free-fall. Mathematical techniques from nonlinear control theory were used to study the nature of the system dynamics and its possible motions. Optimization techniques were applied to plan motions. Image compression techniques were proposed to compress the precomputed motion data for storage. A linearized controller was derived to control the system while it executes preplanned trajectories.

Cameron, Jonathan M.↗

NASA NTRS1991

Infrared radiation parameterizations in numerical climate models

This study presents various approaches to parameterizing the broadband transmission functions for utilization in numerical climate models. One-parameter scaling is applied to approximate a nonhomogeneous path with an equivalent homogeneous path, and the diffuse transmittances are either interpolated from precomputed tables or fit by analytical functions. Two-parameter scaling is applied to parameterizing the carbon dioxide and ozone transmission functions in both the lower and middle atmosphere. Parameterizations are given for the nitrous oxide and methane diffuse transmission functions.

Chou, Ming-Dah↗

NASA NTRS1991

Calculations of transmission functions in the infrared CO2 and O3 bands

An efficient method for computing the transmission function in the 15-micron CO2 and the 9.6-micron O3 bands is presented. An inhomogeneous atmospheric path is treated as homogeneous by applying simple pressure and temperature scaling approximations. The transmission functions are then derived from small precomputed tables. Because the atmospheric cooling rate is primarily contributed from adjacent layers, the simple scaling approximations can be used to accurately compute transmission functions in both the middle and lower atmosphere. Applying the parameterization to vastly different atmospheric conditions, the difference with line-by-line calculations is small. In the region between 0.01 mbar and the earth's surface, the cooling rate difference is less than 0.3 C/d in the 15-micron CO2 band and less than 0.1 C/d in the 9.6-micron O3 band.

Chou, Ming-Dah↗