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All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Measuring Positions of Objects using Two or More Cameras

An improved method of computing positions of objects from digitized images acquired by two or more cameras (see figure) has been developed for use in tracking debris shed by a spacecraft during and shortly after launch. The method is also readily adaptable to such applications as (1) tracking moving and possibly interacting objects in other settings in order to determine causes of accidents and (2) measuring positions of stationary objects, as in surveying. Images acquired by cameras fixed to the ground and/or cameras mounted on tracking telescopes can be used in this method. In this method, processing of image data starts with creation of detailed computer- aided design (CAD) models of the objects to be tracked. By rotating, translating, resizing, and overlaying the models with digitized camera images, parameters that characterize the position and orientation of the camera can be determined. The final position error depends on how well the centroids of the objects in the images are measured; how accurately the centroids are interpolated for synchronization of cameras; and how effectively matches are made to determine rotation, scaling, and translation parameters. The method involves use of the perspective camera model (also denoted the point camera model), which is one of several mathematical models developed over the years to represent the relationships between external coordinates of objects and the coordinates of the objects as they appear on the image plane in a camera. The method also involves extensive use of the affine camera model, in which the distance from the camera to an object (or to a small feature on an object) is assumed to be much greater than the size of the object (or feature), resulting in a truly two-dimensional image. The affine camera model does not require advance knowledge of the positions and orientations of the cameras. This is because ultimately, positions and orientations of the cameras and of all objects are computed in a coordinate system attached to one object as defined in its CAD model.

Klinko, Steve↗
NASA NTRS1993

Small Business Innovations

Under an Army Small Business Innovation Research (SBIR) grant, Symbiotics, Inc. developed a software system that permits users to upgrade products from standalone applications so they can communicate in a distributed computing environment. Under a subsequent NASA SBIR grant, Symbiotics added additional tools to the SOCIAL product to enable NASA to coordinate conventional systems for planning Shuttle launch support operations. Using SOCIAL, data may be shared among applications in a computer network even when the applications are written in different programming languages. The product was introduced to the commercial market in 1993 and is used to monitor and control equipment for operation support and to integrate financial networks. The SBIR program was established to increase small business participation in federal R&D activities and to transfer government research to industry. InQuisiX is a reuse library providing high performance classification, cataloging, searching, browsing, retrieval and synthesis capabilities. These form the foundation for software reuse, producing higher quality software at lower cost and in less time. Software Productivity Solutions, Inc. developed the technology under Small Business Innovation Research (SBIR) projects funded by NASA and the Army and is marketing InQuisiX in conjunction with Science Applications International Corporation (SAIC). The SBIR program was established to increase small business participation in federal R&D activities and to transfer government research to industry.

Source record↗
NASA NTRS2001

Factorizable Upwind Schemes: the Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid was introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation, without explicitly mentioning a particular coordinate frame. We describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Nielsen, Eric J.↗
NASA NTRS2001

Factorizable Upwind Schemes: The Triangular Unstructured Grid Formulation

The upwind factorizable schemes for the equations of fluid were introduced recently. They facilitate achieving the Textbook Multigrid Efficiency (TME) and are expected also to result in the solvers of unparalleled robustness. The approach itself is very general. Therefore, it may well become a general framework for the large-scale, Computational Fluid Dynamics. In this paper we outline the triangular grid formulation of the factorizable schemes. The derivation is based on the fact that the factorizable schemes can be expressed entirely using vector notation. without explicitly mentioning a particular coordinate frame. We, describe the resulting discrete scheme in detail and present some computational results verifying the basic properties of the scheme/solver.

Sidilkover, David↗
NASA NTRS2002

Application of the generalized vertical coordinate ocean model for better representing satellite data

It is found that two adaptive parametric functions can be introduced into the basic ocean equations for utilizing the optimal or hybrid features of commonly used z-level, terrain- following, isopycnal, and pressure coordinates in numerical ocean models. The two parametric functions are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara (1 974), the Jacobian pressure gradient formulation of Song (1 998), and a newly developed metric factor that permits both compressible (non-Boussinesq) and incompressible (Boussinesq) approximations. Based on the new formulation, an adaptive modeling strategy is proposed and a staggered finite volume method is designed to ensure conservation of important physical properties and numerical accuracy. Implementation of the combined techniques to SCRUM (Song and Haidvogel1994) shows that the adaptive modeling strategy can be applied to any existing ocean model without incurring computational expense or altering the original numerical schemes. Such a generalized coordinate model is expected to benefit diverse ocean modelers for easily choosing optimal vertical structures and sharing modeling resources based on a common model platform. Several representing oceanographic problems with different scales and characteristics, such as coastal canyons, basin-scale circulation, and global ocean circulation, are used to demonstrate the model's capability for multiple applications. New results show that the model is capable of simultaneously resolving both Boussinesq and non-Boussinesq, and both small- and large-scale processes well. This talk will focus on its applications of multiple satellite sensing data in eddy-resolving simulations of Asian Marginal Sea and Kurosio. Attention will be given to how Topex/Poseidon SSH, TRMM SST; and GRACE ocean bottom pressure can be correctly represented in a non- Boussinesq model.

numerical ocean model generalized coordinate syste↗
NASA NTRS1978

On the use of co-ordinate stretching in the numeral computation of high frequency scattering

The scattering of the sound of a jet engine by an airplane fuselage is modeled by solving the axially symmetric Helmholtz equation exterior to a long thin ellipsoid. The integral equation method based on the single layer potential formulation is used. A family of coordinate systems on the body is introduced and an algorithm is presented to determine the optimal coordinate system. Numerical results verify that the optimal choice enables the solution to be computed with a grid that is coarse relative to the wavelength.

Bayliss, A.↗
NASA NTRSDate not supplied

Feasibility Study of Distributed Decision-Making on the Edge for Urban Air Mobility

The Concept of Operations for Urban Air Mobility (UAM) put forward by FAA, NASA, and several industry stakeholders acknowledges the diversity and complexity in UAM operations and, thereby, envisions a federated architecture for UAM management. In this architecture, the decision-making is distributed to a set of service providers who collectively manage the shared airspace usage by different stakeholders. This notionally brings autonomy closer to the UAM businesses and encourages to explore the feasibility of decision making on the very edge, which is the topic of the presented research. This paper reports research conducted on the hypothesis based on which the residual compute capability onboard smart unmanned aerial systems (UASs) is utilized to build situational awareness and resolve conflicts by passive and active coordination among multiple UASs, thereby implementing a layer of distributed autonomy in UAM. Key features of the edge-computing approach involve inter-UAS information exchange, independent assessment of own flight and environmental conditions, and estimation of other UASs’ flight preferences, incorporating machine learning techniques in the last two. Parallel computing on portable graphics processing unit (GPU) enables the machine learning workflow on the edge. A custom-built 3D simulator is used to evaluate the efficacy of the distributed decision-making on the edge. Each edge node, representing a smart UAS, connects to the simulator from a remote location and independently controls the behavior of the corresponding virtual asset in the simulator, analogous to participants in an online multi-player game. The presented edge-computing-based distributed decision-making framework is envisioned to pave the way for collective mobility of autonomous air vehicles in the future shared airspace, while allowing the inclusion of the business preferences of the UAS operators within allowed regulatory limits.

Edge computing↗
NASA NTRSDate not supplied

Feasibility Study of Distributed Decision-Making on the Edge for Urban Air Mobility

The Concept of Operations for Urban Air Mobility (UAM) put forward by FAA, NASA, and several industry stakeholders acknowledges the diversity and complexity in UAM operations and, thereby, envisions a federated architecture for UAM management. In this architecture, the decision-making is distributed to a set of service providers who collectively manage the shared airspace usage by different stakeholders. This notionally brings autonomy closer to the UAM businesses and encourages to explore the feasibility of decision making on the very edge, which is the topic of the presented research. This paper reports research conducted on the hypothesis based on which the residual compute capability onboard smart unmanned aerial systems (UASs) is utilized to build situational awareness and resolve conflicts by passive and active coordination among multiple UASs, thereby implementing a layer of distributed autonomy in UAM. Key features of the edge-computing approach involve inter-UAS information exchange, independent assessment of own flight and environmental conditions, and estimation of other UASs’ flight preferences, incorporating machine learning techniques in the last two. Parallel computing on portable graphics processing unit (GPU) enables the machine learning workflow on the edge. A custom-built 3D simulator is used to evaluate the efficacy of the distributed decision-making on the edge. Each edge node, representing a smart UAS, connects to the simulator from a remote location and independently controls the behavior of the corresponding virtual asset in the simulator, analogous to participants in an online multi-player game. The presented edge-computing-based distributed decision-making framework is envisioned to pave the way for collective mobility of autonomous air vehicles in the future shared airspace, while allowing the inclusion of the business preferences of the UAS operators within allowed regulatory limits.

Edge computing↗
NASA NTRS1982

The reduction, verification and interpretation of MAGSAT magnetic data over Canada

Consideration is being given to representing the magnetic field in the area 40 deg N to 83 deg N by means of functions in spherical coordinates. A solution to Laplace's equation for the magnetic potential over a restricted area was found, and programming and testing are currently being carried out. Magnetic anomaly modelling is proceeding. The program SPHERE, which was adapted to function correctly on the Cyber computer, is now operational, for deriving gravity and magnetic models in a spherical coordinate system.

Coles, R. L.↗
NASA NTRS1972

Geometric field-line calculations

Procedure for calculating three components of vector field from spherical harmonic using either geocentric or geodetic coordinates as input and output is described. Three subroutines of computer program are explained. Program is written in FORTRAN for IBM 360 computer.

Stassinopoulos, E. G.↗
NASA NTRS1972

Numerical calculation of transonic flow about swept wings.

Description of a mixed elliptic-hyperbolic relaxation algorithm which calculates solutions to the three-dimensional, nonlinear transonic small disturbance potential equation for flows about thin swept lifting wings with free-stream Mach number less than 1. The algorithm is designed to treat supercritical flows, including cases with embedded shock waves. Nonrectangular planform shapes, including sweep and taper, are treated by a coordinate transformation which maps the wing planform into a rectangle. Computed results at angles of attack of 0 and 2 deg for a AR = 4, constant chord, 23.75 deg sweptback planform model with a Lockheed C141 airfoil section are compared with data obtained experimentally for both subcritical and supercritical flows. Subcritical results are also compared with those obtained by a subsonic 'panel' method.

Ballhaus, W. F.↗
NASA NTRS1974

Orientational invariance of the rotational transition probability in the sudden approximation

Semiclassical collisions of an atom with a rigid-rotor molecule are examined in the sudden approximation. The rotational transition probability is shown to be invariant with respect to the choice of orientation for the molecular coordinate system; this fact contradicts recently reported results of a computer analysis. The present analysis may lead to an improved interpretation of recent molecular beam measurements.

Stallcop, J. R.↗
NASA NTRS1977

Numerical solution of three-dimensional free turbulent shear flows

Numerical results are presented for three-dimensional compressible turbulent jet and wake flows. An alternating direction implicit numerical procedure is used to solve the finite-difference form of the parabolic elliptic Navier-Stokes equations. A coordinate transformation maps the boundaries at infinity into a finite computational domain in order to properly specify infinity boundary conditions as well as contain the downstream growth of the viscous flow field in a fixed computational grid. Turbulence closure is achieved through an algebraic mixing length eddy viscosity model. Numerical results for supersonic flow are presented for an axisymmetric jet, an elliptical jet, an elliptical wake, and two interacting rectangular jets. Experimental data were not available for comparison with the numerical results. However, the results compare well with empirical results for free shear flows.

Oh, Y. H.↗
NASA NTRS1978

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗
NASA NTRS1978

Computation of acoustic waves in a jet

A numerical treatment of acoustic waves in a jet is described. The full time dependent Euler equations are used in both linear and nonlinear formulations. The computational region of integration is artificially bounded and boundary conditions are developed to simulate outgoing waves and to enable the computational domain to be substantially restricted. Higher order methods and coordinate transformations are introduced to further reduce the number of grid points as well as to increase the efficiency of the program. Numerical results are presented for time harmonic sources as well as for sources with more complicated time dependence.

Bayliss, A.↗
NASA NTRS1979

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Robinson, J. C.↗