Results for “Coordinate transformations” — Page 22

NASA NTRS2012

Optimal Control Modification for Time-Scale Separated Systems

Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.

Adaptive Control↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

Boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗

NASA NTRS1993

Movable Cameras And Monitors For Viewing Telemanipulator

Three methods proposed to assist operator viewing telemanipulator on video monitor in control station when video image generated by movable video camera in remote workspace of telemanipulator. Monitors rotated or shifted and/or images in them transformed to adjust coordinate systems of scenes visible to operator according to motions of cameras and/or operator's preferences. Reduces operator's workload and probability of error by obviating need for mental transformations of coordinates during operation. Methods applied in outer space, undersea, in nuclear industry, in surgery, in entertainment, and in manufacturing.

Diner, Daniel B.↗

NASA NTRS1973

Correlation of ERTS MSS data and earth coordinate systems

Experience has revealed a problem in the analysis and interpretation of ERTS multispectral scanner (MSS) data. The problem is one of accurately correlating ERTS MSS pixels (picture elements) with analysis areas specified on aerial photographs or topographic maps for training recognition computers and/or evaluating recognition results. A computer-aided procedure to correlate coordinates from topographic maps and/or aerial photographs with ERTS data coordinates has been developed. In the procedure, a map transformation from earth coordinates to ERTS scan line and point numbers is calculated using selected ground control points and the method of least squares. The map transformation is then applied to the earth coordinates of selected areas to obtain the corresponding ERTS point and line numbers.

Malila, W. A.↗

NASA NTRS1973

Correlation of ERTS MSS data and earth coordinate systems

The author has identified the following significant results. Experience has revealed a problem in the analysis and interpretation of ERTS-1 multispectral scanner (MSS) data. The problem is one of accurately correlating ERTS-1 MSS pixels with analysis areas specified on aerial photographs or topographic maps for training recognition computers and/or evaluating recognition results. It is difficult for an analyst to accurately identify which ERTS-1 pixels on a digital image display belong to specific areas and test plots, especially when they are small. A computer-aided procedure to correlate coordinates from topographic maps and/or aerial photographs with ERTS-1 data coordinates has been developed. In the procedure, a map transformation from earth coordinates to ERTS-1 scan line and point numbers is calculated using selected ground control points nad the method of least squares. The map transformation is then applied to the earth coordinates of selected areas to obtain the corresponding ERTS-1 point and line numbers. An optional provision allows moving the boundaries of the plots inward by variable distances so the selected pixels will not overlap adjacent features.

Malila, W. A.↗

NASA NTRS2011

Geometric registration of images by similarity transformation using two reference points

A method for registering a first image to a second image using a similarity transformation. The each image includes a plurality of pixels. The first image pixels are mapped to a set of first image coordinates and the second image pixels are mapped to a set of second image coordinates. The first image coordinates of two reference points in the first image are determined. The second image coordinates of these reference points in the second image are determined. A Cartesian translation of the set of second image coordinates is performed such that the second image coordinates of the first reference point match its first image coordinates. A similarity transformation of the translated set of second image coordinates is performed. This transformation scales and rotates the second image coordinates about the first reference point such that the second image coordinates of the second reference point match its first image coordinates.

Kang, Yong Q.↗

NASA NTRS1976

Transformation from proper time on earth to coordinate time in solar system barycentric space-time frame of reference

An expression was derived for the time transformation t - tau, where t is coordinate time in the solar system barycentric space-time frame of reference and tau is proper time obtained from a fixed atomic clock on earth. This transformation is suitable for use in the computation of high-precision earth-based range and Doppler observables of a spacecraft or celestial body located anywhere in the solar system; it can also be used in obtaining computed values of very long baseline interferometry data types. The formulation for computing range and Doppler observables, which is an explicit function of the transformation t - tau, is described briefly.

Moyer, T. D.↗

NASA NTRS1981

Measurements of Aerodynamic Damping in the MIT Transonic Rotor

A method was developed and demonstrated for the direct measurement of aerodynamic forcing and aerodynamic damping of a transonic compressor. The method is based on the inverse solution of the structural dynamic equations of motion of the blade disk system in order to determine the forces acting on the system. The disturbing and damping forces acting on a given blade are determined if the equations of motion are expressed in individual blade coordinates. If the structural dynamic equations are transformed to multiblade coordinates, the damping can be measured for blade disk modes, and related to a reduced frequency and interblade phase angle. In order to measure the aerodynamic damping in this way, the free response to a known excitation is studied.

Crawley, E. F.↗

NASA NTRS1975

Reference systems and transformations

The verification accomplished to assure correct computation of the many geometrical relationships between the several coordinate systems and transformation matrices defined for the Saturn 1B mission was discussed. This is accomplished by demonstrating the following: (1) the program has the ability to correctly establish the initial vector coordinate system from external input data for use as a reference, (2) the program logic is capable of properly executing the calculations necessary to transform vectorial parameters from one coordinate system to another, and (3) the presettings used for vector component calculations are valid.

Source record↗

NASA NTRS1991

A controls engineering approach for analyzing airplane input-output characteristics

An engineering approach for analyzing airplane control and output characteristics is presented. State-space matrix equations describing the linear perturbation dynamics are transformed from physical coordinates into scaled coordinates. The scaling is accomplished by applying various transformations to the system to employ prior engineering knowledge of the airplane physics. Two different analysis techniques are then explained. Modal analysis techniques calculate the influence of each system input on each fundamental mode of motion and the distribution of each mode among the system outputs. The optimal steady state response technique computes the blending of steady state control inputs that optimize the steady state response of selected system outputs. Analysis of an example airplane model is presented to demonstrate the described engineering approach.

Arbuckle, P. Douglas↗

NASA NTRS2019

A Streamlined Approach to Spatial Mapping of Complex 3D Thermal Boundary Condition Data

Spatial mapping of 1D, 2D, and particularly 3D thermal boundary condition data is essential for accurate thermal simulation of spacecraft and launch vehicles. This information typically is available in simple ASCII file format but can be problematic to use for thermal simulations. Difficulties that can be encountered include the ability to directly use the available file format, transformation of the data into the desired reference coordinate system in 3D space, and accurate interpolation of the data onto the thermal calculation domain. This paper presents a streamlined approach to spatial mapping of complex unsymmetrical 3D cold wall heat flux data using the fields’ capability in Simcenter3D. A recent example of 3D thermal plume simulation at MSFC will be employed to illustrate the use of text, csv, and Excel files, specifying coordinate systems for transformation of data in 3D space, and use of the various interpolation schemes available for spatial mapping. Spatial boundary condition verification is also very important, and the spacecraft thermal analyst needs effective visualization tools to develop confidence in the boundary condition definitions. Visualization of the spacecraft plume raw field data, the calculated field data, and the interpolated field data onto the thermal calculation domain will be discussed, with a particular focus on real-time viewing of the interpolated data for available interpolation schemes. The objective of this paper is to outline the modeling techniques used with the integrated thermal analysis of a terrestrial lunar lander demonstrator. Specifically, the techniques outlined herein focus on spatial mapping of convective and radiative exhaust plume results from a computational fluid dynamics (CFD) analysis. Two cases were investigated, however, the modeling techniques that were utilized translate to both cases seamlessly. Those two cases were as follows: • Lunar lander demonstrator firing on-pad (worst case). • Lunar lander demonstrator hovering at an elevated position above the launch pad. For the purposes of information control, this paper will focus on the modeling techniques only, using altered or dimensionless data where necessary. BACKGROUND The thermal model examined in this paper is of the lunar lander demonstrator known as XL-1T (terrestrial), born from a collaborative effort between Masten Space Systems (MSS) and NASA, under NASA’s Lunar CATALYST (also known as Lunar Cargo Transportation and Landing by Soft Touchdown) initiative. The lander is a reusable vertical takeoff/vertical landing (VTVL) test bed which is controlled by four throttleable main engines utilizing green hypergolic propellants.

Hawkins, Robert F.↗

NASA NTRS1993

Astrometric Models of the Phobos Orbiter TV Cameras

Astrometric models of the 3 Phobos Orbiter TV cameras, their pointing in inertial space, the position of the Phobos Orbiter with respect to Mars, Phobos and Deimos, and transformations from inertial to body-fixed coordinates are needed to transform between the image coordinates of a picture element (.

Mars Phobos Deimos TV images↗

NASA NTRS1971

Geomagnetic potential in dipole coordinates

International geomagnetic reference field 1965 geomagnetic potential rate of change and transformation to dipole coordinates

Stern, D. P.↗

NASA NTRS1973

Use of ERTS data for a multidisciplinary analysis of Michigan resources

The author has identified the following significant results. A computerized procedure has been developed to correlate coordinates from topographic maps and/or aerial photographs with ERTS data coordinates. Application to data from other multispectral scanners is anticipated. In the procedure, a map transformation from earth coordinates to ERTS point and line numbers is calculated using selected ground control points and the method of least squares. The map transformation is then applied to the earth coordinates of selected areas to obtain the corresponding ERTS point and line numbers. An optional provision allows moving the boundaries of the plots inwards by variable distances (typically half a resolution element) so the selected pixels will not overlap adjacent features.

Anderson, A. L.↗

NASA NTRS2022

Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits

The purpose and direction of this document is to provide U.S. government agencies, specifically National Aeronautics and Space Administration (NASA) and Department of Defense (DoD) space related centers, with a foundational summary of astrodynamics concepts for trajectory design, navigation, and operations in the cislunar, lunar, and libration point regions. This document is provided in response to an Interagency Agreement (IAA) between NASA and the National Geospatial-Intelligence Agency (NGA). With applications to these regions of the Earth-Moon system, this document summarizes: the definitions of standard and unique coordinate systems for Positioning, Navigation, Timing and targeting (PNT), transformations between those coordinate frames, definitions of common time systems, a description of numerical integration, description of a widely-used and approximate dynamical model of a three-body system for preliminary analysis and nomenclature definition, description of higher-fidelity models of cislunar space, and the application of these concepts to sample scenarios with a focus on common steps in trajectory and maneuver design for a spacecraft in cislunar space. This information is critical to mission design and navigation far above the geosynchronous orbit region, where lunar perturbations are required to be modeled accurately and consistently but render trajectory design and analysis a complex procedure. Software tools such as the Goddard Space Flight Center (GSFC) open source General Mission Analysis Tool (GMAT) is used as a reference, along with a wide variety of resources constructed by NASA and other government agencies, academia, and industry, for mathematical specifications and practical considerations. This document has been prepared by and under the auspices of NASA. The GSFC Mission Engineering and Systems Analysis (MESA) Division (Code 590) and the Navigation and Mission Design Branch (Code 595) are part of NASA. Their engineers and scientists have expertise in lunar, cislunar, and libration point region trajectory guidance and navigation and timing. NASA GSFC has supported many successful lunar and cislunar missions over the past several decades. These missions include the Lunar Reconnaissance Orbiter (LRO), the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft, Transiting Exoplanet Survey Satellite (TESS), Lunar Prospector, Lunar Crater Observation and Sensing Satellite (LCROSS), Clementine, and several Sun-Earth libration point missions such as WIND and Deep Space Climate Observatory (DSCOVR), dating back four decades. NASA GSFC also supports the upcoming Gateway lunar mission, the Artemis Lunar Program and Human Landing Systems, and leads both the Lunar IceCube low thrust mission and concept design for the Lunar Communication Relay and Navigation System (LCRNS).

Lunar, CisLunar, Libration, trajectory dynamics, p↗

NASA NTRS1992

Recognizing Patterns In Log-Polar Coordinates

Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.

Weiman, Carl F. R.↗