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At least 91 records · Page 5

Vehicle path-planning in three dimensions using optics analogs for optimizing visibility and energy cost

Path planning is an important issue for space robotics. Finding safe and energy-efficient paths in the presence of obstacles and other constraints can be complex although important. High-level (large-scale) path planning for robotic vehicles was investigated in three-dimensional space with obstacles, accounting for: (1) energy costs proportional to path length; (2) turn costs where paths change trajectory abruptly; and (3) safety costs for the danger associated with traversing a particular path due to visibility or invisibility from a fixed set of observers. Paths optimal with respect to these cost factors are found. Autonomous or semi-autonomous vehicles were considered operating either in a space environment around satellites and space platforms, or aircraft, spacecraft, or smart missiles operating just above lunar and planetary surfaces. One class of applications concerns minimizing detection, as for example determining the best way to make complex modifications to a satellite without being observed by hostile sensors; another example is verifying there are no paths (holes) through a space defense system. Another class of applications concerns maximizing detection, as finding a good trajectory between mountain ranges of a planet while staying reasonably close to the surface, or finding paths for a flight between two locations that maximize the average number of triangulation points available at any time along the path.

Rowe, Neil C.↗

Vector magnetic field measurements along a cooled stereo-imaged coronal loop

The variation of the vector magnetic field along structures in the solar corona remains unmeasured. Using a unique combination of spectropolarimetry and stereoscopy, we infer and compare the vector magnetic field structure and three-dimensional morphology of an individuated coronal loop structure undergoing a thermal instability. We analyze spectropolarimetric data of the He i λ10830 triplet (1s2s{sup 3}S{sub 1}−1s2p{sup 3}P{sub 2,1,0}) obtained at the Dunn Solar Telescope with the Facility Infrared Spectropolarimeter on 2011 September 19. Cool coronal loops are identified by their prominent drainage signatures in the He i data (redshifts up to 185 km s{sup −1}). Extinction of EUV background radiation along these loops is observed by both the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory and the Extreme Ultraviolet Imager on board spacecraft A of the Solar Terrestrial Relations Observatory, and is used to stereoscopically triangulate the loop geometry up to heights of 70 Mm (0.1R {sub Sun}) above the solar surface. The He i polarized spectra along this loop exhibit signatures indicative of atomic-level polarization, as well as magnetic signatures through the Hanle and Zeeman effects. Spectropolarimetric inversions indicate that the magnetic field is generally oriented along the coronal loop axis, and provide the height dependence of the magnetic field intensity. The technique we demonstrate is a powerful one that may help better understand the thermodynamics of coronal fine-structure magnetism.

79 ASTRONOMY AND ASTROPHYSICS↗

SUN-TO-EARTH CHARACTERISTICS OF THE 2012 JULY 12 CORONAL MASS EJECTION AND ASSOCIATED GEO-EFFECTIVENESS

We analyze multi-spacecraft observations associated with the 2012 July 12 coronal mass ejection (CME), covering the source region on the Sun from the Solar Dynamics Observatory , stereoscopic imaging observations from the Solar Terrestrial Relations Observatory ( STEREO ), magnetic field characteristics from Mercury Surface, Space Environment, Geochemistry, and Ranging ( MESSENGER ), and type II radio burst and in situ measurements from Wind . A triangulation method based on STEREO stereoscopic observations is employed to determine the kinematics of the CME, and the outcome is compared with the results derived from the type II radio burst using a solar wind electron density model. A Grad–Shafranov technique is applied to Wind in situ data to reconstruct the flux-rope structure and compare it with the observations of the solar source region, which helps in understanding the geo-effectiveness associated with the CME structure. Our conclusions are as follows: (1) the CME undergoes an impulsive acceleration, a rapid deceleration before reaching MESSENGER , and then a gradual deceleration out to 1 au, which should be considered in CME kinematics models; (2) the type II radio burst was probably produced from a high-density interaction region between the CME-driven shock and a nearby streamer or from the shock flank with lower heights, which implies uncertainties in the determination of CME kinematics using solely type II radio bursts; (3) the flux-rope orientation and chirality deduced from in situ reconstructions at Wind agree with those obtained from solar source observations; (4) the prolonged southward magnetic field near the Earth is mainly from the axial component of the largely southward inclined flux rope, which indicates the importance of predicting both the flux-rope orientation and magnetic field components in geomagnetic activity forecasting.

79 ASTRONOMY AND ASTROPHYSICS↗

Vision-based inspection of prefabricated components using camera poses: Addressing inherent limitations of image-based 3D reconstruction

Modular construction can lead to additional cost overruns and delays when a defect is found on the construction site and is not easily repairable. Researchers have developed various methods that use image-based 3D reconstruction for quality assessment, but they have inherent limitations, such as inconsistency and dealing with surfaces with reflectivity and limited visual features. Therefore, this paper presents a vision-based quality assessment method using cameras for prefabricated components by addressing these limitations. Specifically, this paper proposes a novel quality inspection method with sub-millimeter accuracy using cameras focused on leveraging camera poses (as opposed to 3D point clouds that are often not consistent in quality) from the image-based 3D reconstruction. The 3D point estimation by computing triangulation was used for achieving accurate measurement. The proposed method is validated using six different variances and two case studies – an aluminum pipe with a reflective surface and a fabricated concrete column. Furthermore, the results demonstrate the accuracy and effectiveness of the proposed method.

42 ENGINEERING↗

Tactile Robotic Topographical Mapping Without Force or Contact Sensors

A method of topographical mapping of a local solid surface within the range of motion of a robot arm is based on detection of contact between the surface and the end effector (the fixture or tool at the tip of the robot arm). The method was conceived to enable mapping of local terrain by an exploratory robot on a remote planet, without need to incorporate delicate contact switches, force sensors, a vision system, or other additional, costly hardware. The method could also be used on Earth for determining the size and shape of an unknown surface in the vicinity of a robot, perhaps in an unanticipated situation in which other means of mapping (e.g., stereoscopic imaging or laser scanning with triangulation) are not available. The method uses control software modified to utilize the inherent capability of the robotic control system to measure the joint positions, the rates of change of the joint positions, and the electrical current demanded by the robotic arm joint actuators. The system utilizes these coordinate data and the known robot-arm kinematics to compute the position and velocity of the end effector, move the end effector along a specified trajectory, place the end effector at a specified location, and measure the electrical currents in the joint actuators. Since the joint actuator current is approximately proportional to the actuator forces and torques, a sudden rise in joint current, combined with a slowing of the joint, is a possible indication of actuator stall and surface contact. Hence, even though the robotic arm is not equipped with contact sensors, it is possible to sense contact (albeit with reduced sensitivity) as the end effector becomes stalled against a surface that one seeks to measure.

Burke, Kevin↗

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

Multi-spacecraft Observations of the Coronal and Interplanetary Evolution of a Solar Eruption Associated with Two Active Regions

We investigate the coronal and interplanetary evolution of a coronal mass ejection (CME) launched on 2010 September 4 from a source region linking two active regions (ARs), 11101 and 11103, using extreme ultraviolet imaging, magnetogram, white-light, and in situ observations from SDO , STEREO , SOHO , VEX , and Wind . A potential-field source-surface model is employed to examine the configuration of the coronal magnetic field surrounding the source region. The graduated cylindrical shell model and a triangulation method are applied to determine the kinematics of the CME in the corona and interplanetary space. From the remote sensing and in situ observations, we obtain some key results: (1) the CME was deflected in both the eastward and southward directions in the low corona by the magnetic pressure from the two ARs, and possibly interacted with another ejection, which caused that the CME arrived at VEX that was longitudinally distant from the source region; (2) although VEX was closer to the Sun, the observed and derived CME arrival times at VEX are not earlier than those at Wind , which suggests the importance of determining both the frontal shape and propagation direction of the CME in interplanetary space; and (3) the ICME was compressed in the radial direction while the longitudinal transverse size was extended.

79 ASTRONOMY AND ASTROPHYSICS↗

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

High-Speed Laser Scanner Maps a Surface in Three Dimensions

A scanning optoelectronic instrument generates the digital equivalent of a threedimensional (X,Y,Z) map of a surface that spans an area with resolution on the order of 0.005 in. ( 0.125mm). Originally intended for characterizing surface flaws (e.g., pits) on space-shuttle thermal-insulation tiles, the instrument could just as well be used for similar purposes in other settings in which there are requirements to inspect the surfaces of many objects. While many commercial instruments can perform this surface-inspection function, the present instrument offers a unique combination of capabilities not available in commercial instruments. This instrument utilizes a laser triangulation method that has been described previously in NASA Tech Briefs in connection with simpler related instruments used for different purposes. The instrument includes a sensor head comprising a monochrome electronic camera and two lasers. The camera is a high-resolution

Lavelle, Joseph↗

Preliminary Study of a Model Rotor in Descent

Within a program designed to develop experimental techniques for measuring the trajectory and structure of vortices trailing from the tips of rotor blades, the present preliminary study focuses on a method for quantifying the trajectory of the trailing vortex during descent flight conditions. This study also presents rotor loads and blade surface pressures for a range of tip-path plane angles and Mach numbers. Blade pressures near the leading edge and along the outer radius are compared with data obtained on the same model rotor, but in open jet facilities. A triangulation procedure based on two directable laser-light sheets, each containing an embedded reference, proved effective in defining the spatial coordinates of the trailing vortex. When interrogating a cross section of the flow that contains several trailing vortices, the greatest clarity was found to result when the flow is uniformly seeded. Surface pressure responses during blade-vortex interactions appeared equally sensitive near the leading edge and along the outer portion of the blade, but diminished rapidly as the distance along the blade chord increased. The pressure response was virtually independent of whether the tip-path plane angle was obtained through shaft tilt or cyclic pitch. Although the shape and frequency of the pressure perturbations on the advancing blade during blade-vortex interaction are similar to those obtained in open-jet facilities, the angle of the tip-path plane may need to be lower than the range covered in this study.

McAlister, K. W.↗

On triangulations of the plane by pencils of conics. II

The present work continues our previous paper in which all possible triangulations of the plane using three pencils of circles were listed. In the present article we find all projectively distinct triangulations of the plane by pencils of conics that are obtained by projecting regular three-webs, cut out on a nondegenerate cubic surface by three pencils of planes, whose axes lie on this surface. Bibliography: 6 titles.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

K-decompositions and 3d gauge theories

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli space $\mathcal{L}$ K (M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $\mathcal{L}$ K (M) as a Lagrangian subvariety in the symplectic moduli space X un K (∂M) of framed flat connections on the boundary — and more so, as a “K 2 -Lagrangian,” meaning that the K 2 -avatar of the symplectic form restricts to zero. We construct an open part of $\mathcal{L}$ K (M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $\mathcal{L}$ K (M) is K 2 -isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $\mathcal{L}$ K (M) is K 2 -Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2 -Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality between N f = 1 SQED and the XYZ model. In the large K limit, we find evidence that the degrees of freedom of T K [M] grow cubically in K.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Apollo 15 surface science summary.

The Apollo 15 mission was the fourth manned lunar landing and the northernmost location yet visited. The landing site on the southeastern edge of the Imbrium Basin afforded the opportunity of studying several unique lunar features, the Apennine Mountains, Hadley Rille, and the Imbrium Basin fill. Detailed geological study of the data returned from the mission provided new insight into the structure and history of the Basin. A third Apollo Lunar Surface Experiment Package was deployed during the mission containing seven experiments: Passive Seismometer (PSE), Heat Flow (HFE), Surface Magnetometer (LSM), Suprathermal Ion Detector (SIDE), Cold Cathode Gauge (CCGE), Solar Wind Spectrometer (SWS), and a Dust Detector. We have been able to triangulate on the sources of moonquakes and to observe simultaneous nighttime and daytime changes in the moon's magnetic field, solar wind flux, and the neutral and ionized components of the moon's tenuous atmosphere.

Beattie, D. A.↗

SU-C-18A-02: Image-Based Camera Tracking: Towards Registration of Endoscopic Video to CT

Purpose: Endoscopic examinations are routinely performed on head and neck and esophageal cancer patients. However, these images are underutilized for radiation therapy because there is currently no way to register them to a CT of the patient. The purpose of this work is to develop a method to track the motion of an endoscope within a structure using images from standard clinical equipment. This method will be incorporated into a broader endoscopy/CT registration framework. Methods: We developed a software algorithm to track the motion of an endoscope within an arbitrary structure. We computed frame-to-frame rotation and translation of the camera by tracking surface points across the video sequence and utilizing two-camera epipolar geometry. The resulting 3D camera path was used to recover the surrounding structure via triangulation methods. We tested this algorithm on a rigid cylindrical phantom with a pattern spray-painted on the inside. We did not constrain the motion of the endoscope while recording, and we did not constrain our measurements using the known structure of the phantom. Results: Our software algorithm can successfully track the general motion of the endoscope as it moves through the phantom. However, our preliminary data do not show a high degree of accuracy in the triangulation of 3D point locations. More rigorous data will be presented at the annual meeting. Conclusion: Image-based camera tracking is a promising method for endoscopy/CT image registration, and it requires only standard clinical equipment. It is one of two major components needed to achieve endoscopy/CT registration, the second of which is tying the camera path to absolute patient geometry. In addition to this second component, future work will focus on validating our camera tracking algorithm in the presence of clinical imaging features such as patient motion, erratic camera motion, and dynamic scene illumination.

60 APPLIED LIFE SCIENCES↗

National Geodetic Satellite Program, Part II: National Geodetic Society

Satellite geodesy and the creation of worldwide geodetic reference systems is discussed. The geometric description of the surface and the analytical description of the gravity field of the earth by means of worldwide reference systems, with the aid of satellite geodesy, are presented. A triangulation method based on photogrammetric principles is described in detail. Results are derived in the form of three dimensional models. These mathematical models represent the frame of reference into which one can fit the existing geodetic results from the various local datums, as well as future measurements.

Schmid, H.↗

Positive amplitudes in the amplituhedron

The all-loop integrand for scattering amplitudes in planar N=4 SYM is determined by an “amplitude form” with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural “bosonization” of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a “dual amplituhedron” formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting inside a co-dimension one surface separating “legal” and “illegal” local singularities of the amplitude. In conclusion, we illustrate this in several simple examples, obtaining new expressions for amplitudes not associated with any triangulations, but following in a more invariant manner from a global view of the positive geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Role of corner interfacial area in uniqueness of capillary pressure-satuation - interfacial area relation under transient conditions

Capillary pressure ( P c ) and phase saturation ( S w ) in two-phase flow are well known to be hysteretically related. Thermodynamically-derived multiphase flow theories conjecture that this hysteresis will be lifted if specific interfacial area ( a nw ) is included as a new state variable to create a unique P c -S-a nw surface. Specific interfacial area is defined as the total interfacial area per volume of a porous medium. Several studies have confirmed the existence of a unique P c -S w -a nw surface under equilibrium conditions for a given porous medium. However, there is only one experimental work in the literature, where the unique- ness of this surface under transient conditions was questioned. However, in the data analysis only the terminal menisci were considered to calculate the specific interfacial area. In this paper, we investigate the uniqueness of P c -S-a nw surfaces with and without the inclusion of corner fluid-fluid interfacial area, under different dynamic conditions, in two different micro-models bearing two different (granular vs. triangulated) pore morphologies. We establish a systematic metric to analyze hysteresis under different hydrodynamic conditions.

Godinez-Brizuela, Omar E.↗

Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles

Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.

Blake, Kenneth R.↗