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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.

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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Real-time Detection of Moving Objects from Moving Vehicles Using Dense Stereo and Optical Flow

Dynamic scene perception is very important for autonomous vehicles operating around other moving vehicles and humans. Most work on real-time object tracking from moving platforms has used sparse features or assumed flat scene structures. We have recently extended a real-time. dense stereo system to include realtime. dense optical flow, enabling more comprehensive dynamic scene analysis. We describe algorithms to robustly estimate 6-DOF robot egomotion in the presence of moving objects using dense flow and dense stereo. We then use dense stereo and egomotion estimates to identify other moving objects while the robot itself is moving. We present results showing accurate egomotion estimation and detection of moving people and vehicles under general 6DOF motion of the robot and independently moving objects. The system runs at 18.3 Hz on a 1.4 GHz Pentium M laptop. computing 160x120 disparity maps and optical flow fields, egomotion, and moving object segmentation. We believe this is a significant step toward general unconstrained dynamic scene analysis for mobile robots, as well as for improved position estimation where GPS is unavailable.

moving object detection↗
DOE OSTI2025

Signatures of chiral superconductivity in rhombohedral graphene

Chiral superconductors are unconventional superconducting states that break time-reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetralayer and pentalayer graphene without moiré superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with T c up to 300 mK and charge density n e down to 2.4 ×10 11 cm −2 in five devices. Spontaneous time-reversal-symmetry breaking (TRSB) owing to orbital motion of the electron is found and several observations indicate the chiral nature of these superconducting states, including: (1) in the superconducting state, R xx shows magnetic hysteresis in varying out-of-plane magnetic field B ⊥ —absent from all other superconductors; (2) the superconducting states are robust against in-plane magnetic field and are developed within a spin-polarized and valley-polarized quarter-metal (QM) phase; (3) the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. Here, we also observed a critical B ⊥ of 1.4 T, higher than any graphene superconductivity, which indicates a strong-coupling superconductivity close to the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensate (BEC) crossover. Our observations establish a pure carbon material for the study of topological superconductivity, with the promise to explore Majorana modes and topological quantum computing.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Real-time detection of moving objects from moving vehicles using dense stereo and optical flow

Dynamic scene perception is very important for autonomous vehicles operating around other moving vehicles and humans. Most work on real-time object tracking from moving platforms has used sparse features or assumed flat scene structures. We have recently extended a real-time, dense stereo system to include realtime, dense optical flow, enabling more comprehensive dynamic scene analysis. We describe algorithms to robustly estimate 6-DOF robot egomotion in the presence of moving objects using dense flow and dense stereo. We then use dense stereo and egomotion estimates to identify & other moving objects while the robot itself is moving. We present results showing accurate egomotion estimation and detection of moving people and vehicles under general 6-DOF motion of the robot and independently moving objects. The system runs at 18.3 Hz on a 1.4 GHz Pentium M laptop, computing 160x120 disparity maps and optical flow fields, egomotion, and moving object segmentation. We believe this is a significant step toward general unconstrained dynamic scene analysis for mobile robots, as well as for improved position estimation where GPS is unavailable.

egomotion↗
NASA NTRS2016

GOES-16 On-Orbit Dual Isolation Performance Characterization Results

The Geostationary Operational Environmental Satellite-R Series (GOES-R) is the first of the next generation geostationary weather satellites. GOES-R successfully launched on November19, 2016 and renamed GOES-16 upon entering geostationary orbit. Subsequently, GOES-16post-launch testing began. This paper presents the GOES-16 Satellite Dynamic Interaction Characterization results for the Earth Pointed Platform (EPP) stowed, referred to as the Reaction Wheel Assembly (RWA) Isolation Only configuration, and deployed, referred to as the Dual Isolation configuration. GOES-R represents a quantum increase in Earth and solar weather observation capabilities, with 4 times the resolution, 5 times the observation rate, and 3 times the number of spectral bands for Earth observations. With the improved resolution, comes the instrument suites increased sensitivity to disturbances over a broad spectrum 0-512Hz. Sources of disturbance include reaction wheels, thruster firings for station keeping and momentum management, gimbal motion, and internal instrument disturbances. To minimize the impact of these disturbances, the baseline design included an EPP, a stiff optical bench to which the two nadir pointed instruments are collocated together with the Guidance Navigation Control (GNC) star trackers and Inertial Measurement Units (IMUs). The EPP is passively isolated from the spacecraft bus with Honeywell D-Strut isolators providing attenuation for frequencies above 5 Hz in all six degrees-of-freedom. To reduce the risk of wheel disturbances impacting performance, a secondary passive isolation system manufactured by Moog CSA Engineering was incorporated under each of the six 160 Nms reaction wheels, tuned to provide attenuation at frequencies above 50 Hz. Integrated wheel and isolator testing was performed on a Kistler table at NASA Goddard Space Flight Center. Pre-launch Satellite Dynamic Interaction Characterization high-fidelity simulations and ground testing were conducted to evaluate jitter performance for two cases: 1) deployed EPP and reaction wheel (Dual Isolation) and 2) EPP hard mounted (RWA Isolation Only) to the spacecraft. A comparison of pre-launch to post-launch Satellite Dynamic Interaction Characterization results are also presented in this paper.

Carter, Delano↗
DOE OSTI2026

Arctic Deployment of a Fully Integrated Self-Powered Drifting Buoy Harvesting Wave Energy via a Triboelectric Nanogenerator

The Arctic Ocean remains one of the most poorly sampled regions on Earth, where improved in situ environmental monitoring is vital for advancing oceanographic and atmospheric studies. However, data collection efforts are constrained by the short operational lifespans and high costs of conventional systems. Drifting buoys powered by pendulum-driven wave energy harvesters offer a cost-effective alternative, yet earlier designs have neither been optimized for real-world wave conditions nor validated in the Arctic. In this study, we develop a self-powered drifting buoy that integrates a pendulum-driven triboelectric nanogenerator (TENG) system with a mechanical motion rectifier, a high-gear-ratio transmission, and power management circuits. Through coupled buoy–pendulum dynamic simulations and laboratory testing using a motion simulator, we identify an optimal pendulum mass of 1.6 kg (12.7% of total buoy weight) that maximizes energy output while maintaining buoy stability. Laboratory experiments achieved average power outputs of 12.7 mW under Arctic-like wave and temperature conditions. The system was successfully deployed in the Bering Sea, where it generated 11 J of energy in 3.1 m waves, marking the first Arctic deployment of a TENG-based drifting buoy for sea surface temperature monitoring. This work establishes a cost-effective framework for designing self-powered Arctic monitoring platforms and advances the feasibility of long-term environmental observations in real Arctic waters.

marine enerby↗
NASA NTRS1989

Space station dynamics, attitude control and momentum management

The Space Station Attitude Control System software test-bed provides a rigorous environment for the design, development and functional verification of GN and C algorithms and software. The approach taken for the simulation of the vehicle dynamics and environmental models using a computationally efficient algorithm is discussed. The simulation includes capabilities for docking/berthing dynamics, prescribed motion dynamics associated with the Mobile Remote Manipulator System (MRMS) and microgravity disturbances. The vehicle dynamics module interfaces with the test-bed through the central Communicator facility which is in turn driven by the Station Control Simulator (SCS) Executive. The Communicator addresses issues such as the interface between the discrete flight software and the continuous vehicle dynamics, and multi-programming aspects such as the complex flow of control in real-time programs. Combined with the flight software and redundancy management modules, the facility provides a flexible, user-oriented simulation platform.

Sunkel, John W.↗
NASA NTRS1989

GPS-aided gravimetry at 30 km altitude from a balloon-borne platform

A balloon-borne experiment, flown at 30 km altitude over New Mexico, was used to test dynamic differential Global Positioning System (GPS) tracking in support of gravimetry at high-altitudes. The experiment package contained a gravimeter (Vibrating String Accelerometer), a full complement of inertial instruments, a TI-4100 GPS receiver and a radar transponder. The flight was supported by two GPS receivers on the ground near the flight path. From the 8 hour flight, about a forty minute period was selected for analysis. Differential GPS phase measurements were used to estimate changes in position over the sample time interval, or average velocity. In addition to average velocity, differential positions and numerical averages of acceleration were obtained in three components. Gravitational acceleration was estimated by correcting for accelerations due to translational motion, ignoring all rotational effects.

Lazarewicz, Andrew R.↗
DOE OSTI2023

High-fidelity imaging of a band insulator in a three-dimensional optical lattice clock

Here, we report on the observation of a high-density, band insulating state in a three-dimensional optical lattice clock. Filled with a nuclear-spin-polarized degenerate Fermi gas of 87 Sr, the three-dimensional (3D) lattice has one atom per site in the ground motional state, thus guarding against frequency shifts due to contact interactions. At this high density where the average distance between atoms is comparable to the probe wavelength, conventional imaging techniques at saturation intensity suffer from large systematic errors. To spatially probe frequency shifts in the clock and measure thermodynamic properties of this system, accurate imaging techniques at high optical depths are required. Using a combination of highly saturated fluorescence and absorption imaging, we confirm the density distribution in our 3D optical lattice in agreement with a single spin band insulating state. Combining our clock platform with this high filling fraction opens the door to studying new classes of long-lived, many-body states arising from dipolar interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2004

Real-time detection of moving objects from moving vehicles using dense stereo and optical flow

Dynamic scene perception is very important for autonomous vehicles operating around other moving vehicles and humans. Most work on real-time object tracking from moving platforms has used sparse features or assumed flat scene structures. We have recently extended a real-time, dense stereo system to include real-time, dense optical flow, enabling more comprehensive dynamic scene analysis. We describe algorithms to robustly estimate 6-DOF robot egomotion in the presence of moving objects using dense flow and dense stereo. We then use dense stereo and egomotion estimates to identity other moving objects while the robot itself is moving. We present results showing accurate egomotion estimation and detection of moving people and vehicles under general 6-DOF motion of the robot and independently moving objects. The system runs at 18.3 Hz on a 1.4 GHz Pentium M laptop, computing 160x120 disparity maps and optical flow fields, egomotion, and moving object segmentation. We believe this is a significant step toward general unconstrained dynamic scene analysis for mobile robots, as well as for improved position estimation where GPS is unavailable.

egomotion↗
DOE OSTI2023

Isolating the Source Region of Infrasound Travel Time Variability Using Acoustic Sensors on High-Altitude Balloons

High-altitude balloons carrying infrasound sensor payloads can be leveraged toward monitoring efforts to provide some advantages over other sensing modalities. On 10 July 2020, three sets of controlled surface explosions generated infrasound waves detected by a high-altitude floating sensor. One of the signal arrivals, detected when the balloon was in the acoustic shadow zone, could not be predicted via propagation modeling using a model atmosphere. Considering that the balloon’s horizontal motion showed direct evidence of gravity waves, we examined their role in infrasound propagation. Implementation of gravity wave perturbations to the wind field explained the signal detection and aided in correctly predicting infrasound travel times. Our results show that the impact of gravity waves is negligible below 20 km altitude; however, their effect is important above that height. The results presented here demonstrate the utility of balloon-borne acoustic sensing toward constraining the source region of variability, as well as the relevance of complexities surrounding infrasound wave propagation at short ranges for elevated sensing platforms.

47 OTHER INSTRUMENTATION↗
NASA NTRS1989

Global models: Robot sensing, control, and sensory-motor skills

Robotics research has begun to address the modeling and implementation of a wide variety of unstructured tasks. Examples include automated navigation, platform servicing, custom fabrication and repair, deployment and recovery, and science exploration. Such tasks are poorly described at onset; the workspace layout is partially unfamiliar, and the task control sequence is only qualitatively characterized. The robot must model the workspace, plan detailed physical actions from qualitative goals, and adapt its instantaneous control regimes to unpredicted events. Developing robust representations and computational approaches for these sensing, planning, and control functions is a major challenge. The underlying domain constraints are very general, and seem to offer little guidance for well-bounded approximation of object shape and motion, manipulation postures and trajectories, and the like. This generalized modeling problem is discussed, with an emphasis on the role of sensing. It is also discussed that unstructured tasks often have, in fact, a high degree of underlying physical symmetry, and such implicit knowledge should be drawn on to model task performance strategies in a methodological fashion. A group-theoretic decomposition of the workspace organization, task goals, and their admissible interactions are proposed. This group-mechanical approach to task representation helps to clarify the functional interplay of perception and control, in essence, describing what perception is specifically for, versus how it is generically modeled. One also gains insight how perception might logically evolve in response to needs of more complex motor skills. It is discussed why, of the many solutions that are often mathematically admissible to a given sensory motor-coordination problem, one may be preferred over others.

Schenker, Paul S.↗
NASA NTRS2018

Overview of the Digitization Workflow Post Image Acquisition of Apollo Lunar and Antarctic Meteorite Samples Using Agisoft Photoscan for the NASA 3D Astromaterials Virtual Samples Collection

The 3D Virtual Astromaterials Samples (3DVAS) collection is a multi-year funded project to create a digital database of sixty Apollo Lunar and Antarctic Meteorite samples following non-destructive documentation conservation protocols. After initial image processing, the photos are evaluated and processed using unique structure-from-motion photogrammetric techniques in a high performance modelling software designed to create a 3D model from 2D images: Agisoft Photoscan Pro. Agisoft Photoscan Pro uses image processing algorithms and techniques originating in computer vision to resolve 3D models for accurate and detailed visualization of a subject. The software provides a stepwise process that is tailored per model based on spatial and specular reflectance properties, for example. The process includes: photo alignment, creation of a dense point cloud, mesh, and finally texture. Photo alignment is dependent on model properties. The 3DVAS process requires a special rotation platform with calibrated photogrammetric targets, specific distance rotation protocols, and a contrasting background for alignment and scale accuracy. As a result of the photographic process, alignment will complete with two mirrored hemispheres that, in a sense, represent the 2D images overlapping to create a 3D model. Each dense point cloud is analyzed with provided statistical measures in a gradual selection process to eliminate outliers. The point cloud is reduced to include only data valuable to the final model. When a precise dense point cloud is achieved, a mesh and texture are applied. Each model is scaled with scale bar accuracies within 100 microns. Each sample has its own intimate process for modelling; there is no standard for the parameters required in the final creation of a high resolution model. By processing multiple samples, a skill is gained in practice to allow a close definition of the original sample and will result in the most detailed version of the sample shell. This process completes one-fifth of the 3DVAS protocol for providing accurate digital documentation. Each model shell is merged with X-ray Computed Tomography data to create a full volumetric sample. All 3DVAS data will be served on NASA's Astromaterials Acquisition and Curation website with an early subset of data available in 2019 and the 3D Virtual Astromaterials Samples Collection launch in 2020.

Thomas, Andi B.↗
NASA NTRS2004

Bioinspired Engineering of Exploration Systems (BEES) - its Impact on Future Missions

This paper describes an overview of our "Bioinspired Engineering of Exploration Systems for Mars" ( "BEES for Mars") project. The BEES approach distills selected biologically inspired strategies utilizing motion cues/optic flow, bioinspired pattern recognition, biological visual and neural control systems, bioinspired sensing and communication techniques, and birds of prey inspired search and track algorithmic systems. Unique capabilities so enabled, provide potential solutions to future autonomous robotic space and planetary mission applications. With the first series of tests performed in September 2003, August 2004 and September 2004, we have demonstrated the BEES technologies at the El Mirage Dry Lakebed site in the Mojave Desert using Delta Wing experimental prototypes. We call these test flyers the "BEES flyer", since we are developing them as dedicated test platform for the newly developed bioinspired sensors, processors and algorithmic strategies. The Delta Wing offers a robust airframe that can sustain high G launches and offers ease of compact stowability and packaging along with scaling to small size and low ReynOld's number performance for a potential Mars deployment. Our approach to developing light weight, low power autonomous flight systems using concepts distilled from biology promises to enable new applications, of dual use to NASA and DoD needs. Small in size (0.5 -5 Kg) BEES Flyers are demonstrating capabilities for autonomous flight and sensor operability in Mars analog conditions. The BEES project team spans JPL, NASA Ames, Australian National University (ANU), Brigham Young University(BYU), DC Berkeiey, Analogic Computers Inc. and other institutions. The highlights from our recent flight demonstrations exhibiting new Mission enabling capabilities are described. Further, this paper describes two classes of potential new missions for Mars exploration: (1) the long range exploration missions, and (2) observation missions, for real time imaging of critical ephemeral phenomena, that can be enabled by use of BEES flyers. For example, such flyers can serve as a powerful black-box for critical descent and landing data and enablers for improved science missions complementing and supplementing the existing assets like landers and rovers by providing valuable exploration and quick extended low-altitude aerial coverage of the sites of interest by imaging them and distributing instruments to them. Imaging done by orbiters allows broad surface coverage at limited spatial resolution. Low altitude air-borne exploration of Mars offers a means for imaging large areas, perhaps up to several hundred kilometers, quickly and efficiently, providing a close-up birds-eye view of the planetary terrain and close-up approach to constrained difficult areas like canyons and craters. A novel approach to low-mass yet highly capable flyers is enabled by small aircraft equipped using sensors and processors and algorithms developed using BEES technology. This project is focused towards showing the direct impact of blending the best of artificial intelligence attributes and bioinspiration to create a leap beyond existing capability for our future Missions.

navigation↗
DOE OSTI2023

Observation of skyrmion bubbles in multilayer [Pt/Co/Cu] n using spin-polarized STM

Magnetic multilayers are a promising platform for storage and logic devices based on skyrmion spin textures, due to the large materials phase space for tuning properties. Epitaxial superlattice structures of [Pt/Co/Cu]n thin films were grown by molecular beam epitaxy at room temperature. Spin-polarized scanning tunneling microscopy (SP-STM) of these samples was used to probe the connection between surface structure and skyrmion morphology with nanoscale spatial resolution. Irregular-shaped skyrmion bubbles were observed, with effective diameters from 20 to 200 nm that are much larger than the nanoscale grain structure of the surface topography. Nucleation, annihilation, and motion of skyrmion bubbles could be driven using the stray field of the ferromagnetic tip in repeated imaging, and spin-polarized current/voltage pulses. Furthermore, our detailed comparison of STM topography and differential conductance images shows that there are no surface defects or inhomogeneities at length scales that could account for the range in skyrmion bubble size or shape observed in the measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Hydrogen Bonding and Its Effect on the Orientational Dynamics of Water Molecules inside Polyelectrolyte Brush-Induced Soft and Active Nanoconfinement

Despite being the most ubiquitous compound on Earth, the fundamental properties of water are not fully understood, especially in nanoconfinement. Densely grafted polyelectrolyte (PE) molecules attain the configuration of a “brush”: these PE brushes, due to their ability to form hydrogen bonds (HBs) with water via the PE functional groups, act as a source of soft and active nanoconfinement for the brush-trapped water molecules. In this paper, we study the effects of PE brush-induced confinement on the structure, dynamics and energetics of the water-water and water-PE HBs. Our results indicate a significant weakening of the HBs from bulk to sparsely grafted to densely grafted brushes. i.e., by increasing the degree of brush-induced nanoconfinement. We explain that this weakening of water-water HBs is caused by the disruption of the extended network of water molecules within the brush-induced nanoconfinement. This is confirmed by performing a ring structure analysis of the water molecules, which yields a reduction in the average ring size at higher degrees of brush-induced nanoconfinement (i.e., at higher brush grafting densities). Furthermore, we investigate the role of HB on the orientational dynamics of the water molecules. Here, we observe that the rotational motion of the water molecules becomes sluggish inside the PE brushes. Recent findings have indicated that the water and counterions trapped in brush-induced nanoconfinement demonstrate structures (in combination with the PE functional group) analogous to that in “water-in-salt” electrolytes that have seen extensive recent uses for Li-ion battery applications. However, the rotational dynamics of water molecules inside the brush-induced nanoconfinement is found to be distinctly different from that of conventional “water-in-salt” electrolytes in absence of any confinement; therefore, the present study will provide the necessary platform towards conceptualizing polymer-based nanoconfinement for battery applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Maximized lateral inhibition in paired magnetic domain wall racetracks for neuromorphic computing

Lateral inhibition is an important functionality in neuromorphic computing, modeled after the biological neuron behavior that a firing neuron deactivates its neighbors belonging to the same layer and prevents them from firing. In most neuromorphic hardware platforms lateral inhibition is implemented by external circuitry, thereby decreasing the energy efficiency and increasing the area overhead of such systems. Recently, the domain wall—magnetic tunnel junction (DW-MTJ) artificial neuron is demonstrated in modeling to be intrinsically inhibitory. Without peripheral circuitry, lateral inhibition in DW-MTJ neurons results from magnetostatic interaction between neighboring neuron cells. However, the lateral inhibition mechanism in DW-MTJ neurons has not been studied thoroughly, leading to weak inhibition only in very closely-spaced devices. This work approaches these problems by modeling current- and field- driven DW motion in a pair of adjacent DW-MTJ neurons. We maximize the magnitude of lateral inhibition by tuning the magnetic interaction between the neurons. The results are explained by current-driven DW velocity characteristics in response to an external magnetic field and quantified by an analytical model. Dependence of lateral inhibition strength on device parameters is also studied. Finally, lateral inhibition behavior in an array of 1000 DW-MTJ neurons is demonstrated. Our results provide a guideline for the optimization of lateral inhibition implementation in DW-MTJ neurons. Finally, with strong lateral inhibition achieved, a path towards competitive learning algorithms such as the winner-take-all are made possible on such neuromorphic devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Mode-multiplexed photonic integrated vector dot-product core from inverse design

Photonic computing has the potential to harness the full degrees of freedom (DOFs) of the light field, including the wavelength, spatial mode, spatial location, phase quadrature, and polarization, to achieve a higher level of computing parallelism and scalability than digital electronic processors. While multiplexing using the wavelength and other DOFs can be readily integrated on silicon photonics platforms with compact footprints, conventional mode-division multiplexed (MDM) photonic designs occupy areas exceeding tens to hundreds of microns for a few spatial modes, significantly limiting their scalability. Here, we utilize inverse design to demonstrate an ultracompact photonic computing core that calculates vector dot products based on MDM coherent mixing. Our dot-product core integrates the functionalities of two-mode multiplexers and one multimode coherent mixer within a nominal footprint of 5 μm x 3 μm . We have experimentally demonstrated computing examples on the fabricated dot-product core, including complex number multiplication and motion estimation using optical flow. The compact dot-product core design enables large-scale on-chip integration in a parallel photonic computing primitive cluster for high-throughput scientific computing and computer vision tasks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Software Development for the Hobby-Eberly Telescope's Segment Alignment Maintenance System using LABView

The software development for an upgrade to the Hobby-Eberly Telescope (HET) was done in LABView. In order to improve the performance of the HET at the McDonald Observatory, a closed-loop system had to be implemented to keep the mirror segments aligned during periods of observation. The control system, called the Segment Alignment Maintenance System (SAMs), utilized inductive sensors to measure the relative motions of the mirror segments. Software was developed in LABView to tie the sensors, operator interface, and mirror-control motors together. Developing the software in LABView allowed the system to be flexible, understandable, and able to be modified by the end users. Since LABView is built using block diagrams, the software naturally followed the designed control system's block and flow diagrams, and individual software blocks could be easily verified. LABView's many built-in display routines allowed easy visualization of diagnostic and health-monitoring data during testing. Also, since LABView is a multi-platform software package, different programmers could develop the code remotely on various types of machines. LABView s ease of use facilitated rapid prototyping and field testing. There were some unanticipated difficulties in the software development, but the use of LABView as the software "language" for the development of SAMs contributed to the overall success of the project.

Hall, Drew P.↗