Search NASA⌕ Search

SEARCH · Search NASA

Results for “Simultaneous Localization and Mapping”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

151 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

The Pascal Discovery Mission: A Mars Climate Network Mission

The climate of Mars is a major focus of Mars exploration. With the loss of MCO, however, it remains uncertain how it will be achieved. We argue that a truly dedicated climate mission to Mars should have both orbital and landed components, and that these should operate simultaneously for at least 1 Mars year if not longer. Pascal is a Discovery mission that emphasizes the landed component. Its principal goal is to establish a network of 24 small weather stations on the surface of Mars that will operate for 2 Mars years, with an extended mission option for an additional 8 Mars years bringing the total mission lifetime up to 10 Mars years. The stations will collect hourly measurements of pressure, temperature, and optical depth. After delivering the probes to Mars, Pascal's carrier spacecraft will go into an elliptical orbit which will serve as a relay for the landers, and a platform for synoptic imaging. These simultaneous measurements from the surface and from orbit will allow us to characterize the planet's general circulation and its interaction with the dust, water, and CO2 cycles. During entry, descent, and landing, each of Pascal's 24 probes will also measure the temperature structure of the atmosphere and acquire images of the surface. These data will allow us to determine the global structure of the atmosphere between 15 and 130 km, and characterize the local terrain to help interpret the landed data. The descent images are part of Pascal's outreach program, as the probe camera system will be developed by faculty-supervised student project. The intent is to generate enthusiasm for the Pascal mission by directly involving students. Pascal will be launched on a Delta II-7925 in August of 2005. A type I trajectory will deliver Pascal to Mars in January of 2006. On approach, the three-axis stabilized carrier spacecraft will spring deploy the Pascal probes in 4 separate salvo's of 6 each. Global coverage is achieved with small time-of-arrival adjustments in between each salvo. Pascal's probes utilize an aeroshell, parachute, and crushable material for entry, descent and landing. On the surface, their long life and global coverage is enabled by a Micro Thermal Power Source with demonstrated heritage. After all probes are released, the carrier spacecraft will execute a small burn for insertion into an elliptical orbit. The long lifetime of the Pascal network was chosen in part to maximize the chances that orbital sounding, like that planned with MCO, would occur at some point during the mission. If Pascal is selected for launch in '05, this could occur if MCO-like science is reflown in the '05 opportunity or, if it is reflown in '03, the mission is extended to overlap with Pascal. The combination of temperature sounding from orbit, and surface pressure mapping from the surface will allow a direct determination of the full 3-D wind field for the first time.

Haberle, R. M.↗
NASA NTRS2000

The Pascal Discovery Mission: A Mars Climate Network Mission

The climate of Mars is a major focus of Mars exploration. With the loss of MCO, however, it remains uncertain how it will be achieved. We argue that a truly dedicated climate mission to Mars should have both orbital and landed components, and that these should operate simultaneously for at least I Mars year if not longer. Pascal is Discovery mission that emphasizes the landed component. Its principal goal is to establish a network of 24 small weather stations on the surface of Mars that will operate for 2 Mars years, with an extended mission option for an additional 8 Mars years bringing the total mission lifetime up to 10 Mars years. The stations will collect hourly measurements of pressure, temperature, and optical depth. After delivering the probes to Mars, Pascal's carrier spacecraft will go into an elliptical orbit which will serve as a relay for the landers, and a platform for synoptic imaging. These simultaneous measurements from the surface and from orbit will allow us to characterize the planet's general circulation and its interaction with the dust, water, and CO2 cycles. During entry, descent, and landing, each of Pascal's 24 probes will also measure the temperature structure of the atmosphere and acquire images of the surface. These data will allow us to determine the global structure of the atmosphere between 15 and 130 km, and characterize the local terrain to help interpret the landed data. The descent images are part of Pascal's outreach program, as the probe camera system will be developed by faculty-supervised student project. The intent is to generate enthusiasm for the Pascal mission by directly involving students. Pascal will be launched on a Delta 11-7925 in August of 2005. A type I trajectory will deliver Pascal to Mars in January of 2006. On approach, the three-axis stabilized carrier spacecraft will spring deploy the Pascal probes in 4 separate salvo's of 6 each. Global coverage is achieved with small time-of-arrival adjustments in between each salvo. Pascal's probes utilize an aeroshell, parachute, and crushable material for entry, descent and landing. On the surface, their long life and global coverage is enabled by a Micro Thermal Power Source with demonstrated heritage. After all probes are released, the carrier spacecraft will execute a small bum for insertion into an elliptical orbit. The long lifetime of the Pascal network was chosen in part to maximize the chances that orbital sounding, like that planned with MCO, would occur at some point during the mission. If Pascal is selected for launch in -05, this could occur if MCO-like science is reflown in the '05 opportunity or, if it is reflown in '03, the mission is extended to overlap with Pascal. The combination of temperature sounding from orbit, and surface pressure mapping from the surface will allow a direct determination of the full 3-D wind field for the first time.

Haberle, Robert M.↗
NASA NTRS2017

HST WFC3 Observations of Uranus' 2014 Storm Clouds and Comparison with VLT/SINFONI and IRTF/Spex Observations

In November 2014 Uranus was observed with the Wide Field Camera 3 (WFC3) instrument of the Hubble Space Telescope as part of the Hubble 2020: Outer Planet Atmospheres Legacy program, OPAL. OPAL annually maps Jupiter, Uranus and Neptune (and will also map Saturn from 2018) in several visible near- infrared wavelength filters. The Uranus 2014 OPAL observations were made on the 89th November at a time when a huge cloud complex, first observed by de Pater et al. (2015) and subsequently tracked by professional and amateur astronomers (Sayanagi et al., 2016), was present at 30-40deg N. We imaged the entire visible atmosphere, including the storm system, in seven filters spanning 467924 nm, capturing variations in the coloration of Uranus clouds and also vertical distribution due to wavelength dependent changes in Rayleigh scattering and methane absorption optical depth. Here we analyse these new HST observations with the NEMESIS radiative-transfer and retrieval code in multiple-scattering mode to determine the vertical cloud structure in and around the storm cloud system. The same storm system was also observed in the H-band (1.4-1.8 micrometers) with the SINFONI Integral Field Unit Spectrometer on the Very Large Telescope (VLT) on 31st October and 11th November, reported by Irwin et al. (2016, 10.1016j.icarus.2015.09.010). To constrain better the cloud particle sizes and scattering properties over a wide wavelength range we also conducted a limb-darkening analysis of the background cloud structure in the 30-40deg N latitude band by simultaneously fitting: a) these HSTOPAL observations at a range of zenith angles; b) the VLTSINFONI observations at a range of zenith angles; and c) IRTFSpeX observations of this latitude band made in 2009 at a single zenith angle of 23deg, spanning the wavelength range 0.8-1.8 micrometers (Irwin et al., 2015, 10.1016j.icarus.2014.12.020). We find that the HST observations, and the combined HSTVLTIRTF observations at all locations are well modelled with a three-component cloud comprised of: 1) a vertically thin, but optically thick deep tropospheric cloud at a pressure of approximately 2 bars; 2) a methane-ice cloud based at the methane-condensation level of approximately 1.23 bar, with variable vertical extent; and 3) a vertically extended tropospheric haze, also based at the methane-condensation level of 1.23 bar. We find that modelling both haze and tropospheric cloud with particles having an effective radius of approximately 0.1 micron provides a good fit the observations, although for the tropospheric cloud, particles with an effective radius as large as 1.0 micron provide a similarly good fit. We find that the particles in both the tropospheric cloud and haze are more scattering at short wave- lengths, giving them a blue color, but are more absorbing at longer wavelengths, especially for the tropospheric haze. We find that the spectra of the storm clouds are well modelled by localized thickening and vertical extension of the methane-ice cloud. For the particles in the storm clouds, which we assume to be composed of methane ice particles, we find that their mean radii must lie somewhere in the range 0. 1 1. 0 m. We find that the high clouds have low integrated opacity, and that streamers reminiscent of convective thunderstorm anvils are confined to levels deeper than 1 bar. These results argue against vigorous moist convective origins for the cloud features.

atmospheres↗
DOE OSTI2022

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Geochemistry & Geophysics↗
NASA NTRS2010

Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results

We present new full-sky temperature and polarization maps in five frequency bands from 23 to 94 GHz, based on data from the first five years of the Wilkinson Microwave Anisotropy Probe (WMAP) sky survey. The new maps are consistent with previous maps and are more sensitive. The five-year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the instrument calibration and in-flight beam response. We present several new tests for systematic errors in the polarization data and conclude that W-band polarization data is not yet suitable for cosmological studies, but we suggest directions for further study. We do find that Ka-band data is suitable for use; in conjunction with the additional years of data, the addition of Ka band to the previously used Q- and V-band channels significantly reduces the uncertainty in the optical depth parameter, tau. Further scientific results from the five-year data analysis are presented in six companion papers and are summarized in Section 7 of this paper. With the five-year WMAP data, we detect no convincing deviations from the minimal six-parameter ACDM model: a flat universe dominated by a cosmological constant, with adiabatic and nearly scale-invariant Gaussian fluctuations. Using WMAP data combined with measurements of Type Ia supernovae and Baryon Acoustic Oscillations in the galaxy distribution, we find (68% CL uncertainties): OMEGA(sub b)h(sup 2) = 0.02267(sup +0.00058)(sub -0.00059), OMEGA(sub c)h(sup 2) = 0.1131 plus or minus 0.0034, OMEGA(sub logical and) = 0.726 plus or minus 0.015, ns = .960 plus or minus 0.013, tau = 0.84 plus or minus 0.016, and DELTA(sup 2)(sub R) = (22.445 plus or minus 0.096) x 10(exp -9) at k = 0.002 Mpc(exp -1). From these we derive sigma(sub 8) = 0.812 plus or minus 0.026, H(sub 0) = 70.5 plus or minus 1.3 kilometers per second Mpc(exp -1), OMEGA(sub b) = 0.0456 plus or minus 0.0015, OMEGA(sub c) = .228 plus or minus 0.013, OMEGA(sub m)h(sup 2) = 0.1358(sup +0.0037)(sub -0.0036), z reion = 10.9 plus or minus 1.4, and t(sub 0) = 13.72 plus or minus 0.12 Gyr. The new limit on the tensor-to-scalar ration is r less than 0.22 (95% CL), while the evidence for a running spectral index is insignificant, dn(sub s)/d ln k = -0.028 plus or minus 0.020 (68% CL). We obtain tight, simultaneous limits on the (constant) dark energy equation of state and the spatial curvature of the universe: -0.14 less than 1 + w less than 0.12 (95% CL) and -0.0179 less than OMEGA(sub k) less than 0.0081 (95% CL). The number of relativistic degrees of freedom, expressed in units of the effective number of neutrino species, is found to be N(sub eff) = 4.4 plus or minus 1.5 (69% CL), consistent with the standard value of 3.04. Models with N(sub eff) = 0 are disfavored at greater than 99% confidence. Finally, new limits on physically motivated primordial non-Gaussianity parameters are -9 less than f(sup local)(sub NL) less than 111 (95% CL) and -151 less than f(sup equal)(sub NL) less than 253 (95% CL) for the local and equilateral models, respectively.

Hinshaw, G.↗
NASA NTRS1998

Deep Basalt Aquifers in Orcus Patera, Elysium Basin Mars: Perspectives for Exobiology Exploration

Direct indicators of shorelines, spillways, and terraces allowed to determine the extent of the Elysium Paleolake between the contour-lines 1000 and 500 m below the Martian datum. The Elysium Paleolake is bordered north by Orcus Patera (14N/181W), which lies west of the Tartarus Montes and Tartarus Colles. The Orcus Patera displays an ellipse-shaped collapsed caldera of 360-km long and 100-km wide. Viking topographic data show that the bottom of the caldera is located at 2500 below the Martian datum, and surrounded by a steep-walled ram art which crest is located at about 0 m elevation. Considering the localization of Orcus Patera in the Elysium paleolake, its altimetry, and the magmatic origin of this caldera, we propose the existence of a paleolake in Orcus Patera generated (a) by juvenile water from magma during the Noachian period, and (b) by intermittent influx of the Elysium Basin from Hesperian to Amazonian. Results are encouraging to consider this site as a potential high-energy source environment for microbial communities. are circumscribed by a 50-km wide lava field mapped as Noachian material. The structure of Orcus Patera represents the record of material erupted from a magmatic reservoir. The caldera is enclosed by steep inner walls (25% measured from topographic data), values which could be in agreement with the presence of a deep magmatic reservoir, as suggested by the typology of Crumpler et.al. The depth of the caldera might be due to the collapse of the magma reservoir, and the release of gases accompanying the magma thermal evolution. Origins of water for the paleolake(s): The water that generated a paleolake in Orcus Patera may have come from two origins: (1) Juvenile water: Plescia and Crips estimated a magma H20 content by weight between 0.5% and 1.5% using for the first value a comparison with terrestrial basalt, and for the second values from a Martian meteorite. The amount of H20 can be estimated by the volume of erupted lava, and the lava content of the caldera. In this study, we adopt a water content of 1%. The total volume of magma that has been contained in the caldera, and the volume of lava contained in the observed lava field is about 110 x 10(exp 6) cubic km, that gives a total volume of 1.10 x 10(exp 6) cubic km of water. The juvenile water expelled by the overpressure within the magma chamber charged with desolved water-vapor may have moved into the crust. The decrease in overburden pressure led to bubble formation. The ascent of these bubbles generated a pressurization of the magma, which was sufficient to fracture the overlaying magma layer, (2) Water from Elysium paleolake. During the Amazonian, the rise of the Elysium paleolake level generated an overspilling that supplied the caldera with water. The southern portion of the crest shows a deep gap 12-km wide at -1500 m elevation, locating the gap between 500 to 1000 in below the assumed water of Elysium paleolake, thus facilitating the influx of Elysium paleolake water into Orcus Patera. Bathymetric calculations give a floor area of 25,500 sq km at -2000 m elevation, and a water volume of 42,000 cubic km, with a lake-level at -1500 m. A substantial amount of water may have percolated through the fractured lava, and part of the volume may have overspilled the northern crest of Orcus Patera to debouch in the Tartarus Montes region. We envision the formation of a subsurface aqueous environment in basaltic rocks at the contact of the two water-source origins, possibly the percolating surface lake water, and more likely the juvenile water. Similarly to terrestrial calderas, Orcus Patera might be surrounded by ring-fractures caused by the collapse of the magma chamber that followed the release of gases. These ring-fractures may have been covered later by sedimentation in the caldera (lacustrine, aeolian, and volcanic), and by mass wasting. The detumescence of the magma in the caldera, and the vesiculation of the juvenile water may have operated simultaneously. Comparatively to terrestrial melts, Martian iron-rich melts are denser. This greater density implies greater effusion rates (eight-times terrestrial values), and larger fissuration widths (two-times terrestrial ones). With increasing vesiculation of magma, the bubbles interact with one-another because there are of similar pressure. They make a magma froth at the contact with the caldera surface, and on the walls of the fractures. In the saturated magma, froth, where the volume ratio of gases-to-liquid is about 4:1, the bubbles form a huge surface area of interconnected spaces. Bubbles near the caldera surface disrupt the magma, and fragmentation takes place, which moves downward through the magma column. On Earth, the bubbles are likely to grow between 1 and 50 mm in diameter due to the difference between the magma surface tension, and the bubble supersaturation pressure. The Martian low-pressure at surface level is likely to accelerate the expansion of the bubbles, and increase their final diameter and number, creating more voids in the magma. The strong magma froth with enclosed juvenile water bubbles interconnected with exsolved gas bubbles constitute a potential geothermal environment for geochemical energy production from basalt and water that does not require excessive temperatures. This process can start at +20C. Similar types of environments have been shown on Earth as potential energy sources for microbial metabolism, and could have provided deep aqueous basaltic niches for possible Martian microorganisms, even geologically recently. During the Amazonian, combination of volcanism and water activity still existed on Mars. Moreover, this type of potential niches open ways for investigation of possible oases of extinct or extant life, not only on paleolakes, and surface hydrothermalism spring areas, but also all large systems of fossae, which combine hydrologic and volcanic activities, and which provide an energy source, and an underground shelter to prevent surface UV bombardment. Additional information contained in the original.

Grin, E. A.↗
NASA NTRS2000

Navigation Strategy for the Mars 2001 Lander Mission

The Mars Surveyor Program (MSP) is an ongoing series of missions designed to robotically study, map and search for signs of life on the planet Mars. The MSP 2001 project will advance the effort by sending an orbiter, a lander and a rover to the red planet in the 2001 opportunity. Each vehicle will carry a science payload that will Investigate the Martian environment on both a global and on a local scale. Although this mission will not directly search for signs of life, or cache samples to be returned to Earth, it will demonstrate certain enabling technologies that will be utilized by the future Mars Sample Return missions. One technology that is needed for the Sample Return mission is the capability to place a vehicle on the surface within several kilometers of the targeted landing site. The MSP'01 Lander will take the first major step towards this type of precision landing at Mars. Significant reduction of the landed footprint will be achieved through two technology advances. The first, and most dramatic, is hypersonic aeromaneuvering; the second is improved approach navigation. As a result, the guided entry will produce in a footprint that is only tens of kilometers, which is an order of magnitude improvement over the Pathfinder and Mars Polar Lander ballistic entries. This reduction will significantly enhance scientific return by enabling the potential selection of otherwise unreachable landing sites with unique geologic interest and public appeal. A landed footprint reduction from hundreds to tens of kilometers is also a milestone on the path towards human exploration of Mars, where the desire is to place multiple vehicles within several hundred meters of the planned landing site. Hypersonic aeromaneuvering is an extension of the atmospheric flight goals of the previous landed missions, Pathfinder and Mars Polar Lander (MPL), that utilizes aerodynamic lift and an autonomous guidance algorithm while in the upper atmosphere. The onboard guidance algorithm will control the direction of the lift vector, via bank angle modulation, to keep the vehicle on the desired trajectory. While numerous autonomous guidance algorithms have been developed for use during hypersonic flight at Earth, this will be the first flight of an autonomously directed lifting entry vehicle at Mars. However, without sufficient control and knowledge of the atmospheric entry conditions, the guidance algorithm will not perform effectively. The goal of the interplanetary navigation strategy is to deliver the spacecraft to the desired entry condition with sufficient accuracy and knowledge to enable satisfactory guidance algorithm performance. Specifically, the entry flight path angle must not exceed 0.27 deg. to a 3 sigma confidence level. Entry errors will contribute directly to the size of the landed footprint and the most significant component is entry flight path angle. The size of the entry corridor is limited on the shallow side by integrated heating constraints, and on the steep side by deceleration (g-load) and terminal descent propellant. In order to meet this tight constraint it is necessary to place a targeting maneuver seven hours prior to the time of entry. At this time the trajectory knowledge will be quite accurate, and the effects of maneuver execution errors will be small. The drawback is that entry accuracy is dependent on the success of this final late maneuver. Because propulsive maneuvers are critical events, it is desirable to minimize their occurrence and provide the flight team with as much response time as possible in the event of a spacecraft fault. A mission critical maneuver at Entry - 7 hours does not provide much fault tolerance, and it is desirable to provide a strategy that minimizes reliance on this maneuver. This paper will focus on the Improvements in interplanetary navigation that will decrease entry errors and will reduce the landed footprint, even in the absence of aeromaneuvering. The easiest to take advantage of are Improvements In the knowledge of the Mars ephemeris and gravity field due to the MGS and MSP'98 missions. Improvements In data collection and reduction techniques such as "precislon ranging' and near-simultaneous tracking will also be utilized. In addition to precise trajectory control, a robust strategy for communications and flight operations must also be demonstrated. The result Is a navigation and communications strategy on approach that utilizes optimal maneuver placement to take advantage of trajectory knowledge, minimizes risk for the flight operations team, is responsive to spacecraft hardware limitations, and achieves the entry corridor. The MSP2001 mission Is managed at JPL under the auspices of the Mars Exploration Directorate. The spacecraft flight elements are built and managed by Lockheed-Martin Astronautics in Denver, Colorado.

Mase, Robert A.↗