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NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗
NASA NTRS2003

The Laser Astrometric Test of Relativity (LATOR) Mission

This paper discusses new fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, proportional to G(sup 2). The Laser Astrometric Test Of Relativity (LATOR) mission uses laser interferometry between two micro-spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (100 m) multi-channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangle s three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy. LATOR will not only improve the value of the parameterized post-Newtonian (PPN) gamma to unprecedented levels of accuracy of 1 part in 10(exp 8), it will also reach ability to measure effects of the next post-Newtonian order (c(sup -4)) of light deflection resulting from gravity s intrinsic non-linearity. The solar quadrupole moment parameter, J(sub 2), will be measured with high precision, as well as a variety of other relativistic effects including Lense-Thirring precession. LATOR will lead to very robust advances in the tests of Fundamental physics: this mission could discover a violation or extension of general relativity, or reveal the presence of an additional long range interaction in the physical law. There are no analogs to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments.

Turyshev, Slava G.↗
NASA NTRS2004

Environmental impacts on the developing CNS: CD15, NCAM-L1, and GFAP expression in rat neonates exposed to hypergravity

We have previously reported that the developing rat cerebellum is affected by hypergravity exposure. The effect is observed during a period of both granule and glial cell proliferation and neuronal migration in the cerebellum and coincides with changes in thyroid hormone levels. The present study begins to address the molecular mechanisms involved in the cerebellar response to hypergravity. Specifically, the study focuses on the expression of cerebellar proteins that are known to be directly involved in cell-cell interactions [protein expressing 3-fucosyl-N-acetyl-lactosamine antigen (CD15), neuronal cell adhesion molecule (NCAM-L1)] and those that affect cell-cell interactions indirectly [glial fibrillary acidic protein (GFAP)] in rat neonates exposed to centrifuge-produced hypergravity. Cerebellar mass and protein expression in rat neonates exposed to hypergravity (1.5 G) from gestational day (G) 11 to postnatal day (P) 30 were compared at one of six time points between P6 and P30 against rat neonates developing under normal gravity. Proteins were analyzed by quantitative western blots of cerebellar homogenates prepared from male or female neonates. Cerebellar size was most clearly reduced in male neonates on P6 and in female neonates on P9, with a significant gender difference; differences in cerebellar mass remained significant even when change in total body mass was factored in. Densitometric analysis of western blots revealed both quantitative and temporal changes in the expression of selected cerebellar proteins that coincided with changes in cerebellar mass and were gender-specific. In fact, our data indicated certain significant differences even between male and female control animals. A maximal decrease in expression of CD15 was observed in HG females on P9, coinciding with maximal change in their cerebellar mass. A shift in the time-course of NCAM-L1 expression resulted in a significant increase in NCAM-L1 in HG males on P18, an isolated time at which cerebellar mass does not significantly differ between HG and SC neonates. A maximal decrease in expression of GFAP was observed in HG males on P6, coinciding with maximal change in their cerebellar mass. Altered expression of cerebellar proteins is likely to affect a number of developmental processes and contribute to the structural and functional alterations seen in the CNS developing under altered gravity. Our data suggest that both cerebellar development and its response to gravitational manipulations differ in males and females. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Program Fundamental Space Biology↗
NASA NTRS1992

Research objectives, opportunities, and facilities for microgravity science

Microgravity Science in the U.S.A. involves research in fluids science, combustion science, materials science, biotechnology, and fundamental physics. The purpose is to achieve a thorough understanding of the effects of gravitational body forces on physical phenomena relevant to those disciplines. This includes the study of phenomena which are usually overwhelmed by the presence of gravitational body forces and, therefore, chiefly manifested when gravitational forces are weak. In the pragmatic sense, the research involves gravity level as an experimental parameter. Calendar year 1992 is a landmark year for research opportunities in low earth orbit for Microgravity Science. For the first time ever, three Spacelab flights will fly in a single year: IML-1 was launched on January 22; USML-1 was launched on June 25; and, in September, SL-J will be launched. A separate flight involving two cargo bay carriers, USMP-1, will be launched in October. From the beginning of 1993 up to and including the Space Station era (1997), nine flights involving either Spacelab or USMP carriers will be flown. This will be augmented by a number of middeck payloads and get away specials flying on various flights. All of this activity sets the stage for experimentation on Space Station Freedom. Beginning in 1997, experiments in Microgravity Science will be conducted on the Space Station. Facilities for doing experiments in protein crystal growth, solidification, and biotechnology will all be available. These will be joined by middeck-class payloads and the microgravity glove box for conducting additional experiments. In 1998, a new generation protein crystal growth facility and a facility for conducting combustion research will arrive. A fluids science facility and additional capability for conducting research in solidification, as well as an ability to handle small payloads on a quick response basis, will be added in 1999. The year 2000 will see upgrades in the protein crystal growth and fluids science facilities. From the beginning of 1997 to the fall of 1999 (the 'man-tended capability' era), there will be two or three utilization flights per year. Plans call for operations in Microgravity Science during utilization flights and between utilization flights. Experiments conducted during utilization flights will characteristically require crew interaction, short duration, and less sensitivity to perturbations in the acceleration environment. Operations between utilization flights will involve experiments that can be controlled remotely and/or can be automated. Typically, the experiments will require long times and a pristine environment. Beyond the fall of 1999 (the 'permanently-manned capability' era), some payloads will require crew interaction; others will be automated and will make use of telescience.

Bayuzick, Robert J.↗
NASA NTRS2019

The Afterglow and Kilonova of the Short GRB 160821B

GRB 160821B is a short duration gamma-ray burst (GRB) detected and localized by the Neil Gehrels Swift Observatory in the outskirts of a spiral galaxy at z = 0.1613, at a projected physical offset of 16 kpc from the galaxy’s center. We present X-ray, optical/nIR, and radio observations of its counterpart and model them with two distinct components of emission: a standard afterglow, arising from the interaction of the relativistic jet with the surrounding medium, and a kilonova, powered by the radioactive decay of the sub-relativistic ejecta. Broadband modelling of the afterglow data reveals a weak reverse shock propagating backward into the jet, and a likely jet-break at 3.5 d. This is consistent with a structured jet seen slightly off-axis (θview ∼ θcore) while expanding into a low-density medium (n ≈ 10−3 cm−3). Analysis of the kilonova properties suggests a rapid evolution towards red colours, similar toAT2017gfo, and a low-nIR luminosity, possibly due to the presence of a long-lived neutron star. The global properties of the environment, the inferred low mass (Mej <~ 0.006 Msun) and velocities (vej >~ 0.05c) of lanthanide-rich ejecta are consistent with a binary neutron star merger progenitor.

Gravitational waves↗
NASA NTRS1999

"Electrostructural Phase Changes" In Charged Particulate Clouds: Planetary and Astrophysical Implications

There is empirical evidence that freely-suspended triboelectrostatically charged particulate clouds of dielectric materials undergo rapid conversion from (nominally) monodispersed "aerosols" to a system of well-defined grain aggregates after grain motion or fluid turbulence ceases within the cloud. In United States Microgravity Laboratory Space Shuttle experiments USML-1 and USML-2, it was found that ballistically-energized grain dispersions would rapidly convert into populations of filamentary aggregates after natural fluid (air) damping of grain motion. Unless continuously disrupted mechanically, it was impossible to maintain a non-aggregated state for the grain clouds of sand-size materials. Similarly, ground- based experiments with very fine dust-size material produced the same results: rapid, impulsive "collapse" of the dispersed grains into well-defined filamentary structures. In both ground-based and microgravity experiments, the chains or filaments were created by long-range dipole electrostatic forces and dipole-induced dielectric interactions, not by monopole interactions. Maintenance of the structures was assisted by short-range static boundary adhesion forces and van der Waals interactions. When the aggregate containers in the USML experiments were disturbed after aggregate formation, the quiescently disposed filaments would rearrange themselves into fractal bundles and tighter clusters as a result of enforced encounters with one another. The long-range dipole interactions that bring the grains together into aggregates are a product of randomly-distributed monopole charges on the grain surfaces. In computer simulations, it has been shown that when the force vectors of all the random charges (of both sign) on a grain are resolved mathematically by assuming Coulombic interaction between them, the net result is a dipole moment on individual grains, even though the grains are electrically neutral insofar as there is no predominance, on their surface, of one charge sign over another. The random charges of both sign derive from natural grain-to-grain interactions that produce triboelectrification via charge exchange every time grain surfaces make contact with one another. The conversion from a random distribution of grains (upon which there are randomly distributed charges) into an organization of electrostatically-ordered aggregates, can be regarded (within the framework of granular-material science) as an "electrical or Coulombic phase change" of the particulate cloud. It is not totally dissimilar from the more normal phase-change concept in which, for example, a gas with long free-path-molecules suddenly becomes a solid as a result of structural ordering of the molecules (notably, also the result of electronic forces, albeit at a different scale). In both the gas-to-solid case, and the aerosol-to-aggregate case, the same materials and charges are present before and after the phase change, but their arrangement now has a higher degree of order and a lower-energy configuration. An input of energy into the system is required to reverse the situation. The aggregates in the USML experiments were observed to undergo at least two phase changes as noted above. The point about phase changes, and by implication, the "electrostructural" reorganizations in particulate clouds, is the following: (a) they can occur very rapidly, almost spontaneously, above a critical cloud density, (b) in going from a higher energy state to a lower energy state, they convert to a denser system, (c) energy must be required to reverse the situation, implying that energy is released during the high-to-low energy phase change. In applying this information to natural particulate clouds, some inferences can be made (it is stressed that reference is still to dielectric materials attracted by dipole forces). There are several natural settings to which the USML observations apply, and to which the phase-change implications likewise apply. Dense clouds of triboelectrically-charged, kinetically-energized grains are to be found in volcanic eruptions (particularly on earth), aeolian dust storms (particularly on Mars), meteorite impact ejecta curtains (on all planets), in "immature" debris rings around planets (e.g., that from which our own Moon may have condensed), and in gravitationally collapsing protoplanetary dust/planetesimal debris disks where dielectric granules are being increasingly brought into collisional relationships with one another (increasing both charge exchange and physical proximity). It is noted that in many of these cases, the degree of electrical charging on the grains is likely to be much higher than that in the USML experiments where charging was not enhanced above the "normal", naturally encountered level for the particular materials (quartz, glass, and various silicate minerals). Application of the phase-change concept suggests that volcanic, aeolian, and impact debris clouds may, under certain circumstances, undergo rapid, impulsive, or even catastrophic collapse into a denser state that will lead to rapid precipitation or fall-out of suspended particulates. Although this idea has been suggested previously by the author , the phase change concept possibly permits some new insights into cloud-system behavior. For example, in a protoplanetary debris disk, the work of gravity may suddenly be enhanced by electrostatically driven collapse of the system when materials reach a critical intergranular spacing or grain number density. This might reduce the rate of planet formation by orders of magnitude (considering the ratio of g-forces to electrostatic ones for very small grains in close proximity), and indeed, it might drive the collapse into a system configuration that would perhaps not be created by gravity alone. Additional information is contained in the original.

Marshall, J. R.↗
NASA NTRS2000

How the science and engineering of spaceflight contribute to understanding the plasticity of spinal cord injury

Space programs support experimental investigations related to the unique environment of space and to the technological developments from many disciplines of both science and engineering that contribute to space studies. Furthermore, interactions between scientists, engineers and administrators, that are necessary for the success of any science mission in space, promote interdiscipline communication, understanding and interests which extend well beyond a specific mission. NASA-catalyzed collaborations have benefited the spinal cord rehabilitation program at UCLA in fundamental science and in the application of expertise and technologies originally developed for the space program. Examples of these benefits include: (1) better understanding of the role of load in maintaining healthy muscle and motor function, resulting in a spinal cord injury (SCI) rehabilitation program based on muscle/limb loading; (2) investigation of a potentially novel growth factor affected by spaceflight which may help regulate muscle mass; (3) development of implantable sensors, electronics and software to monitor and analyze long-term muscle activity in unrestrained subjects; (4) development of hardware to assist therapies applied to SCI patients; and (5) development of computer models to simulate stepping which will be used to investigate the effects of neurological deficits (muscle weakness or inappropriate activation) and to evaluate therapies to correct these deficiencies.

Review↗
NASA NTRS1998

Planetesimal Formation in the Protoplanetary Nebula

In this talk we will address two distinct phases of planetesimal formation, each of which is fundamentally dependent upon the coupled interactions of particles and turbulent nebula gas. It has been shown both numerically and experimentally that 3-D (three dimensional) turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Rev(sub m)/cH, where v(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha is greater than 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C is approximately equal to 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation. Once large particles (meter-size mass equivalent) reach the midplane, perhaps in the form of dense aggregates of the sort formed in 3D turbulence, they remain stable against gravitational instability but might grow rapidly by accretion of their drifting neighbors, depending on the level of global turbulence.

Cuzzi, Jeffrey N.↗
NASA NTRS1998

Interaction of semicircular canal stimulation with carotid baroreceptor reflex control of heart rate

The carotid-cardiac baroreflex contributes to the prediction of orthostatic tolerance; experimental attenuation of the reflex response leads to orthostatic hypotension in humans and animals. Anecdotal observations indicate that rotational head movements about the vertical axis of the body can also induce orthostatic bradycardia and hypotension through increased parasympathetic activity. We therefore measured the chronotropic response to carotid baroreceptor stimulation in 12 men during varying conditions of vestibulo-oculomotor stimulation to test the hypothesis that stimulation of the semicircular canals associated with head movements in the yaw plane inhibits cardioacceleration through a vagally mediated baroreflex. Carotid-cardiac baroreflex response was assessed by plotting R-R intervals (ms) at each of 8 neck pressure steps with their respective carotid distending pressures (mmHg). Calculated baroreflex gain (maximal slope of the stimulus-response relationship) was measured under 4 experimental conditions: 1) sinusoidal whole-body yaw rotation of the subject in the dark without visual fixation (combined vestibular-oculomotor stimulation); 2) yaw oscillation of the subject while tracking a small head-fixed light moving with the subject (vestibular stimulation without eye movements); 3) subject stationary while fixating on a small light oscillating in yaw at the same frequency, peak acceleration, and velocity as the chair (eye movements without vestibular stimulation); and 4) subject stationary in the dark (no eye or head motion). Head motion alone and with eye movement reduced baseline baroreflex responsiveness to the same stimulus by 30%. Inhibition of cardioacceleration during rotational head movements may have significant impact on functional performance in aerospace environments, particularly in high-performance aircraft pilots during high angular acceleration in aerial combat maneuvers or in astronauts upon return from spaceflight who already have attenuated baroreflex functions.

Review, Tutorial↗
NASA NTRS1988

The influence of calcium and pH on growth in primary roots of Zea mays

We investigated the interaction of Ca2+ and pH on root elongation in Zea mays L. cv. B73 x Missouri 17 and cv. Merit. Seedlings were raised to contain high levels of Ca2+ (HC, imbibed and raised in 10 mM CaCl2) or low levels of Ca2+ (LC, imbibed and raised in distilled water). In HC roots, lowering the pH (5 mM MES/Tris) from 6.5 to 4.5 resulted in strong, long-lasting growth promotion. Surprisingly, increasing the pH from 6.5 to 8.5 also resulted in strong growth promotion. In LC roots acidification of the medium (pH 6.5 to 4.5) resulted in transient growth stimulation followed by a gradual decline in the growth rate toward zero. Exposure of LC roots to high pH (pH shift from 6.5 to 8.5) also promoted growth. Addition of EGTA resulted in strong growth promotion in both LC and HC roots. The ability of EGTA to stimulate growth appeared not to be related to H+ release from EGTA upon Ca2+ chelation since, 1) LC roots showed a strong and prolonged response to EGTA, but only a transient response to acid pH, and 2) promotion of growth by EGTA was observed in strongly buffered solutions. We also examined the pH dependence of the release of 45Ca2+ from roots of 3-day-old seedlings grown from grains imbibed in 45Ca2+. Release of 45Ca2+ from the root into agar blocks placed on the root surface was greater the more acidic the pH of the blocks. The results indicate that Ca2+ may be necessary for the acid growth response in roots.

Non-NASA Center↗