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NASA NTRS1997

Inertial orientation tracker apparatus having automatic drift compensation for tracking human head and other similarly sized body

A self contained sensor apparatus generates a signal that corresponds to at least two of the three orientational aspects of yaw, pitch and roll of a human-scale body, relative to an external reference frame. A sensor generates first sensor signals that correspond to rotational accelerations or rates of the body about certain body axes. The sensor may be mounted to the body. Coupled to the sensor is a signal processor for generating orientation signals relative to the external reference frame that correspond to the angular rate or acceleration signals. The first sensor signals are impervious to interference from electromagnetic, acoustic, optical and mechanical sources. The sensors may be rate sensors. An integrator may integrate the rate signal over time. A drift compensator is coupled to the rate sensors and the integrator. The drift compensator may include a gravitational tilt sensor or a magnetic field sensor or both. A verifier periodically measures the orientation of the body by a means different from the drift sensitive rate sensors. The verifier may take into account characteristic features of human motion, such as stillness periods. The drift compensator may be, in part, a Kalman filter, which may utilize statistical data about human head motion.

Foxlin, Eric M.↗

NASA NTRS2002

Inertial orientation tracker having gradual automatic drift compensation for tracking human head and other similarly sized body

Foxlin, Eric M.↗

NASA NTRS1994

The broad emission line and continuum variations of Seyfert galaxies. 2: Broad-line region structure and kinematics

Spectroscopic observations of 13 Seyfert 1 galaxies made from 1979 to 1984 at Palomar and Steward Observatories were analyzed for H beta line profile variations. Significant profile changes were detected in five galaxies. These variations are often associated with changes in continuum and/or H beta strength, suggesting a causal connection between variations in the continuum source and changes in emission-line profiles. Moreover, the overall strength of H beta line flux variations is strongly correlated with line width in the far wings, whereas no such correlation was found in the line core. This finding is consistent with previous observations (Shuder 1982) which suggest that higher velocity gas lies closer to the central continuum source, since this inner gas would be expected to track variations more closely. In each of the five galaxies in which H beta line profile variations were detected, particularly NGC 5548 and Mrk 6, only two distinct line profile shapes were observed. Since intermediate profile types were not detected, the transition from one type to the other must occur rapidly (within a few months). These rapid line profile variations are thus consistent with numerous other studies which strongly point to a small broad-line region (BLR) size in Seyfert galaxies. Observational models of BLR kinematics and structure for each of the galaxies in the present sample are presented. Line asymmetries suggest that radial motions exist in the BLRs of most of these objects. Chaotic motions also appear to be quite common. However, evidence for rotational motion was observed in only one case. A model that is consistent with the majority of this sample incorporates both radial and chaotic motions combined with some form of external obscuration such as an optically and geometrically thick torus.

Rosenblatt, Edward I.↗

NASA NTRS2004

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

Source record↗

NASA NTRS1996

Stereo Imaging Velocimetry

Stereo imaging velocimetry (SIV) will permit the collection of quantitative, three-dimensional flow data from any optically transparent fluid that can be seeded with tracer particles. This includes such diverse experiments as the study of multiphase flow, bubble nucleation and migration, pool combustion, and crystal growth. This technique will be useful to the microgravity science community as our investigations of fluid behavior in reduced-gravity environments enhance our knowledge of heat transfer, surface tension, concentration-gradient-driven anomalies, and residual effects from g-jitter. In its proposed configuration, the NASA Lewis Research Center's Stereo Imaging Velocimeter will consist of at least two charged coupled device (CCD) cameras, oriented at some relative angle with respect to each other. The cameras will observe a fluid experiment that has been seeded with tracer particles that are neutrally buoyant to permit accurate flow tracking. Except for the tracer particles, this measurement technique will be nonintrusive. Velocity accuracies will be on the order of 1 to 5 percent of full field. Each camera will make a two-dimensional record of the motion of the seed particles in the observation volume. Three-dimensional data will be obtained by computationally combining the two-dimensional information.

Source record↗

NASA NTRS1995

Time-to-Passage Judgments in Nonconstant Optical Flow Fields

The time until an approaching object will pass an observer (time to passage, or TTP) is optically specified by a global flow field even in the absence of local expansion or size cues. Kaiser and Mowafy have demonstrated that observers are in fact sensitive to this global flow information. The present studies investigate two factors that are usually ignored in work related to TTP: (1) non-constant motion functions and (2) concomitant eye rotation. Non-constant velocities violate an assumption of some TTP derivations, and eye rotations may complicate heading extraction. Such factors have practical significance, for example, in the case of a pilot accelerating an aircraft or executing a roll. In our studies, a flow field of constant-sized stars was presented monocularly on a large screen. TIP judgments had to be made on the basis of one target star. The flow field varied in its acceleration pattern and its roll component. Observers did not appear to utilize acceleration information. In particular, TTP with decelerating motion were consistently underestimated. TTP judgments were fairly robust with respect to roll, even when roll axis and track vector were decoupled. However, substantial decoupling between heading and track vector led to a decrement in performance, in both the presence and the absence of roll.

Kaiser, Mary K.↗

NASA NTRS2011

Long-Term Evolution of the Aerosol Debris Cloud Produced by the 2009 Impact on Jupiter

We present a study of the long-term evolution of the cloud of aerosols produced in the atmosphere of Jupiter by the impact of an object on 19 July 2009. The work is based on images obtained during 5 months from the impact to 31 December 2009 taken in visible continuum wavelengths and from 20 July 2009 to 28 May 2010 taken in near-infrared deep hydrogen-methane absorption bands at 2.1-2.3 micron. The impact cloud expanded zonally from approximately 5000 km (July 19) to 225,000 km (29 October, about 180 deg in longitude), remaining meridionally localized within a latitude band from 53.5 deg S to 61.5 deg S planetographic latitude. During the first two months after its formation the site showed heterogeneous structure with 500-1000 km sized embedded spots. Later the reflectivity of the debris field became more homogeneous due to clump mergers. The cloud was mainly dispersed in longitude by the dominant zonal winds and their meridional shear, during the initial stages, localized motions may have been induced by thermal perturbation caused by the impact's energy deposition. The tracking of individual spots within the impact cloud shows that the westward jet at 56.5 deg S latitude increases its eastward velocity with altitude above the tropopause by 5- 10 m/s. The corresponding vertical wind shear is low, about 1 m/s per scale height in agreement with previous thermal wind estimations. We found evidence for discrete localized meridional motions with speeds of 1-2 m/s. Two numerical models are used to simulate the observed cloud dispersion. One is a pure advection of the aerosols by the winds and their shears. The other uses the EPIC code, a nonlinear calculation of the evolution of the potential vorticity field generated by a heat pulse that simulates the impact. Both models reproduce the observed global structure of the cloud and the dominant zonal dispersion of the aerosols, but not the details of the cloud morphology. The reflectivity of the impact cloud decreased exponentially with a characteristic timescale of 15 days; we can explain this behavior with a radiative transfer model of the cloud optical depth coupled to an advection model of the cloud dispersion by the wind shears. The expected sedimentation time in the stratosphere (altitude levels 5-100 mbar) for the small aerosol particles forming the cloud is 45-200 days, thus aerosols were removed vertically over the long term following their zonal dispersion. No evidence of the cloud was detected 10 months after the impact.

Sanchez-Lavega, A.↗

NASA NTRS2000

Scanning Lidar Transceiver Telescopes Using Holographic Optical Elements

Scanning enables remote measurements perpendicular to the ground track of airborne and spaceborne lidar systems, giving us three dimensional images of atmospheric backscatter or other measurable parameters. For ground based systems, scanning allows one to record a time series of data in multiple spatial dimensions. The large size and cost of scanning systems for atmospheric lidars using conventional scanning technologies is prohibitive for space based systems. By replacing the conventional reflective telescope with a holographic optical element (HOE) in the lidar, single axis conical scanning can be achieved with a mechanically simple system. Relatively inexpensive to produce, HOES can be used to satisfy a variety of scanning lidar applications. I will introduce the concept of the HOE and describe its production and use as a scanning lidar transceiver telescope. I will describe the advantages as well as the disadvantages and limitations of HOES in this application. Optical performance test results and two lidar systems currently using HOES will be described. Examples of data taken with these systems will be presented. Current and planned future developments will be described, including scanning without mechanical motion and wide field-of-view lidar imaging.

Schwemmer, Geary K.↗

NASA NTRS2021

The Long-term Transport and Radiative Impacts of the 2017 British Columbia Pyrocumulonimbus Smoke Aerosols in the Stratosphere

Interactions of meteorology with wildfires in British Columbia, Canada during August 2017 led to three major pyrocumulonimbus (pyroCb) events that resulted in the injection of large amounts of smoke aerosols and other combustion products at the local upper troposphere and lower stratosphere (UTLS). These plumes of UTLS smoke with elevated values of aerosol extinction and backscatter compared to the background state were readily tracked by multiple satellite-based instruments as they spread across the Northern Hemisphere (NH). The plumes were observed in the lower stratosphere for about 8-10 months following the fire injections, with a stratospheric aerosol e-folding time of about 5 months. To investigate the radiative impacts of these events on the Earth system, we performed a number of simulations with the Goddard Earth Observing System (GEOS) atmospheric general circulation model (AGCM). Observations from multiple remote-sensing instruments were used to calibrate the injection parameters (location, amount, composition and heights) and optical properties of the smoke aerosols in the model. The resulting simulations of three-dimensional smoke transport were evaluated for a year from the day of injections using daily observations from OMPS-LP (Ozone Mapping Profiler Suite Limb Profiler). The model simulated rate of ascent, hemispheric spread and residence time (or e-folding time) of the smoke aerosols in the stratosphere are in close agreement with OMPS-LP observations. We found that both aerosol self-lofting and the large-scale atmospheric motion play important roles in lifting the smoke plumes from near the tropopause altitudes (~12 km) to about 22-23 km into the atmosphere. Further, our estimations of the radiative impacts of the pyroCb-emitted smoke aerosols showed that the smoke caused an additional warming of the atmosphere by about 0.6-1 W/m2 (zonal mean) that persisted for about 2-3 months after the injections in regions north of 40oN. The surface experienced a comparable magnitude of cooling. The atmospheric warming is mainly located in the stratosphere, coincident with the location of the smoke plumes, leading to an increase in zonal mean shortwave (SW) heating rates of 0.02-0.04 K/day during September 2017.

pyrocumulonimbus (pyroCb) events↗

NASA NTRS2020

Investigation Of Prandtl-Ishlinskii Hysteresis Compensation for Deep Space Optical Communications Pointing Control

This paper studies the simulated performance of the Deep Space Optical Communication (DSOC) laser downlink pointing control system that has a pointing requirement at the sub-microradian scale. To achieve the required pointing precision, the DSOC Flight Laser Transceiver (FLT) point-ahead mirror (PAM) employs piezoelectric actuators, which are widely used in precision applications due to their high motion resolution, rapid response, and high output forces. However, a piezoelectric actuator's performance is often limited by nonlinearities in their response, most significantly hysteresis. To study the effect of hysteresis on our simulated pointing performance, an invertible hysteresis model is developed using the Classical Prantdl-Ishlinskii (CPI) method. The simulation includes models of DSOC hardware and electronic system components based on key parameters (bias, frequency response, noise), with the hysteresis modeled in the PAM piezo actuator dynamics. A Proportional-Integral controller provides feedback with measurements from two potential sources: strain gauge sensors or a photon-counting camera. To compensate for hysteresis behavior, a feedforward inverse CPI hysteresis model is implemented in the control system. Two CPI models are built using different sampling methods (uniform sampling and cosine spacing) and controller performance is compared. For the maximum command range of ±400 μrad at 1 mHz, results show that the feedforward combined with feedback control reduces output tracking error by 50% or 58% (to 0.20 or 0.38 μrad) compared to feedback control alone (from 0.40 or 0.90 μrad), corresponding to the uniform-sampled and cosine-sampled CPI models, respectively.

Marinello, Lindsey A.↗

NASA NTRS2004

Libration Point Navigation Concepts Supporting Exploration Vision

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

Carpenter, J. Russell↗

NASA NTRS2011

Diagonal-Axes Stage for Pointing an Optical Communications Transceiver

Traditional azimuth-elevation ("az-el") stages are used to point a variety of devices ranging from large optical telescopes to tank guns. Such a stage typically has an elevation stage having a horizontal axis mounted on an azimuth stage with a vertical axis. Both stages are often motorized. Optical communications transceivers often require two-axis motorized control, as when the communications link is between a ground station and an aircraft or satellite. In such applications, the traditional azimuth-elevation stage has two important drawbacks: a gimbal lock exclusion zone at zenith and susceptibility to pointing errors caused by backlash. Az-el stages in which the azimuth stage cannot rotate a full 360deg have the additional drawback of an azimuth exclusion zone. The diagonal-axes stage described here mitigates or eliminates all of these problems. Instead of one vertical axis and one horizontal axis, a diagonal-axes stage has two horizontal axes, both oriented at 45 to the trajectory of the target. For example, a ground station located on the equator tracking a satellite with an equatorial orbit would have one axis parallel to northeast and southwest, and the other axis parallel to northwest and southeast. The diagonal-axes stage is considerably less vulnerable to backlash. If it is correctly oriented, its axes rotate in only one direction during an overhead pass by a satellite. As a result, the effects of backlash may be inherently eliminated. If the gravity-induced torque on either axis changes during the pass, then backlash may become important during the part of the pass where the gravity torque, instead of opposing the motion of the stage, pushes the stage in the direction of motion. This can result in the loss of gear-to-gear contact in one or more stages of the gear reduction mechanism. In this case, a preload spring used to eliminate backlash need only be sufficiently strong to overcome the gravity torque, i.e. it need not overcome friction in the gear train. The diagonal-axes stage is not backlash-free for arbitrary target trajectories such as an aircraft might execute. If properly oriented for any particular satellite, however, it is backlash-free for all passes of that satellite, which will trace out parallel paths on the sky, and for all passes of any other satellite that are perpendicular to the first. It will also be backlash-free for some fraction of other satellite trajectories.

Regehr, Martin W.↗

NASA NTRS2007

GEO Population Estimates using Optical Survey Data

Optical survey data taken using the NASA Michigan Orbital Debris Survey Telescope (MODEST) gives us an opportunity to statistically sample faint object population in the Geosynchronous (GEO) and near-GEO environment. This paper will summarize the MODEST survey work that has been conducted by NASA since 2002, and will outline the techniques employed to arrive at the current population estimates in the GEO environment for dim objects difficult to detect and track using current systems in the Space Surveillance Network (SSN). Some types of orbits have a higher detection rate based on what parts of the GEO belt is being observed, a straightforward statistical technique is used to debias these observations to arrive at an estimate of the total population potentially visible to the telescope. The size and magnitude distributions of these fainter debris objects are markedly different from the catalogued population. GEO debris consists of at least two different populations, one which follows the standard breakup power law and one which has anomalously high Area-to-Mass Ratios (1 to approx. 30 square meters per kilogram; a sheet of paper = approx. 13 square meters per kilogram). The Inter-Agency Space Debris Coordination Committee (IADC) is investigating objects in GEO orbits with anomalously high Area-to-Mass Ratios (AMRs). The ESA Space Debris Telescope discovered this population and has and its properties of inclinations (0 to 30 degrees), changing eccentricities (0 and 0.6), and mean motions (approx. 1 rev), will be presented. The accepted interpretation of this orbital behavior is that solar radiation pressure drives the perturbations causing time varying inclinations and eccentricities. The orbital parameters are unstable for this population and thus difficult to predict. Their dim visual magnitudes and photometric variability make observations a challenge. The IADC has enlisted a series of observatories (participating institutions: University of Michigan/CTIO, Astronomical Institute University of Bern, Boeing LTS / AMOS, Keldysh Institute of Applied Mathematics) at different longitudes. Complete observational coverage over periods of days to months will provide a better understanding of the properties, such as solar radiation pressure effects on orbital elements, size, shape, attitude, color variations, and spectral characteristics. Results from recent observational programs will be summarized, and includes a description of the orbit elements prediction processes, a summary of the metric tracking performance, and some photometric characteristics of this class of debris.

Barker, Edwin S.↗

NASA NTRS2006

A Countermeasure for Space Motion Sickness

Overall, the results obtained in both the U.S. and the Russian space programs indicate that most space crews will experience some symptoms of motion sickness (MS) causing significant impact on the operational objectives that must be accomplished to assure mission success. At this time the primary countermeasure for MS requires the administration of Promethazine. Promethazine is not a benign drug, and is most frequently administered just prior to the sleep cycle to prevent its side effects from further compromising mission objectives. Clearly other countermeasures for SMS must be developed. Currently the primary focus is on two different technologies: (1) developing new and different pharmacological compounds with less significant side effects, (2) preflight training. The primary problem with all of these methods for controlling MS is time. New drugs that may be beneficial are years from testing and development, and preflight training requires a significant investment of crew time during an already intensive pre-launch schedule. Granted, motion sickness symptoms can be minimized with either of the two methods detailed above, however, it may be possible to develop a countermeasure that does not require either extensive adaptation time or exposure to motion sickness. Approximately 25 years ago Professor Geoffrey Melvill Jones presented his work on adaptation of the vestibuloocular reflex (VOR) using optically reversed vision (left-right prisms) during head rotations in the horizontal plane. It was of no surprise that most subjects experienced motion sickness while wearing the optically reversing prisms. However, a serendipitous finding emerged during this research showing that the same subjects did not experience motion sickness symptoms when wearing the reversing prisms under stroboscopic illumination. The mechanism, by which this side-effect was believed to have occurred, is not clearly understood. However, the fact that no motion sickness was ever noted, suggests the possibility of producing functionally useful adaptation during space flight without the penalty of disabling motion sickness by controlling the rate of the adaptive process by means of an appropriate stroboscopically presented environment. After several recent meetings with Professor Melvill Jones, we were encouraged to repeat the motion sickness portions of his and Mandl's 1981 stroboscopic experiment. In conducting this experiment we used a randomized cross-over design where subjects were randomly assigned to either a stroboscopic flash or no strobe for their first exposure in the experimental design. Twenty subjects (19 subjects completed the study) read a short passage from Treasure Island mounted on the wall approximately 1 m from their eyes while wearing left-right reversing prisms. The strobe on time of 3 microseconds and flash frequency of 4 Hz was set to equal that used in the original study. Motion sickness was scored using a modified Miller and Graybiel scale that we constructed to include symptoms that may be elicited under conditions where reversing prisms are worn. On this scale a score of 5 represented Malaise IIa (mild motion sickness) and a score of 8 or above is approaching frank sickness. Symptoms were tracked and recorded every 5 min during the task. Testing was limited to 30 min unless the subject had reached the MIIa score, at which time the test was terminated. Performance under stroboscopic illumination was significantly better than when the subjects read under normal room illumination while wearing the left-right reversing prisms. Based on these results we developed a goggle system using LCD material that can be strobed. To evaluate the effectiveness of stroboscopic goggles we tested an additional 9 subjects in addition to retesting 10 used in the stroboscopic pilot study described above. These 19 subjects wore a pair of strobing LCD goggles that could be cycled at 4 Hz. These subjects wore the goggles while also wearing left-right reversg prisms. Results while wearing the goggles showed that none of the 19 subjects scored at the MIIa level on the motion sickness rating scale. When the goggles did not flash (no strobe), 11 of the 19 developed symptoms above the MIIa criteria. As a countermeasure the goggles seem to be effective, even with an on time of 10 msec (time the goggles are clear). We have also collected anecdotal data, from our personnel in the Neuroscience Laboratory at the Johnson Space Center, suggesting that the goggles may effective in preventing carsickness.

Reschke, M. F.↗

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↗