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NASA NTRS1996

Means for Positioning and Repositioning Scanning Instruments

A method is presented for positioning a scanning instrument to point toward the center of the desired scan wherein the scan is achieved by rotating unbalanced masses (RUMs) rotating about fixed axes of rotation relative to and associated with the instrument, the RUMs being supported on drive shafts spaced from the center of the mass of the instrument and rotating 180 degrees out-of-phase with each other and in planes parallel to each other to achieve the scan. The elevation and cross-elevation angles of the instrument are sensed to determine any offset and offset time rate-of-change, and the magnitude and direction are converted to a RUM cycle angular velocity component to be superimposed on the nominal velocity of the RUMs. This RUM angular velocity component modulates the RUM angular velocity to cause the speed of the RUMs to increase and decrease during each revolution to drive the instrument toward the desired center of the scan.

Polites, Michael E.↗

NASA NTRS1988

Embedding of attitude determination in n-dimensional spaces

The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1994

Motion models in attitude estimation

Attitude estimator use observations from different times to reduce the effects of noise. If the vehicle is rotating, the attitude at one time needs to be propagated to that at another time. If the vehicle measures its angular velocity, attitude propagating entails integrating a rotational kinematics equation only. If a measured angular velocity is not available, torques can be computed and an additional rotational dynamics equation integrated to give the angular velocity. Initial conditions for either of these integrations come from the estimation process. Sometimes additional quantities, such as gyro and torque parameters, are also solved for. Although the partial derivatives of attitude with respect to initial attitude and gyro parameters are well known, the corresponding partial derivatives with respect to initial angular velocity and torque parameters are less familiar. They can be derived and computed numerically in a way that is analogous to that used for the initial attitude and gyro parameters. Previous papers have demonstrated the feasibility of using dynamics models for attitude estimation but have not provided details of how each angular velocity and torque parameters can be estimated. This tutorial paper provides some of that detail, notably how to compute the state transition matrix when closed form expressions are not available. It also attempts to put dynamics estimation in perspective by showing the progression from constant to gyro-propagated to dynamics-propagated attitude motion models. Readers not already familiar with attitude estimation will find this paper an introduction to the subject, and attitude specialists may appreciate the collection of heretofore scattered results brought together in a single place.

Chu, D.↗

NASA NTRS1985

Method for driving two-phase turbines with enhanced efficiency

A method for driving a two phase turbine characterized by an output shaft having at least one stage including a bladed rotor connected in driving relation with the shaft is described. A two phase fluid is introduced into one stage at a known flow velocity and caused to pass through the rotor for imparing angular velocity thereto. The angular velocity of the rotor is maintained at a value such that the angular velocity of the tips of the blades of the rotor is a velocity equal to at least 50% of the velocity of the flow of the two phase fluid.

Elliott, D. G.↗

NASA NTRS1960

A Homing Missile Control System to Reduce the Effects of Radome Diffraction

The problem of radome diffraction in radar-controlled homing missiles at high speeds and high altitudes is considered from the point of view of developing a control system configuration which will alleviate the deleterious effects of the diffraction. It is shown that radome diffraction is in essence a kinematic feedback of body angular velocities which causes the radar to sense large apparent line-of-sight angular velocities. The normal control system cannot distinguish between the erroneous and actual line-of-sight rates, and entirely wrong maneuvers are produced which result in large miss distances. The problem is resolved by adding to the control system a special-purpose computer which utilizes measured body angular velocity to extract from the radar output true line-of-sight information for use in steering the missile. The computer operates on the principle of sampling and storing the radar output at instants when the body angular velocity is low and using this stored information for maneuvering commands. In addition, when the angular velocity is not low the computer determines a radome diffraction compensation which is subtracted from the radar output to reduce the error in the sampled information. Analog simulation results for the proposed control system operating in a coplanar (vertical plane) attack indicate a potential decrease in miss distance to an order of magnitude below that for a conventional system. Effects of glint noise, random target maneuvers, initial heading errors, and missile maneuverability are considered in the investigation.

Smith, Gerald L.↗

NASA NTRS2013

Catching a Rolling Stone: Dynamics and Control of a Spacecraft and an Asteroid

In a recent report, a robotic spacecraft mission is proposed for the purpose of collecting a small asteroid, or a small part of a large one, and transporting it to an orbit in the Earth-Moon system. Such an undertaking will require solutions to many of the engineering problems associated with deflection of an asteroid that poses a danger to Earth. In both cases, it may be necessary for a spacecraft to approach an asteroid from a nearby position, hover for some amount of time, move with the same angular velocity as the asteroid, descend, perhaps ascend, and finally arrest the angular velocity of the asteroid. Dynamics and control in each of these activities is analyzed in order to determine the velocity increments and control torque that must be provided by a reaction control system, and the mass of the propellant that will be consumed. Two attitude control algorithms are developed, one to deal with synchronizing the spacecraft s angular velocity with that of the asteroid, and the other to arrest the asteroid s angular velocity. A novel approach is proposed for saving fuel in the latter case.

Roithmayr, Carlos M.↗

NASA NTRS2001

On-Orbit Calibration of Redundant Spacecraft Gyros by Optimal Reduction to Three Axes

The Aqua spacecraft will carry four single-axis gyros configured with three orthogonal axes and one skew axis. This redundancy presents a challenge for batch methods of on-orbit gyro calibration that use a spacecraft rotation model deterministically related to gyro data, in that sensor data can respond to at most three angular velocity components. When the number of gyros, N, is greater than 3, the 3xN matrix, G, that reduces the N gyro measurements to three body-frame angular-velocity components cannot be fully determined by such methods; there are many such matrices that produce essentially the same angular velocity history. In such a case, spacecraft operators require information about the Nx3 gyro linear response matrix, R, that relates gyro outputs to the body-frame angular velocities causing them. This matrix provides sufficient information to determine multiple reduced-dimension G-matrices for use in case of failure or degradation of one or more gyros, as well as to determine an optimal 3xN G for the fully-functional configuration. A viable proposal is to apply a 3xN pre-filter matrix, F, to the N gyro outputs before carrying out a conventional gyro calibration procedure. The angular-velocity history emerging from conventional calibration may then be used as input data, together with the same gyro data that generated it, to fit the alignment, scale-factor, and bias parameters of each gyro axis in turn. A difficulty of such a proposal is the arbitrariness in the choice of F. Due to gyro noise, different pre-filter matrices produce different calibrations. This paper presents a method of choosing F that is based on optimizing gyro consistency in the limit of infinite weight on gyro data, as compared to sensor data. The choice of F is independent of a priori alignment and is based on the gyro data alone. The method is applicable to any N of three or more, but reduces to conventional batch-estimation methodologies when N = 3. Results of computational comparison among calibration simulations using various choices of F will be presented for the Aqua gyro configuration with N = 4.

Radomski, M. S.↗

NASA NTRS1973

Spacecraft attitude sensor

A system for sensing the attitude of a spacecraft includes a pair of optical scanners having a relatively narrow field of view rotating about the spacecraft x-y plane. The spacecraft rotates about its z axis at a relatively high angular velocity while one scanner rotates at low velocity, whereby a panoramic sweep of the entire celestial sphere is derived from the scanner. In the alternative, the scanner rotates at a relatively high angular velocity about the x-y plane while the spacecraft rotates at an extremely low rate or at zero angular velocity relative to its z axis to provide a rotating horizon scan. The positions of the scanners about the x-y plane are read out to assist in a determination of attitude. While the satellite is spinning at a relatively high angular velocity, the angular positions of the bodies detected by the scanners are determined relative to the sun by providing a sun detector having a field of view different from the scanners.

Davidson, A. C.↗

DOE OSTI2025

Evolution of intermittent filaments in the scrape-off layer of NSTX

Filamentary structures naturally arise from background turbulence in the scrape-off layer (SOL) of plasmas, leading to significant particle and heat transport that can degrade overall plasma confinement. This enhanced transport can contribute to unacceptably high heat loads on plasma-facing components. As such, understanding the physics of SOL plasma filaments is critical for predicting and mitigating their effects in future fusion devices. On the National Spherical Torus Experiment (NSTX), plasma filaments—commonly referred to as “blobs”—were investigated using the gas-puff imaging (GPI) diagnostic in the edge and SOL regions. The analysis involved identifying, segmenting, and tracking the characteristic contours of the blobs in each frame of the GPI video sequences. Their evolution was characterized through shape descriptors, velocity, and angular velocity derived from their contour coordinates. The results indicate that as the blob area increases, their shapes become more concave and less circular, suggesting reduced structural stability in larger blobs. This result aligns with previous theoretical results where it was shown that larger blobs are more susceptible to instabilities [Krasheninnikov et al., J. Plasma Phys. 74, 679–717 (2008) and D'Ippolito et al., Phys. Plasmas 18, 060501 (2011)]. A positive correlation was observed between radial velocity and radial position, suggesting radially outward acceleration of the filaments, potentially driven by decreasing viscous drag toward the far SOL. Interestingly, blobs in background SOL turbulence exhibited minimal spinning in contrast to filaments originating from edge localized modes, which show substantial rotation during their paths [Lampert et al., Phys. Plasmas 29, 102502 (2022)]. Statistical analysis of the solidity and total curvature shape descriptors, along with their temporal evolution, revealed relatively broad, near-Gaussian distributions. This suggests that blob morphology is strongly influenced by stochastic turbulent processes in the surrounding plasma environment. Blob parameters were also compared with bulk plasma and radial profile measurements. Notable trends were found between blob rotation and poloidal velocity with collisionality and line-integrated density. These findings contribute to a deeper understanding of blob dynamics and provide valuable insights for refining SOL turbulence models.

Covariance and correlation↗

NASA NTRS1970

A quantitative study of vestibular adaptation in humans, part 3

Mathematical model for short-term adaptation to vestibular stimuli in relation to angular velocity of nystagmus and angular velocity of head rotation

Malcolm, R.↗

NASA NTRS1976

Eye movements during afterimage tracking under sinusoidal and random vestibular stimulation

The smooth portion of the horizontal vestibulo-ocular reflex was analyzed in terms of the frequency response, relating slow-phase eye velocity to angular velocity of a rotating chair under four different cases: sinusoidal rotation about a vertical axis in total darkness, sinusoidal rotation during afterimage tracking, pseudorandom head rotation in total darkness, and pseudorandom head rotation during afterimage tracking. Eye movements were recorded using a photoelectric limbus tracking method. The observation that the presence of an afterimage during vestibular stimulation increases the velocity of slow-phase eye movements is in support of the theory that such slow-phase movements are generated, at least in part, by the perceived velocity of the target. Since the target is immobilized on the retina, this perceived velocity is clearly not generated by retinal slip, but rather by a mechanism related to the eye movement such as corollary discharge.

Yasui, S.↗

NASA NTRS1987

Real-time model-based vision system for object acquisition and tracking

A machine vision system is described which is designed to acquire and track polyhedral objects moving and rotating in space by means of two or more cameras, programmable image-processing hardware, and a general-purpose computer for high-level functions. The image-processing hardware is capable of performing a large variety of operations on images and on image-like arrays of data. Acquisition utilizes image locations and velocities of the features extracted by the image-processing hardware to determine the three-dimensional position, orientation, velocity, and angular velocity of the object. Tracking correlates edges detected in the current image with edge locations predicted from an internal model of the object and its motion, continually updating velocity information to predict where edges should appear in future frames. With some 10 frames processed per second, real-time tracking is possible.

Wilcox, Brian↗

NASA NTRS1989

Autonomous sensor-based dual-arm satellite grappling

Dual-arm satellite grappling involves the integration of technologies developed in the Sensing and Perception (S&P) Subsystem for object acquisition and tracking, and the Manipulator Control and Mechanization (MCM) Subsystem for dual-arm control. S&P acquires and tracks the position, orientation, velocity, and angular velocity of a slowly spinning satellite, and sends tracking data to the MCM subsystem. MCM grapples the satellite and brings it to rest, controlling the arms so that no excessive forces or torques are exerted on the satellite or arms. A 350-pound satellite mockup which can spin freely on a gimbal for several minutes, closely simulating the dynamics of a real satellite is demonstrated. The satellite mockup is fitted with a panel under which may be mounted various elements such as line replacement modules and electrical connectors that will be used to demonstrate servicing tasks once the satellite is docked. The subsystems are housed in three MicroVAX II microcomputers. The hardware of the S&P Subsystem includes CCD cameras, video digitizers, frame buffers, IMFEX (a custom pipelined video processor), a time-code generator with millisecond precision, and a MicroVAX II computer. Its software is written in Pascal and is based on a locally written vision software library. The hardware of the MCM Subsystem includes PUMA 560 robot arms, Lord force/torque sensors, two MicroVAX II computers, and unimation pneumatic parallel grippers. Its software is written in C, and is based on a robot language called RCCL. The two subsystems are described and test results on the grappling of the satellite mockup with rotational rates of up to 2 rpm are provided.

Wilcox, Brian↗

NASA NTRS1991

A study of high alpha dynamics and flow visualization for a 2.5-percent model of the F-18 HARV undergoing wing rock

Free-to-roll experiments and flow visualization studies have been conducted for a 2.5-percent model of the F-18 undergoing unsteady wing rock oscillations. Data have been acquired in the form of roll angle time histories as well as video recordings and 35 mm photography of the forebody and leading edge extension vortices. The time histories were differentiated to produce angular velocity and angular acceleration. From this the roll moment as a function of time and/or roll angle could be estimated. A thorough analysis of the data has revealed a genuine wing-rock phenomenon. Off-surface flow visualization was used to identiify the forebody and LEX vortex core positions and their interaction in both static and dynamic configurations. A direct correlation between the dynamic data and visualized vortex activity during the wing-rock motion has been made.

Quast, Thomas↗

NASA NTRS2007

Estimation of Cometary Rotation Parameters Based on Camera Images

The purpose of the Rosetta mission is the in situ analysis of a cometary nucleus using both remote sensing equipment and scientific instruments delivered to the comet surface by a lander and transmitting measurement data to the comet-orbiting probe. Following a tour of planets including one Mars swing-by and three Earth swing-bys, the Rosetta probe is scheduled to rendezvous with comet 67P/Churyumov-Gerasimenko in May 2014. The mission poses various flight dynamics challenges, both in terms of parameter estimation and maneuver planning. Along with spacecraft parameters, the comet's position, velocity, attitude, angular velocity, inertia tensor and gravitatonal field need to be estimated. The measurements on which the estimation process is based are ground-based measurements (range and Doppler) yielding information on the heliocentric spacecraft state and images taken by an on-board camera yielding informaton on the comet state relative to the spacecraft. The image-based navigation depends on te identification of cometary landmarks (whose body coordinates also need to be estimated in the process). The paper will describe the estimation process involved, focusing on the phase when, after orbit insertion, the task arises to estimate the cometary rotational motion from camera images on which individual landmarks begin to become identifiable.

Spindler, Karlheinz↗

NASA NTRS1995

Uncertainties for two-dimensional models of solar rotation from helioseismic eigenfrequency splitting

Observed solar p-mode frequency splittings can be used to estimate angular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e.g., least-squares), the distribution of errors in the observations, and the parameterization imposed on the angular velocity. We obtain lower bounds on the uncertainties that do not depend on the method of estimation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the 'true' uncertainty does not. Ninety-five percent confidence intervals for estimates of the angular velocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 3659 element tensor-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compared with estimates of the solar rotation, these bounds reveal that useful inferences based on pointwise estimates of the angular velocity using 1986 BBSO splitting data are not feasible over most of the Sun's volume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point values based on splittings are extremely uncertain. Functionals that measure distributed 'smooth' properties are, in general, better constrained than estimates of the rotation at a point. For example, the uncertainties in estimated differences of average rotation between adjacent blocks of about 0.001 solar volumes across the base of the convective zone are much smaller, and one of several estimated differences we compute appears significant at the 95% level.

Genovese, Christopher R.↗

NASA NTRS1989

COBE nonspinning attitude propagation

The Cosmic Background Explorer (COBE) spacecraft will exhibit complex attitude motion consisting of a spin rate of approximately -0.8 revolution per minute (rpm) about the x-axis and simultaneous precession of the spin axis at a rate of one revolution per orbit (rpo) about the nearly perpendicular spacecraft-to-Sun vector. The effect of the combined spinning and precession is to make accurate attitude propagation difficult and the 1-degree (3 sigma) solution accuracy goal problematic. To improve this situation, an intermediate reference frame is introduced, and the angular velocity divided into two parts. The nonspinning part is that which would be observed if there were no rotation about the X-axis. The spinning part is simply the X-axis component of the angular velocity. The two are propagated independently and combined whenever the complete attitude is needed. This approach is better than the usual one-step method because each of the two angular velocities look nearly constant in their respective reference frames. Since the angular velocities are almost constant, the approximations made in discrete time propagation are more nearly true. To demonstrate the advantages of this nonspinning method, attitude is propagated as outlined above and is then compared with the results of the one-step method. Over the 100-minute COBE orbit, the one-step error grows to several degrees while the nonspinning error remains negligible.

Chu, D.↗