Results for “Body Reference Frame” — Page 2

NASA NTRS1978

Three dimensional steady and unsteady asymmetric flow past wings of arbitrary planforms

The nonlinear discrete vortex method is extended to treat the problem of asymmetric flows past a wing with leading edge separation, including steady and unsteady flows. The problem is formulated in terms of a body fixed frame of reference and the nonlinear-discrete vortex method is modified accordingly. Although the method is general, only examples of flows past delta wings are presented due to the availability of experimental data as well as approximate theories. Comparison of results with experimental results for a delta wing undergoing a steady rolling motion at zero angle of attack demonstrate the superiority of the present method over existing approximate theories in obtaining highly accurate loads. Numerical results for yawed wings at large angles of attack are also presented. In all cases, total load coefficients, pressure distributions, and shapes of the free vortex sheets are shown.

Kandil, O. A.↗

NASA NTRS1989

Rotation of Halley's comet

Numerical simulations supported by analytical calculations are used to model the suspected condition of Comet Halley's nucleus, which has been suggested to not be in a state of principal-axis rotation. It is found easy to numerically generate lightcurves from modulated jets of material which exhibit both of the observed periodicities of 2.2 and 7.4 days, after choosing initial conditions for a representative nucleus such that the shorter period is the rotation period, and the longer period is that of precession of the spin vector in the body frame-of-reference. The improbability of exciting a spin precession about the axis of minimum moment-of-inertia, the relative instability of this state to the jet-induced torques, and the smaller probability of observing significant seasonal changes in the lightcurve in this state, all favor the model in which Halley's nucleus precesses about the axis of maximum moment-of-inertia.

Peale, S. J.↗

NASA NTRS1989

A decoupled recursive approach for constrained flexible multibody system dynamics

A variational-vector calculus approach is employed to derive a recursive formulation for dynamic analysis of flexible multibody systems. Kinematic relationships for adjacent flexible bodies are derived in a companion paper, using a state vector notation that represents translational and rotational components simultaneously. Cartesian generalized coordinates are assigned for all body and joint reference frames, to explicitly formulate deformation kinematics under small deformation kinematics and an efficient flexible dynamics recursive algorithm is developed. Dynamic analysis of a closed loop robot is performed to illustrate efficiency of the algorithm.

Lai, Hao-Jan↗

NASA NTRS1977

Floating reference frames for flexible spacecraft

Floating reference frames which move with the flexible body under dynamic analysis offer the advantages of a linear vibration analysis in the presence of large system rotations. When the deformations of an elastic continuum are expanded in terms of the free-free modes on an unconstrained system, the rigid body modes are found to be fixed in a reference frame called the Tisserand frame, with respect to which the relative momentum is zero. This result also guarantees the independence of small variations of frame motions and coordinates for all modes with nonzero natural frequencies, a condition which can greatly simplify the formulation of equations of motion. A Modified Tisserand Constraint is introduced in order to define a floating reference frame with similar properties for an elastic body which contains spinning rotors.

Canavin, J. R.↗

NASA NTRS2000

Inertial orientation tracker 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 NTRS1998

Inertial orientation tracker apparatus method 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 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

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 NTRS2004

inertial orientation tracker having automatic drift compensation using an at rest sensor for tracking parts of a human 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 sate 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 NTRS1991

Nonlinear dynamic analysis of flexible multibody systems

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Bauchau, Olivier A.↗

NASA NTRS1998

Optimal integer resolution for attitude determination using global positioning system signals

In this paper, a new motion-based algorithm for GPS integer ambiguity resolution is derived. The first step of this algorithm converts the reference sightline vectors into body frame vectors. This is accomplished by an optimal vectorized transformation of the phase difference measurements. The result of this transformation leads to the conversion of the integer ambiguities to vectorized biases. This essentially converts the problem to the familiar magnetometer-bias determination problem, for which an optimal and efficient solution exists. Also, the formulation in this paper is re-derived to provide a sequential estimate, so that a suitable stopping condition can be found during the vehicle motion. The advantages of the new algorithm include: it does not require an a-priori estimate of the vehicle's attitude; it provides an inherent integrity check using a covariance-type expression; and it can sequentially estimate the ambiguities during the vehicle motion. The only disadvantage of the new algorithm is that it requires at least three non-coplanar baselines. The performance of the new algorithm is tested on a dynamic hardware simulator.

Crassidis, John L.↗

NASA NTRS2018

Tests of Gravitational Symmetries with Pulsar Binary J1713+0747

Symmetries play a fundamental role in modern theories of gravity. The strong equivalence principle (SEP) constitutes a collection of gravitational symmetries which are all implemented by general relativity. Alternative theories, however, are generally expected to violate some aspects of SEP. We test three aspects of SEP using observed change rates in the orbital period and eccentricity of binary pulsar J1713+0747: (1) the gravitational constant’s constancy as part of locational invariance of gravitation; (2) the universality of free fall (UFF) for strongly self-gravitating bodies; (3) the post-Newtonian parameter ˆα3 in gravitational Lorentz invariance. Based on the pulsar timing result of the combined data set from the North American Nanohertz Gravitational Observatory and the European Pulsar Timing Array, we find G˙ /G = (−0.1 ± 0.9) × 10−12 yr−1, which is weaker than Solar system limits, but applies for strongly self-gravitating objects. Furthermore, we obtain an improved test for a UFF violation by a strongly self-gravitating mass falling in the gravitational field of our Galaxy, with a limit of |Delta| < 0.002 (95 per cent C.L.). Finally, we derive an improved limit on the self-acceleration of a gravitationally bound rotating body, to a preferred reference frame in the Universe, with −3 × 10−20 < ˆα3 < 4 × 10−20 (95 per cent C.L.). These results are based on direct UFF and ˆα3 tests using pulsar binaries, and they overcome various limitations of previous tests of this kind.

W W Zhu↗

NASA NTRS1988

Using the Hubble Space Telescope to relate the Hipparcos and extragalactic reference frames

The Hipparcos satellite will produce positions, motions, and parallaxes of celestial objects with previously unattained accuracy. This Hipparcos Instrumental System, however, will have an unknown solid body rotation with respect to an inertial reference frame. One aspect of the program of astrometric observations with the Hubble Space Telescope is to determine the rotation of the Hipparcos reference frame with respect to an extragalactic reference system.

Hemenway, P. D.↗

NASA NTRS1966

Satellite motion for arbitrary eccentricity and inclination around the smaller primary in the restricted three-body problem.

Motion of close satellite of smaller primary in restricted three-body problem referred to conventional rotating frame in which central angle is chosen as independent variable

ORBIT EQUATION↗

NASA NTRS1994

Orientation of human optokinetic nystagmus to gravity: a model-based approach

Optokinetic nystagmus (OKN) was induced by having subjects watch a moving display in a binocular, head-fixed apparatus. The display was composed of 3.3 degrees stripes moving at 35 degrees/s for 45 s. It subtended 88 degrees horizontally by 72 degrees vertically of the central visual field and could be oriented to rotate about axes that were upright or tilted 45 degrees or 90 degrees. The head was held upright or was tilted 45 degrees left or right on the body during stimulation. Head-horizontal (yaw axis) and head-vertical (pitch axis) components of OKN were recorded with electro-oculography (EOG). Slow phase velocity vectors were determined and compared with the axis of stimulation and the spatial vertical (gravity axis). With the head upright, the axis of eye rotation during yaw axis OKN was coincident with the stimulus axis and the spatial vertical. With the head tilted, a significant vertical component of eye velocity appeared during yaw axis stimulation. As a result the axis of eye rotation shifted from the stimulus axis toward the spatial vertical. Vertical components developed within 1-2 s of stimulus onset and persisted until the end of stimulation. In the six subjects there was a mean shift of the axis of eye rotation during yaw axis stimulation of approximately 18 degrees with the head tilted 45 degrees on the body. Oblique optokinetic stimulation with the head upright was associated with a mean shift of the axis of eye rotation toward the spatial vertical of 9.2 degrees. When the head was tilted and the same oblique stimulation was given, the axis of eye rotation rotated to the other side of the spatial vertical by 5.4 degrees. This counterrotation of the axis of eye rotation is similar to the "Muller (E) effect," in which the perception of the upright is counterrotated to the opposite side of the spatial vertical when subjects are tilted in darkness. The data were simulated by a model of OKN with a "direct" and "indirect" pathway. It was assumed that the direct visual pathway is oriented in a body, not a spatial frame of reference. Despite the short optokinetic after-nystagmus time constants, strong horizontal to vertical cross-coupling could be produced if the horizontal and vertical time constants were in proper ratio and there were no suppression of nystagmus in directions orthogonal to the stimulus direction. The model demonstrates that the spatial orientation of OKN can be achieved by restructuring the system matrix of velocity storage. We conclude that an important function of velocity storage is to orient slow-phase velocity toward the spatial vertical during movement in a terrestrial environment.

Non-NASA Center↗

NASA NTRS2009

Terminal Descent Sensor Simulation

Sulcata software simulates the operation of the Mars Science Laboratory (MSL) radar terminal descent sensor (TDS). The program models TDS radar antennas, RF hardware, and digital processing, as well as the physics of scattering from a coherent ground surface. This application is specific to this sensor and is flexible enough to handle end-to-end design validation. Sulcata is a high-fidelity simulation and is used for performance evaluation, anomaly resolution, and design validation. Within the trajectory frame, almost all internal vectors are represented in whatever coordinate system is used to represent platform position. The trajectory frame must be planet-fixed. The platform body frame is specified relative to arbitrary reference points relative to the platform (spacecraft or test vehicle). Its rotation is a function of time from the trajectory coordinate system specified via dynamics input (file for open loop, callback for closed loop). Orientation of the frame relative to the body is arbitrary, but constant over time. The TDS frame must have a constant rotation and translation from the platform body frame specified at run time. The DEM frame has an arbitrary, but time-constant, rotation and translation with respect to the simulation frame specified at run time. It has the same orientation as sigma0 frame, but is possibly translated. Surface sigma0 has the same arbitrary rotation and translation as DEM frame.

Chen, Curtis W.↗

NASA NTRS2004

Hybrid Image-Plane/Stereo Manipulation

Hybrid Image-Plane/Stereo (HIPS) manipulation is a method of processing image data, and of controlling a robotic manipulator arm in response to the data, that enables the manipulator arm to place an end-effector (an instrument or tool) precisely with respect to a target (see figure). Unlike other stereoscopic machine-vision-based methods of controlling robots, this method is robust in the face of calibration errors and changes in calibration during operation. In this method, a stereoscopic pair of cameras on the robot first acquires images of the manipulator at a set of predefined poses. The image data are processed to obtain image-plane coordinates of known visible features of the end-effector. Next, there is computed an initial calibration in the form of a mapping between (1) the image-plane coordinates and (2) the nominal three-dimensional coordinates of the noted end-effector features in a reference frame fixed to the main robot body at the base of the manipulator. The nominal three-dimensional coordinates are obtained by use of the nominal forward kinematics of the manipulator arm that is, calculated by use of the currently measured manipulator joint angles and previously measured lengths of manipulator arm segments under the assumption that the arm segments are rigid, that the arm lengths are constant, and that there is no backlash. It is understood from the outset that these nominal three-dimensional coordinates are likely to contain possibly significant calibration errors, but the effects of the errors are progressively reduced, as described next. As the end-effector is moved toward the target, the calibration is updated repeatedly by use of data from newly acquired images of the end-effector and of the corresponding nominal coordinates in the manipulator reference frame. By use of the updated calibration, the coordinates of the target are computed in manipulator-reference-frame coordinates and then used to the necessary manipulator joint angles to position and orient the end-effector at the target with respect to the same kinematic model from the calibration step. As the end-effector/target distance decreases, the computed coordinates of the end-effector and target become more nearly affected by the same errors, so that the differences between their coordinates become increasingly precise. When the end-effector reaches the target, the remaining effective position error is the distance that corresponds to more than about one pixel in the stereoscopic images of the target.

Baumgartner, Eric↗

NASA NTRS2007

Kalman Filter for Spinning Spacecraft Attitude Estimation

This paper presents a Kalman filter using a seven-component attitude state vector comprising the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. The relatively slow variation of these parameters makes this parameterization advantageous for spinning spacecraft attitude estimation. The filter accounts for the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames by employing a reduced six-component error state. Four variants of the filter, defined by different choices for the reduced error state, are tested against a quaternion-based filter using simulated data for the THEMIS mission. Three of these variants choose three of the components of the error state to be the infinitesimal attitude error angles, facilitating the computation of measurement sensitivity matrices and causing the usual 3x3 attitude covariance matrix to be a submatrix of the 6x6 covariance of the error state. These variants differ in their choice for the other three components of the error state. The variant employing the infinitesimal attitude error angles and the angular momentum components in an inertial reference frame as the error state shows the best combination of robustness and efficiency in the simulations. Attitude estimation results using THEMIS flight data are also presented.

Markley, F. Landis↗