Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quaternions”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 163 records · Page 9

Realtime Absolute Orientation with Outlier Rejection for Visual Odometry and Mesh Merging

This paper addresses a high level spatio-temporal problem, namely "absolute orientation", which arises in visual-odometry (using stereo), or registering two models created by different Structure from Motion (SFM) reconstructions. We compare the very popular method due to Horn using quaternions and our own independently derive method using the orthonormal rotation matrix R. We also introduce a novel approach for outlier rejection using spectral clustering.

Bandari, Esfandiar↗

Stability Analysis for Constrained Principal Axis Slew Maneuvers

This paper addresses the problem of reorienting a rigid spacecraft from arbitrary initial conditions to prescribed final conditions with zero angular velocity. The control law analyzed is based on quaternion feedback and leaves the user to choose two gains as functions of position, angular rate, and time. For arbitrary initial states, conditions on the controller gains are identified that guarantee global asymptotic stability. For the special case of rest-to-rest reorientations, the control law reduces to earlier results involving a principal axis rotation. The paper also addresses slew rate constraints, both, in terms of the two and infinity norms.

Seywald, Hans↗

Implicit and Explicit Spacecraft Gyro Calibration

This paper presents a comparison between two approaches to sensor calibration. According to one approach, called explicit, an estimator compares the sensor readings to reference readings, and uses the difference between the two to estimate the calibration parameters. According to the other approach, called implicit, the sensor error is integrated to form a different entity, which is then compared with a reference quantity of this entity, and the calibration parameters are inferred from the difference. In particular this paper presents the comparison between these approaches when applied to in-flight spacecraft gyro calibration. Reference spacecraft rate is needed for gyro calibration when using the explicit approach; however, such reference rates are not readily available for in-flight calibration. Therefore the calibration parameter-estimator is expanded to include the estimation of that reference rate, which is based on attitude measurements in the form of attitude-quaternion. A comparison between the two approaches is made using simulated data. It is concluded that the performances of the two approaches are basically comparable. Sensitivity tests indicate that the explicit filter results are essentially insensitive to variations in given spacecraft dynamics model parameters.

Bar-Itzhack, Itzhack Y.↗

Pseudo-Linear Attitude Determination of Spinning Spacecraft

This paper presents the overall mathematical model and results from pseudo linear recursive estimators of attitude and rate for a spinning spacecraft. The measurements considered are vector measurements obtained by sun-sensors, fixed head star trackers, horizon sensors, and three axis magnetometers. Two filters are proposed for estimating the attitude as well as the angular rate vector. One filter, called the q-Filter, yields the attitude estimate as a quaternion estimate, and the other filter, called the D-Filter, yields the estimated direction cosine matrix. Because the spacecraft is gyro-less, Euler s equation of angular motion of rigid bodies is used to enable the estimation of the angular velocity. A simpler Markov model is suggested as a replacement for Euler's equation in the case where the vector measurements are obtained at high rates relative to the spacecraft angular rate. The performance of the two filters is examined using simulated data.

Bar-Itzhack, Itzhack Y.↗

Kalman Filtering of Angular-Momentum-Based Attitude Parameters

This paper presents an extended Kalman filter using an attitude parameterization that is advantageous for attitude estimation of spinning spacecraft. The parameters are the angular momentum components in an inertial reference frame, the angular momentum components in the body frame, and a rotation angle. To avoid the singularity of the 7x7 covariance of this state vector arising from the constraint that the magnitude of the angular momentum vector is the same in the inertial and body frames, the Kalman filter employs the nonsingular 6x6 covariance of a reduced error state. Three of the components of this six-component error state are the usual infinitesimal attitude error angles, so the usual 3x3 attitude covariance matrix is a submatrix of the 6x6 covariance. The performance of the resulting filter is compared with that of a quaternion-based filter.

Markley, F. Landis↗

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↗

Observing Mode Attitude Controller for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) mission is the first of a series of lunar robotic spacecraft scheduled for launch in Fall 2008. LRO will spend at least one year in a low altitude polar orbit around the Moon, collecting lunar environment science and mapping data to enable future human exploration. The LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing mode", provides Lunar Nadir, off-Nadir, and Inertial fine pointing for the science data collection and instrument calibration. The controller combines the capability of fine pointing with that of on-demand large angle full-sky attitude reorientation into a single ACS mode, providing simplicity of spacecraft operation as well as maximum flexibility for science data collection. A conventional suite of ACS components is employed in this mode to meet the pointing and control objectives. This paper describes the design and analysis of the primary LRO fine pointing and attitude re-orientation controller function, known as the "Observing mode" of the ACS subsystem. The control design utilizes quaternion feedback, augmented with a unique algorithm that ensures accurate Nadir tracking during large angle yaw maneuvers in the presence of high system momentum and/or maneuver rates. Results of system stability analysis and Monte Carlo simulations demonstrate that the observing mode controller can meet fine pointing and maneuver performance requirements.

Calhourn, Philip C.↗

Accuracy Analysis on Large Blocks of High Resolution Images

Although high altitude frequencies effects are removed at the time of basic image generation, low altitude (Yaw) effects are still present in form of affinity/angular affinity. They are effectively removed by additional parameters. Bundle block adjustment based on properly weighted ephemeris/altitude quaternions (BBABEQ) are not enough to remove the systematic effect. Moreover, due to the narrow FOV of the HRSI, position and altitude are highly correlated making it almost impossible to separate and remove their systematic effects without extending the geometric model (Self-Calib.) The systematic effects gets evident on the increase of accuracy (in terms of RMSE at GCPs) for looser and relaxed ground control at the expense of large and strong block deformation with large residuals at check points. Systematic errors are most freely distributed and their effects propagated all over the block.

Passini, Richardo M.↗

Observing Mode Attitude Controller for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) mission is the first of a series of lunar robotic spacecraft scheduled for launch in Fall 2008. LRO will spend at least one year in a low altitude polar orbit around the Moon, collecting lunar environment science and mapping data to enable future human exploration. The LRO employs a 3-axis stabilized attitude control system (ACS) whose primary control mode, the "Observing mode", provides Lunar Nadir, off-Nadir, and Inertial fine pointing for the science data collection and instrument calibration. The controller combines the capability of fine pointing with that of on-demand large angle full-sky attitude reorientation into a single ACS mode, providing simplicity of spacecraft operation as well as maximum flexibility for science data collection. A conventional suite of ACS components is employed in this mode to meet the pointing and control objectives. This paper describes the design and analysis of the primary LRO fine pointing and attitude re-orientation controller function, known as the "Observing mode" of the ACS subsystem. The control design utilizes quaternion feedback, augmented with a unique algorithm that ensures accurate Nadir tracking during large angle yaw maneuvers in the presence of high system momentum and/or maneuver rates. Results of system stability analysis and Monte Carlo simulations demonstrate that the observing mode controller can meet fine pointing and maneuver performance requirements.

Calhoun, Philip C.↗

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↗

Lessons Learned

This paper is organized around three themes that have interested me over my career: covariance analysis, constrained estimation, and angular momentum. Both analytical and numerical approaches to covariance analysis are discussed. The section on constraints begins with general considerations arising from the nature of the rotation group before moving to Wahba's Problem and quaternion Kalman filters. The discussion of angular momentum includes its use in attitude determination and control as well as in the detection and diagnosis of spacecraft anomalies. Relevant illustrative examples are included.

Markley, F. Landis↗

Estimation Filter for Alignment of the Spitzer Space Telescope

A document presents a summary of an onboard estimation algorithm now being used to calibrate the alignment of the Spitzer Space Telescope (formerly known as the Space Infrared Telescope Facility). The algorithm, denoted the S2P calibration filter, recursively generates estimates of the alignment angles between a telescope reference frame and a star-tracker reference frame. At several discrete times during the day, the filter accepts, as input, attitude estimates from the star tracker and observations taken by the Pointing Control Reference Sensor (a sensor in the field of view of the telescope). The output of the filter is a calibrated quaternion that represents the best current mean-square estimate of the alignment angles between the telescope and the star tracker. The S2P calibration filter incorporates a Kalman filter that tracks six states - two for each of three orthogonal coordinate axes. Although, in principle, one state per axis is sufficient, the use of two states per axis makes it possible to model both short- and long-term behaviors. Specifically, the filter properly models transient learning, characteristic times and bounds of thermomechanical drift, and long-term steady-state statistics, whether calibration measurements are taken frequently or infrequently. These properties ensure that the S2P filter performance is optimal over a broad range of flight conditions, and can be confidently run autonomously over several years of in-flight operation without human intervention.

Bayard, David↗

Real-Time Visualization of Spacecraft Telemetry for the GLAST and LRO Missions

GlastCam and LROCam are closely-related tools developed at NASA Goddard Space Flight Center for real-time visualization of spacecraft telemetry, developed for the Gamma-Ray Large Area Space Telescope (GLAST) and Lunar Reconnaissance Orbiter (LRO) missions, respectively. Derived from a common simulation tool, they use related but different architectures to ingest real-time spacecraft telemetry and ground predicted ephemerides, and to compute and display features of special interest to each mission in its operational environment. We describe the architectures of GlastCam and LROCam, the customizations required to fit into the mission operations environment, and the features that were found to be especially useful in early operations for their respective missions. Both tools have a primary window depicting a three-dimensional Cam view of the spacecraft that may be freely manipulated by the user. The scene is augmented with fields of view, pointing constraints, and other features which enhance situational awareness. Each tool also has another "Map" window showing the spacecraft's groundtrack projected onto a map of the Earth or Moon, along with useful features such as the Sun, eclipse regions, and TDRS satellite locations. Additional windows support specialized checkout tasks. One such window shows the star tracker fields of view, with tracking window locations and the mission star catalog. This view was instrumental for GLAST in quickly resolving a star tracker mounting polarity issue; visualization made the 180-deg mismatch immediately obvious. Full access to GlastCam's source code also made possible a rapid coarse star tracker mounting calibration with some on the fly code adjustments; adding a fine grid to measure alignment offsets, and introducing a calibration quaternion which could be adjusted within GlastCam without perturbing the flight parameters. This calibration, from concept to completion, took less than half an hour. Both GlastCam and LROCam were developed in the C language, with non-proprietary support libraries, for ease of customization and portability. This no-blackboxes aspect enables engineers to adapt quickly to unforeseen circumstances in the intense operations environment. GlastCam and LROCam were installed on multiple workstations in the operations support rooms, allowing independent use by multiple subsystems, systems engineers and managers, with negligible draw on telemetry system resources.

Stoneking, Eric T.↗

Testing First-Order Logic Axioms in AutoCert

AutoCert [2] is a formal verification tool for machine generated code in safety critical domains, such as aerospace control code generated from MathWorks Real-Time Workshop. AutoCert uses Automated Theorem Provers (ATPs) [5] based on First-Order Logic (FOL) to formally verify safety and functional correctness properties of the code. These ATPs try to build proofs based on user provided domain-specific axioms, which can be arbitrary First-Order Formulas (FOFs). These axioms are the most crucial part of the trusted base, since proofs can be submitted to a proof checker removing the need to trust the prover and AutoCert itself plays the part of checking the code generator. However, formulating axioms correctly (i.e. precisely as the user had really intended) is non-trivial in practice. The challenge of axiomatization arise from several dimensions. First, the domain knowledge has its own complexity. AutoCert has been used to verify mathematical requirements on navigation software that carries out various geometric coordinate transformations involving matrices and quaternions. Axiomatic theories for such constructs are complex enough that mistakes are not uncommon. Second, adjusting axioms for ATPs can add even more complexity. The axioms frequently need to be modified in order to have them in a form suitable for use with ATPs. Such modifications tend to obscure the axioms further. Thirdly, speculating validity of the axioms from the output of existing ATPs is very hard since theorem provers typically do not give any examples or counterexamples.

Ahn, Ki Yung↗

Investigating On-Orbit Attitude Determination Anomalies for the Solar Dynamics Observatory Mission

The Solar Dynamics Observatory (SDO) was launched on February 11, 2010 from Kennedy Space Center on an Atlas V launch vehicle into a geosynchronous transfer orbit. SDO carries a suite of three scientific instruments, whose observations are intended to promote a more complete understanding of the Sun and its effects on the Earth's environment. After a successful launch, separation, and initial Sun acquisition, the launch and flight operations teams dove into a commissioning campaign that included, among other things, checkout and calibration of the fine attitude sensors and checkout of the Kalman filter (KF) and the spacecraft s inertial pointing and science control modes. In addition, initial calibration of the science instruments was also accomplished. During that process of KF and controller checkout, several interesting observations were noticed and investigated. The SDO fine attitude sensors consist of one Adcole Digital Sun Sensor (DSS), two Galileo Avionica (GA) quaternion-output Star Trackers (STs), and three Kearfott Two-Axis Rate Assemblies (hereafter called inertial reference units, or IRUs). Initial checkout of the fine attitude sensors indicated that all sensors appeared to be functioning properly. Initial calibration maneuvers were planned and executed to update scale factors, drift rate biases, and alignments of the IRUs. After updating the IRU parameters, the KF was initialized and quickly reached convergence. Over the next few hours, it became apparent that there was an oscillation in the sensor residuals and the KF estimation of the IRU bias. A concentrated investigation ensued to determine the cause of the oscillations, their effect on mission requirements, and how to mitigate them. The ensuing analysis determined that the oscillations seen were, in fact, due to an oscillation in the IRU biases. The low frequencies of the oscillations passed through the KF, were well within the controller bandwidth, and therefore the spacecraft was actually following the oscillating biases, resulting in movement of the spacecraft on the order of plus or minus 20 arcsec. Though this level of error met the ACS attitude knowledge requirement of [35, 70, 70] arcsec, 3 sigma, the desire of the ACS and instrument teams was to remove as much of the oscillation as possible. The Kearfott IRUs have an internal temperature controller, designed to maintain the IRU temperature at a constant temperature of approximately 70 C, thus minimizing the change in the bias drift and scale factors of the mechanical gyros. During ground testing of the observatory, it was discovered that the 83-Hz control cycle of the IRU heaters put a tremendous amount of stress on the spacecraft battery. Analysis by the power systems team indicated that the constant charge/discharge on the battery due to the IRU thermal control cycle could potentially limit the life of the battery. After much analysis, the decision was made not to run the internal IRU heaters. Analysis of on orbit data revealed that the oscillations in the IRU bias had a connection to the temperature of the IRU; changes in IRU temperature resulted in changes in the amplitude and period of the IRU biases. Several mitigating solutions were investigated, the result of which was to tune the KF with larger IRU noise assumptions which allows the KF to follow and correct for the time-varying IRU biases.

Vess, Melissa F.↗

Q-Method Extended Kalman Filter

A new algorithm is proposed that smoothly integrates non-linear estimation of the attitude quaternion using Davenport s q-method and estimation of non-attitude states through an extended Kalman filter. The new method is compared to a similar existing algorithm showing its similarities and differences. The validity of the proposed approach is confirmed through numerical simulations.

Zanetti, Renato↗

NASA Tech Briefs, December 2012

The topics include: Pattern Generator for Bench Test of Digital Boards; 670-GHz Down- and Up-Converting HEMT-Based Mixers; Lidar Electro-Optic Beam Switch with a Liquid Crystal Variable Retarder; Feedback Augmented Sub-Ranging (FASR) Quantizer; Real-Time Distributed Embedded Oscillator Operating Frequency Monitoring; Software Modules for the Proximity-1 Space Link Interleaved Time Synchronization (PITS) Protocol; Description and User Instructions for the Quaternion to Orbit v3 Software; AdapChem; Mars Relay Lander and Orbiter Overflight Profile Estimation; Extended Testability Analysis Tool; Interactive 3D Mars Visualization; Rapid Diagnostics of Onboard Sequences; MER Telemetry Processor; pyam: Python Implementation of YaM; Process for Patterning Indium for Bump Bonding; Archway for Radiation and Micrometeorite Occurrence Resistance; 4D Light Field Imaging System Using Programmable Aperture; Device and Container for Reheating and Sterilization; Radio Frequency Plasma Discharge Lamps for Use as Stable Calibration Light Sources; Membrane Shell Reflector Segment Antenna; High-Speed Transport of Fluid Drops and Solid Particles via Surface Acoustic Waves; Compact Autonomous Hemispheric Vision System; A Distributive, Non-Destructive, Real-Time Approach to Snowpack Monitoring; Wideband Single-Crystal Transducer for Bone Characterization; Numerical Simulation of Rocket Exhaust Interaction With Lunar Soil; Motion Imagery and Robotics Application (MIRA): Standards-Based Robotics; Particle Filtering for Model-Based Anomaly Detection in Sensor Networks; Ka-band Digitally Beamformed Airborne Radar Using SweepSAR Technique; Composite With In Situ Plenums; Multi-Beam Approach for Accelerating Alignment and Calibration of HyspIRI-Like Imaging Spectrometers; JWST Lifting System; Next-Generation Tumbleweed Rover; Pneumatic System for Concentration of Micrometer-Size Lunar Soil.

Source record↗

Modeling and Simulation for Multi-Missions Space Exploration Vehicle

Asteroids and Near-Earth Objects [NEOs] are of great interest for future space missions. The Multi-Mission Space Exploration Vehicle [MMSEV] is being considered for future Near Earth Object missions and requires detailed planning and study of its Guidance, Navigation, and Control [GNC]. A possible mission of the MMSEV to a NEO would be to navigate the spacecraft to a stationary orbit with respect to the rotating asteroid and proceed to anchor into the surface of the asteroid with robotic arms. The Dynamics and Real-Time Simulation [DARTS] laboratory develops reusable models and simulations for the design and analysis of missions. In this paper, the development of guidance and anchoring models are presented together with their role in achieving mission objectives and relationships to other parts of the simulation. One important aspect of guidance is in developing methods to represent the evolution of kinematic frames related to the tasks to be achieved by the spacecraft and its robot arms. In this paper, we compare various types of mathematical interpolation methods for position and quaternion frames. Subsequent work will be on analyzing the spacecraft guidance system with different movements of the arms. With the analyzed data, the guidance system can be adjusted to minimize the errors in performing precision maneuvers.

Multi-Mission Space Exploration Vehicle [MMSEV]↗