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This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle.
A seven-degree-of-freedom robot arm with a six-degree-of-freedom end effector is controlled by a processor employing a 6-by-7 Jacobian matrix for defining location and orientation of the end effector in terms of the rotation angles of the joints, a 1 (or more)-by-7 Jacobian matrix for defining 1 (or more) user-specified kinematic functions constraining location or movement of selected portions of the arm in terms of the joint angles, the processor combining the two Jacobian matrices to produce an augmented 7 (or more)-by-7 Jacobian matrix, the processor effecting control by computing in accordance with forward kinematics from the augmented 7-by-7 Jacobian matrix and from the seven joint angles of the arm a set of seven desired joint angles for transmittal to the joint servo loops of the arms. One of the kinematic functions constrains the orientation of the elbow plane of the arm. Another one of the kinematic functions minimizing a sum of gravitational torques on the joints. Still another one of the kinematic functions constrains the location of the arm to perform collision avoidance. Generically, one of the kinematic functions minimizes a sum of selected mechanical parameters of at least some of the joints associated with weighting coefficients which may be changed during arm movement. The mechanical parameters may be velocity errors or position errors or gravity torques associated with individual joints.
The G-Guidance software implements a guidance and control (G and C) algorithm for small-body, autonomous proximity operations, developed under the Small Body GN and C task at JPL. The software is written in Matlab and interfaces with G-OPT, a JPL-developed optimization package written in C that provides G-Guidance with guaranteed convergence to a solution in a finite computation time with a prescribed accuracy. The resulting program is computationally efficient and is a prototype of an onboard, real-time algorithm for autonomous guidance and control. Two thruster firing schemes are available in G-Guidance, allowing tailoring of the software for specific mission maneuvers. For example, descent, landing, or rendezvous benefit from a thruster firing at the maneuver termination to mitigate velocity errors. Conversely, ascent or separation maneuvers benefit from an immediate firing to avoid potential drift toward a second body. The guidance portion of this software explicitly enforces user-defined control constraints and thruster silence times while minimizing total fuel usage. This program is currently specialized to small-body proximity operations, but the underlying method can be generalized to other applications.
The bootstrap method is used to determine errors of basic attributes of coronal mass ejections (CMEs) visually identified in images obtained by the Solar and Heliospheric Observatory (SOHO) mission's Large Angle and Spectrometric Coronagraph (LASCO) instruments. The basic parameters of CMEs are stored, among others, in a database known as the SOHO/LASCO CME catalog and are widely employed for many research studies. The basic attributes of CMEs (e.g. velocity and acceleration) are obtained from manually generated height-time plots. The subjective nature of manual measurements introduces random errors that are difficult to quantify. In many studies the impact of such measurement errors is overlooked. In this study we present a new possibility to estimate measurements errors in the basic attributes of CMEs. This approach is a computer-intensive method because it requires repeating the original data analysis procedure several times using replicate datasets. This is also commonly called the bootstrap method in the literature. We show that the bootstrap approach can be used to estimate the errors of the basic attributes of CMEs having moderately large numbers of height-time measurements. The velocity errors are in the vast majority small and depend mostly on the number of height-time points measured for a particular event. In the case of acceleration, the errors are significant, and for more than half of all CMEs, they are larger than the acceleration itself.
The effect of rolling motion of a wing on the magnitude of error induced due to the wing vibration when measuring atmospheric turbulence with a wind probe mounted on the wing tip was investigated. The wing considered had characteristics similar to that of a B-57 Cambera aircraft, and Von Karman's cross spectrum function was used to estimate the cross-correlation of atmospheric turbulence. Although the error calculated was found to be less than that calculated when only elastic bendings and vertical motions of the wing are considered, it is still relatively large in the frequency's range close to the natural frequencies of the wing. Therefore, it is concluded that accelerometers mounted on the wing tip are needed to correct for this error, or the atmospheric velocity data must be appropriately filtered.
Error bounds on position and velocity in satellite orbit theories
Work during the period of this report has been in three areas: (1) pressure transducer error analysis, (2) fluctuating velocity and pressure measurements in the NASA Lewis 6-inch diameter quiet jet facility, and (3) measurement analysis. A theory was developed and experimentally verified to quantify the pressure transducer velocity interference error. The theory and supporting experimental evidence show that the errors are a function of the velocity field's turbulent structure. It is shown that near the mixing layer center the errors are negligible. Turbulent velocity and pressure measurements were made in the NASA Lewis quiet jet facility. Some preliminary results are included.
Error elimination in velocity of light observability for spacecraft trajectory estimation problems
Rigorous error bounds on position and velocity of satellite derived from Hamiltonian theory and von Zeipel method
Rigorous error bounds on position and velocity of satellite derived from Hamiltonian theory and von Zeipel method
Rigorous error bounds on position and velocity for satellite orbits with eccentricity of less than one
An analysis was made of the guidance of a space vehicle approaching the earth at supercircular velocity through an entrance corridor containing a desired perigee altitude. Random errors were assumed in the measurement of velocity and flight-path angle and in obtaining the desired thrust impulse. The method described in NASA Technical Note D-191 of scheduling corrections at different values of the angle between perigee and the vehicle's position vector and a slight modification of this method were investigated as a means of correcting perigee altitude when the vehicle's predicted position was at programmed correction points not within a specified deadband about the desired perigee altitude. The study showed that modifying the angular method of NASA Technical Note D-191 by adding another correction near the initial point did not improve the efficiency and accuracy of the angular method. It was found that in some cases the use of a correction procedure which included a deadband could be more costly in total corrective velocity than a procedure which neglected the deadband. This was especially true if a large degree of confidence was required in the total corrective velocity. It was apparent from the results that a correction with a deadband limit in the guidance scheme was more sensitive to the initial conditions, the corrective procedure, the deadband, and the degree of confidence required than a correction without a deadband limit.
In a very short period of time the MER project successfully developed and tested a system, TIRS/DIMES, to improve the probability of success in the presence of large Martian winds. The successful development of TIRS/DIMES played a big role in the landing site selection process by enabling the landing of Spirit on Gusev crater, a site of very high scientific interest but with known high wind conditions. The performance of TIRS by Spirit at Gusev Crater was excellent. The velocity prediction error was small and Big TIRS was fired reducing the impact horizontal velocity from approximately 23 meters per second to approximately 11 meters per second, well within the airbag capabilities. The performance of TIRS by Opportunity at Meridiani was good. The velocity prediction error was rather large (approximately 6 meters per second, a less than 2 sigma value, but TIRS did not fire which was the correct action.
Algorithms are described for integration of Differential Global Positioning System (DGPS) data with Inertial Navigation System (INS) data to provide an integrated DGPS/INS navigation system. The objective is to establish the benefits that can be achieved through various levels of integration of DGPS with INS for precision navigation. An eight state Kalman filter integration was implemented in real-time on a twin turbo-prop transport aircraft to evaluate system performance during terminal approach and landing operations. A fully integrated DGPS/INS system is also presented which models accelerometer and rate-gyro measurement errors plus position, velocity, and attitude errors. The fully integrated system was implemented off-line using range-domain (seventeen-state) and position domain (fifteen-state) Kalman filters. Both filter integration approaches were evaluated using data collected during the flight test. Flight-test data consisted of measurements from a 5 channel Precision Code GPS receiver, a strap-down Inertial Navigation Unit (INU), and GPS satellite differential range corrections from a ground reference station. The aircraft was laser tracked to determine its true position. Results indicate that there is no significant improvement in positioning accuracy with the higher levels of DGPS/INS integration. All three systems provided high-frequency (e.g., 20 Hz) estimates of position and velocity. The fully integrated system provided estimates of inertial sensor errors which may be used to improve INS navigation accuracy should GPS become unavailable, and improved estimates of acceleration, attitude, and body rates which can be used for guidance and control. Precision Code DGPS/INS positioning accuracy (root-mean-square) was 1.0 m cross-track and 3.0 m vertical. (This AGARDograph was sponsored by the Guidance and Control Panel.)
Dust particles and occasional moisture condensations are unavoidable reality of all wind tunnels. On the path to pursue a goal of velocity and temperature measurements in high-speed wind tunnels we have created a tabletop, spectrally resolved, Rayleigh-Mie scattering setup around a small jet fed by ambient and air with different particle concentration to determine the accuracy of the technique. The other reality of a wind tunnel setup is the spurious reflection and scattering of the incident laser beam by solid surfaces (flare light), which contaminates the Rayleigh-Mie scattered light. This is simulated by backgrounds with different reflectivity towards the collection optics. Light from a CW laser is delivered via an optical fiber and the scattered light from a point on the laser path is spectrally resolved using a stabilized Fabry-Perot interferometer, followed by imaging on an EMCCD camera. A model of the combined background glare, Mie scattering, and the Rayleigh spectrum was fitted to the camera image using maximum likelihood estimation. It was observed that the present modeling approach can extract velocity and temperature with reasonable accuracy when the intensity of the Mie scattered light is less than or comparable to that of the Rayleigh scattered light; beyond that error in velocity measurement remains reasonable ±12m/s but the temperature measurement becomes progressively more inaccurate. Increasingly the flare light is found to cause a bias error in velocity. Similar trend is observed in the presence of both the flare light and the Mie scattered light. The setup has provided a set of data for the future improvement of the modeling procedure, and demonstrated that even in the case of large amount of dust particles and large flare light the present technique can provide measurement of velocity with reasonable accuracy.
This document assesses the magnitude of velocity measurement errors that may arise when performing stereo particle image velocimetry (PIV) with cameras viewing through thick, refractive window and where the calibration is performed in one plane only. The effect of the window is to introduce a refractive error that increases with window thickness and the camera angle of incidence. The calibration should be performed while viewing through the test section window, otherwise a potentially significant error may be introduced that affects each velocity component differently. However, even when the calibration is performed correctly, another error may arise during the stereo reconstruction if the perspective angle determined for each camera does not account for the displacement of the light rays as they refract through the thick window. Care should be exercised when applying in a single-plane calibration since certain implicit assumptions may in fact require conditions that are extremely difficult to meet in a practical laboratory environment. It is suggested that the effort expended to ensure this accuracy may be better expended in performing a more lengthy volumetric calibration procedure, which does not rely upon the assumptions implicit in the single plane method and avoids the need for the perspective angle to be calculated.
A satellite system that employs a spaceborne RF interferometer to determine the location and velocity of data collection platforms attached to meteorological balloons is proposed. This meteorological advanced location and data collection system (MALDCS) is intended to fly aboard a low polar orbiting satellite. The flight instrument configuration includes antennas supported on long deployable booms. The platform location and velocity estimation errors introduced by the dynamic and thermal behavior of the antenna booms and the effects of the presence of the booms on the performance of the spacecraft's attitude control system, and the control system design considerations critical to stable operations are examined. The physical parameters of the Astromast type of deployable boom were used in the dynamic and thermal boom analysis, and the TIROS N system was assumed for the attitude control analysis. Velocity estimation error versus boom length was determined. There was an optimum, minimum error, antenna separation distance. A description of the proposed MALDCS system and a discussion of ambiguity resolution are included.
This paper presents a new control method for coordinated control of two robot arms. The two arms are assumed to work on the same object simultaneously. The control method uses a dynamic coordinator acting on relative position and velocity task space errors and on relative force-torque errors between the two arms as sensed at the end effectors. This method is novel because the position and velocity error feedback could be superimposed with the force-torque error feedback in the task space simultaneously.