Showing papers in "Journal of The Astronautical Sciences in 1998"

Feedback Control Law for Variable Speed Control Moment Gyros

Abstract: Variable speed control moment gyroscopes (CMG) are single-gimbal gyroscopes where the fly wheel speed is allowed to be variable. The equations of motion of a generic rigid body with several such variable speed CMGs attached are presented. The formulation is such that it can easily accommodate the classical cases of having either control moment gyros or reaction wheels to control the spacecraft attitude. A globally asymptotically stabilizing nonlinear feedback control law is presented. For a redundant control system, a weighted minimum norm inverse is used to determine the control vector. This approach allows the variable speed control moment gyroscopes to behave either more like classical reaction wheels or more like control moment gyroscopes, depending on the local optimal steering logic. Where classical control moment gyroscope control laws have to deal with singular gimbal angle configurations, the variable speed control moment gyroscopes are shown not to encounter any singularities for many representative examples considered. Both a gimbal angle velocity and an acceleration-based steering law are presented. Further, the use of the variable speed CMG null motion is discussed to reconfigure the gimbal angles to preferred sets. Having a variable reaction wheel speed allows for a more general redistribution of the internal momentum vector

Quasihalo Orbits Associated with Libration Points

Abstract: Quasihalo orbits are Lissajous trajectories librating about the well known halo orbits. The main feature of these orbits is that they keep an exclusion zone in the same way that halo orbits do. As a result, the knowledge of this type of orbit gives more flexibility to the mission analysis design about collinear libration points of any pair of primaries in the solar system. This paper is devoted to the semianalytical computation of quasihalo orbits in the circular restricted three-body problem by means of an ad hoc Lindstedt-Poincare method. The study of the practical convergence of the procedure and the extension of the orbits to suitable locations in the solar system using Jet Propulsion Laboratory (JPL) ephemerides is also discussed.

Optimal interplanetary spacecraft trajectories via a pareto genetic algorithm

Abstract: A Pareto genetic algorithm is applied to the optimization of low-thrust interplanetary spacecraft trajectories. A multiobjective, nondominated sorting genetic algorithm is developed following existing methodologies. A hybridized scheme is designed integrating the nondominated sorting genetic algorithm with a calculus-of-variations-based trajectory optimization algorithm. “Families” of Pareto optimal trajectories are generated for the cases of Earth-Mars flyby and rendezvous trajectories. A novel trajectory type generated by the genetic algorithm is expanded to develop a series of versatile, high-performance Earth-Mars rendezvous trajectories.

Motion in General Elliptic Orbit with Respect to a Dragging and Precessing Coordinate Frame

Abstract: The full set of second-order nonlinear differential equations describing the exact motion of a spacecraft subject to drag and oblateness perturbations in general elliptic orbit, relative to a rotating reference frame which drags and precesses exactly as a given spacecraft attached to its center is derived. This attached spacecraft is itself flying a general elliptic orbit and can be considered as the passive or nonmaneuvering vehicle. The unaveraged form of the J2 acceleration is used for both vehicles leaving this oblateness perturbation position dependent for more exacting calculations. These equations can be effectively put to use in calculating by an iterative scheme, the impulsive rendezvous maneuvers in elliptic orbit around the Earth or those planets that are either atmosphere bearing or have a dominant second zonal harmonic, or both.

Precision Low Earth Orbit Determination Using Atmospheric Density Calibration

Abstract: Atmospheric drag is the largest uncertainty in determining orbits of low altitude satellites. Deficiencies in operational satellite drag models persist due to empirical model limitations as well as inadequacies of proxy indices used as model drivers. Satellite drag errors result in degraded accuracy, requirements for frequent updates and inadequate predictions of true positions for accurate catalog maintenance, collision avoidance and re-entry operations. Time-dependent global corrections to operational drag models have been derived based on assimilation of satellite tracking data. These corrected drag values circumvent the persisting deficiencies of current drag models and provide significant improvements in precision orbit determination and prediction for low-earth orbit satellites.

Fundamental motions near collinear libration points and their transitions

Abstract: Recent theoretical and numerical advances in trajectory design in the three-body problem have suggested several new mission possibilities. Many of the advances have come from the application of dynamical systems theory. Where the majority of the design applications thus far are based solely on the stable and unstable manifolds associated with libration point orbits, this study seeks to utilize the center manifold. First, a reexamination of some of the fundamental motions near the libration point is presented in the context of dynamical systems theory. This approach may illuminate the relationships and transitions between the various types of motions that exist in this region of space. Additionally, the motion on certain types of tori is explored. A numerical investigation of some such tori leads to an understanding of a certain periodic configuration that may be useful in the development of new mission concepts.

Relative equilibria of a rigid satellite in a circular keplerian orbit

Abstract: We examine relative equilibria of a rigid body free to rotate about its center of mass which is constrained to follow a Keplerian orbit in a central gravitational field. We derive a noncanonical Hamiltonian formulation of this system and show how it relates to the noncanonical system for an unconstrained rigid body in a hierarchy of approximations of the two-body problem. For a particular approximation of the potential, the Keplerian system is equivalent to the classical approximation typically seen in the literature. We determine relative equilibria for this approximation and derive stability conditions for both arbitrary and axisymmetric bodies.

On Satellite Umbra/Penumbra Entry and Exit Positions

Abstract: The problem of computing Earth satellite entry and exit positions through the Earth’s umbra and penumbra, for satellites in elliptical orbits, is solved without the use of a quartic equation. A condition for existence of a solution in the case of a cylindrical shadow is given. This problem is of interest in case one would like to include perturbation force resulting from solar radiation pressure. Most satellites (including geosynchronous) experience periodic eclipses behind the Earth. Of course when the satellite is eclipsed, it’s not exposed to solar radiation pressure. When we need extreme accuracy, we must develop models that turn the solar radiation calculations “on” and “off,” as appropriate, to account for these periods of inactivity.

Accurate Orbit Determination from Short-Arc Dense Observational Data

Abstract: Requirements have existed for several decades for highly accurate satellite orbits. With increased computer power, simplified analytical techniques have lost most of their competitive edge and numerical techniques are experiencing wide-spread popularity. When coupled with increased accuracy requirements from commercial satellites owners and accurate computations for debris and close approach for the International Space Station, a reliable method must be found to form highly-accurate satellite state vectors. This paper explores one approach using dense observational data from short-arcs of geographically distributed sensor sites. In particular, dense observations (consisting of one observation per second for about two minutes) are analyzed to determine the accuracy that can be achieved via high fidelity, numerical, orbit-determination techniques.

High Precision Integration Methods for Orbit Propagation

Abstract: We present four integration methods which exploit efficient numerical techniques for orbit propagation. The methods have been selected to compare the strategy of using first order differential equations, required by the use of regularization, to integrating the equations of motion directly so that second order integrators can be used. All the methods have demonstrated high levels of orbital accuracy as well as very short integration times in astronomical simulations of long term dynamical evolution. We outline the bases of these techniques and illustrate their accuracy by comparing the orbital predictions with data from a GPS receiver on board a satellite in Sun synchronous LEO orbit.

A New Orbital Debris Reference Model

Abstract: This paper presents a new orbital debris environment model (CODRM-97). It includes the objects with a mass ≥ 1 mg produced by international space launches and operations, 140 energetic breakups and 16 liquid metal coolant leaks from nuclear-powered spacecraft. Each fragmentation or leakage was simulated with the most appropriate models and parameters, and the resulting debris clouds were propagated, including all the significant orbital perturbations, to the chosen reference epoch (January 1, 1997). At this point, the particles still in orbit were merged with the cataloged objects present in space at the same time. In total, more than 65 million particles with a mass ≥ 1 mg were generated during the simulations and more than 52 million were found to be still in orbit at the reference epoch. Preliminary comparisons with the measurements available below 1000 km seem to indicate that the CODRM-97 predictions come short by a factor of two for debris with diameters close to 1 cm and by an order of magnitude for particles with diameters approaching 1 mm. This deficiency might reflect, in part, an intrinsic inadequacy of the breakup models adopted, but probably suggests the presence in space of additional debris sources, not yet included in CODRM-97.

Recursive Modeling of Serial Flexible Manipulators

Abstract: This paper discusses the modeling of serial manipulators with flexible links and joints. The model of a flexible link includes bending in two perpendicular directions and torsion around the longitudinal axis. Second-order strain-displacement relationships, coupled with curvatures as generalized coordinates, are used to represent the foreshortening effect. Then, the dynamic equations are exact to first order in terms of the generalized coordinates associated with the flexible links. These generalized coordinates and their first time-derivatives are assumed to be small (of first order). The model developed captures all the important phenomena, such as stiffening due to the angular speed or buckling due to large payloads. The dynamic equations are developed recursively using Jourdain’s principle to allow an efficient symbolic implementation. The equations associated with the flexible links are reformulated to enable off-line symbolic integration. The gyroscopic effects of motors with reducers are included.

Dynamics and Orbit Determination of Tethered Satellite Systems

Abstract: Most analyses of tethered satellite systems have been focused on the relative motion of the satellites either with respect to each other, or with respect to their center of mass. In this paper, we consider how the motion of one of the satellites in a two-body tethered system is perturbed by the presence of the other. This point of view is necessary if the orbits of the satellites in such a system are to be determined correctly when the fact that they are tethered is not known a priori. Rather general equations of motion for the satellites are derived. These equations are simplified by assuming planar motion. From the simplified equations, an expression for an “apparent” gravitational constant is derived. Then, the identification and state determination problem is addressed. Examples obtained using a conventional least-squares batch processor are discussed. It appears that a two-stage method, using both two-body and tethered satellite dynamic models, is a good way to identify and determine the states of some tethered satellite systems.

The Algorithm of the Two-Impulse Time-Fixed Noncoplanar Rendezvous with Drag and Oblateness Effects

Abstract: The algorithm that generates the exact solution of the two-impulse noncoplanar rendezvous in general elliptic orbit is presented in this chapter. The motion of the maneuvering spacecraft is referred to a rotating reference frame attached to the passive spacecraft, and dragging and precessing at the same rate as that spacecraft. An iterative scheme is devised to find the magnitude and orientation of the initiating impulse that brings the active spacecraft to a desired target point in the vicinity of the passive spacecraft in a given time. When the rendezvous point is in the vicinity of the passive spacecraft and not at the passive vehicle location itself, the linear distance between the two vehicles will exhibit variations along their post-rendezvous common orbit which can be of the order of kilometers for highly eccentric orbits. These natural oscillations can be minimized by targeting the active vehicle to the immediate proximity of the passive spacecraft, and be totally eliminated by targeting to the passive vehicle location itself.

Automatic Rendering of Astrodynamics Expressions for Efficient Evaluation

Abstract: In this paper, we describe the automatic rendering of expressions computed using symbolic manipulation. Computations from astrodynamics frequently can be put in a fixed hierarchy of polynomials and Fourier series. Once in this form, FORTRAN subprograms can be generated automatically in a form that lends itself to numerical evaluation. The goal of the current work is to present an approach for using symbolic manipulation techniques to produce a Fortran representation of the normalized Hamiltonian and other supporting equations representing as many of the actual physical effects on satellites as possible.

On the Deployment of a Tether from an Elliptical Orbit

Abstract: A two-phase deployment scheme has been studied for a tethered system being deployed from a spacecraft in a circular orbit. With the proper choice of the ejection parameters-angle and speed–the tether can be left at rest, aligned with the local vertical, in less than one orbital period, regardless of length. For a circular orbit, this position is a relative equilibrium configuration. When the tether mass is small, a perturbation method allows it to be included in the second and higher terms of a power series, whose first term corresponds to the end body and a massless tether. This analysis is extended here to the case of an elliptic orbit. Two new parameters appear: eccentricity and ejection anomaly. Taking only the first term allows a wide and fast scanning of the acceptable ranges for these parameters. It is found that, for most values of the anomaly, there are combinations of initial speed and angle for which the deployment is hardly affected by eccentricity. Initial anomaly always affects the process, but a combination of parameters can still be found to achieve the desired effect. A tether can be completely deployed while in the highest part of the orbit, avoiding the effect of drag in the area around the perigee, for eccentricities of 0.1 and higher.

Ephemeris Compression Using Multiple Fourier Series

Abstract: An ephemeris compression method has been developed which uses multiple Fourier series. The compression itself is performed upon the Cartesian residuals which result from differencing a numerically integrated ephemeris with an ephemeris generated by a widely-used analytical propagator, such as PPT. An accurate estimate of the ephemeris may then be generated by reconstructing the residuals from the Fourier coefficients and superposing these with the analytical propagator’s ephemeris. Statistical results from testing the method with the satellite catalog are presented.

SMART Attitude Acquisition and Control

Abstract: This paper deals with the attitude acquisition and control for the Italian Scientific Microsatellite for Advanced Research and Technology. Since the microsatellite is aimed at remote sensing applications, three-axis fine attitude control (0.1°–0.01°) during station keeping is required. The attitude acquisition technique exploits the magnetic control to despin the microsatellite initial tumbling and uses a small reaction wheel to despin the microsatellite residual rotation around the axis perpendicular to the orbit plane, due to the magnetic control. Three-axis attitude control during station keeping is performed by means of three small reaction wheels, whose reaction torque vector is computed using Proportional Derivative control laws and optimum control theory. Coarse attitude control is first performed in which the microsatellite attitude angles are determined by a technique based on the use of sensors with low mass and power consumption. Fine attitude control is then achieved by using a small star tracker for fine attitude measurement. The proposed techniques for attitude acquisition, determination and control during station keeping are numerically tested with a code that simultaneously integrates the microsatellite attitude dynamics and control. Numerical results show that the attitude acquisition is performed in about 20 orbits, after the separation from the launcher, while coarse attitude determination and control during station keeping are achieved with accuracies 0.7° and ±2°, respectively.

Exact Analytical Solution for Three-Dimensional Interception of a Maneuvering Target

Abstract: The three-dimensional guidance problem has been extensively discussed in the open literature for several decades. However, because of the nonlinearity of the equations of relative motion, the analytical solution is generally expressed in the form of nonintegrable quadratures. A partial closed-form solution for a guidance problem, in which the relative commanded acceleration is applied in the direction normal to the line-of-sight, was obtained by previous researchers. In this paper, we generalize that guidance law to include a component of the relative commanded acceleration along the line-of-sight. In this more general case, in the plane of relative motion which is always parallel to a fixed plane, the relative trajectory is obtained explicitly in closed form. Furthermore, while the previous analysis considered only special integer values for the sole navigation constant, the present analysis obtains the analytical solution for a more general guidance law, and arbitrary values of the two control parameters involved. The relative range, the line-of-sight swept angle, and the flight time are analytically expressed in terms of each other. An application to the interception of a satellite in circular orbit is presented.

Analysis of the pegasus breakup

Abstract: The Pegasus breakup is characterized by distributions of the orbital parameters and radar cross section of the pieces. The accuracy of the Simplified General Perturbations 4 (SGP4) element sets for the Pegasus breakup has been examined using the Space Surveillance Performance Analysis Tool. A graph of the average error growth rate (EGR) of the Pegasus breakup element sets over time shows pronounced spikes on certain days. Comparing graphs of EGR versus BSTAR (the term in SGP4 that accounts for unmodeled in-track forces, including drag) for all the Pegasus breakup pieces on a day when the average EGR is low and a day when the average is high shows that the element sets with large BSTAR values are susceptible to large variations in EGR. A graph of the average EGR and daily maximum planetary geomagnetic index Ap over times shows that the spikes in EGR are associated with geomagnetic storms. To reduce the size of the spikes in EGR, the length of update interval (LUPI) for the batch differential corrections of the element sets was shortened. To support catalog maintenance of the Pegasus breakup pieces with shorter LUPIs, additional sensors were tasked for observations.

Improvements in Mars Gravity Field Determination Using Ridge-Type Estimation Methods

Abstract: The use of ridge-type estimation methods in determining the proper weighting of the a priori covariance appears to improve the accur acy of the Mars50c gravity field model derived from Viking and Mariner 9 Doppler tracking data. These advanced parameter estimation techniques were applied to the calculation of GM and a (50 × 50) field of harmonic coefficients, representing the gravitational potential of Mars. Calculation of the gravity field coefficients involves solving a large, ill-conditioned system of linear equations, whose solution leads to erroneous estimates if not augmented by appropriate a priori information. In calculating Mars50c, an a priori covariance was used in order to provide a set of constraints on the gravity field solution. This study involved the use of ridge-type estimation methods to optimally weight a set of a priori constraints based upon Kaula’s Rule in order to obtain more accurate estimates. The computed gravity field, denoted AUMGM9, was compared to Mars50c on the basis of total variance of the solution and residual sum of squares. Analysis of the results show that through the use of ridge-type estimation methods, AUMGM9 provides more accurate gravity field coefficients than does Mars50c.

Application of Least Mean Square Algorithms to Spacecraft Vibration Compensation

Abstract: This paper describes the application of the Least Mean Square (LMS) algorithm in tandem with the Filtered-X Least Mean Square algorithm for controlling a science instrument's line-of-sight pointing. Pointing error is caused by a periodic disturbance and spacecraft vibration. A least mean square algorithm is used on-orbit to produce the transfer function between the instrument's servo-mechanism and error sensor. The result is a set of adaptive transversal filter weights tuned to the transfer function. The Filtered-X LMS algorithm, which is an extension of the LMS, tunes a set of transversal filter weights to the transfer function between the disturbance source and the servo-mechanism's actuation signal. The servo-mechanism's resulting actuation counters the disturbance response and thus maintains accurate science instrumental pointing. A simulation model of the Upper Atmosphere Research Satellite is used to demonstrate the algorithms.