Journal of the Astronautical Sciences

Published by American Astronautical Society
Print ISSN: 0021-9142
The problem of spacecraft attitude control and momentum management is addressed using nonlinear controllers based on feedback linearization. A chief limitation of the feedback linearization technique is that it requires an exact cancellation of nonlinear terms in order to obtain linear input-output behavior. Adaptive nonlinear controllers for linearizable systems are investigated to overcome this restriction and to achieve asymptotic linear behavior. The adaptive nonlinear approach is shown to effectively control the Space Station attitude and effector momentum, while providing accurate estimates of inertias.
This paper treats the question of large angle rotational manoeuvre and stabilization of an elastic spacecraft (spacecraft-beam-tip body configuration). Based on nonlinear inversion, a control law is derived to decouple the attitude angle and the dominant flexible modes from the remaining elastic modes. The inverse control law decomposes the spacecraft dynamics into a slow and a fast subsystem. The decoupled attitude angle and the dominant elastic modes are the components of the slow state vector and the remaining elastic modes are included in the fast state vector. Based on singular perturbation theory, controllers are designed for each lower-order subsystem. Then a composite state feedback control is obtained by combining the slow and the fast control laws. Simulation results are presented to show that the composite control system accomplishes large rotational manoeuvre and vibration suppression in the closed-loop system
Mode and logic-based switching for formation flying control is motivated and addressed in the context of separated spacecraft optical interferometry. It is shown that logic-based switching is an attractive approach for satisfying multiple performance criteria during the different phases of a representative formation flying mission. Simulation results are included to demonstrate the need for introducing logic-based switching, its mechanism, and its performance; the relevant theoretical results are also presented.
Results of mapping of rock types from the White Sands, New Mexico area using digital tape data from the Skylab S-192 multispectral scanner are presented. Spectral recognition techniques were used to process the geological data and signatures were extracted from the training sets using a set of promising ratio features defined by analysis of ERSIS (Earth Resources Spectral Information System). An analysis of ERSIS spectra of rock types yielded 24 promising spectral channel ratio features for separating the rock types into precambrian, calcareous, and clay materials and those containing ferric iron.
A unique and useful family of ballistic trajectories to Halley's comet is described. The distinguishing feature of this family is that all of the trajectories return to the Earth's vicinity after the Halley intercept. It is shown that, in some cases, the original Earth-return path can be reshaped by Earth-swingby maneuvers to achieve additional small-body encounters. One mission profile includes flybys of the asteroid Geographos and comet Tempel-2 following the Halley intercept. Dual-flyby missions involving comets Encke and Borrelly and the asteroid Anteros are also discussed. Dust and gas samples are collected during the high-velocity (about 70 km/sec) flythrough of Halley, and then returned to a high-apogee Earth orbit. Aerobraking maneuvers are used to bring the sample-return spacecraft to a low-altitude circular orbit where it can be recovered by the Space Shuttle.
The recent discovery of the Amor-class 1989 ML, the most accessible known asteroid for minimum-energy rendezvous missions, has expedited the search for frequent, low cost near-Earth asteroid rendezvous and round-trip missions. This paper identifies trajectory characteristics and assesses mass performance for low ΔV (<5.75 km/s) ballistic rendezvous opportunities to 1989 ML during the period 1996-2010. This asteroid also offers occasional extended mission opportunities, such as the lowest known ΔV requirement for any asteroid sample return mission as well as pre-rendezvous asteroid flyby and post-rendezvous comet flyby opportunities requiring less than 5.25 km/s total ΔV. This paper also briefly comments concerning mission opportunities for asteroid 1991 JW, which recently replaced other known asteroids as the most accessible near-Earth asteroid for fast rendezvous and round-trip missions.
A low cost program that links a dual-comet flyby sample-return mission with a multicomet/asteroid tour is proposed. Two spacecraft are used to carry out this program: a three-axis stabilized Observer-class spacecraft and a smaller spin-stabilized sample-return probe. The Observer spacecraft uses earth-swingby and propulsive maneuvers to accomplish the small-body tour, which includes flybys of three comets (Tempel-1, Tempel-2, and Encke) and two asteroids (46-Hestia and 433-Eros) over a 12-year period. Two of these comets (Tempel-1 and Tempel-2) are also the shared targets, the Observer serves as a navigational aid for the probe, which scoops up dust particles as it flies through the cometary atmosphere. After collecting the cometary dust samples, the probe returns to a low earth orbit where it is recovered by the Space Shuttle.
A diverse collection of unmanned missions to explore the inner planets, outer planets, and small bodies of the solar system is being considered by the National Aeronautics and Space Administration for the remainder of this century and beyond. This paper describes the key navigational problems which are anticipated for some of these missions and the techniques which are likely to be used to solve these problems. Emphasis in this paper is placed on those missions which take place entirely within about 2 Astronomical Units of the sun. The missions studied include Orbiters of Venus, Mars, the moon, and an earth-approaching asteroid, probes of the atmosphere of Venus and the surface of Mars, fast flybys of comets, and sample return missions from Mars and a short-period comet.
A recently developed rendezvous navigation fusion filter that optimally exploits existing distributed filters for rendezvous and GPS navigation to achieve the relative and inertial state accuracies of both in a global solution is utilized here to process actual flight data. Space Shuttle Mission STS-69 was the first mission to date which gathered data from both the rendezvous and Global Positioning System filters allowing, for the first time, a test of the fusion algorithm with real flight data. Furthermore, a precise best estimate of trajectory is available for portions of STS-69, making possible a check on the performance of the fusion filter. In order to successfully carry out this experiment with flight data, two extensions to the existing scheme were necessary: a fusion edit test based on differences between the filter state vectors, and an underweighting scheme to accommodate the suboptimal perfect target assumption made by the Shuttle rendezvous filter. With these innovations, the flight data was successfully fused from playbacks of downlinked and/or recorded measurement data through ground analysis versions of the Shuttle rendezvous filter and a GPS filter developed for another experiment. The fusion results agree with the best estimate of trajectory at approximately the levels of uncertainty expected from the fusion filter's covariance matrix.
Space missions are presented to deflect four fictitious Earth impacting objects by using an advanced magnetoplasma spacecraft designed to deliver a laser ablation payload. The laser energy required to provide sufficient change in velocity is estimated for one long-period comet and three asteroids, and an optimal rendezvous trajectory is provided for each threat scenario. The end-to-end simulations provide an overall concept for solving the deflection problem. These analyses illustrate that the optimal deflection strategy is highly dependent on the size and the orbital elements of the impacting object, as well as the amount of warning time. A rendezvous spacecraft with a multi-megawatt laser ablation payload could be available by the year 2050. This approach could provide a capable and robust orbit modification approach for altering the orbits of Earth-crossing objects with relatively small size or long warning time. Significant technological advances, multiple spacecraft, or alternative deflection techniques are required for a feasible scenario to protect Earth from an impacting celestial body with large size and short warning time.
Manned spacecraft abort guidance and control problems, discussing various modes and emergency conditions
For most imaging sensors, a constant (dc) pointing error is unimportant (unless large), but time-dependent (ac) errors degrade performance by either distorting or smearing the image. When properly quantified, the separation of the root-mean-square effects of random line-of-sight motions into dc and ac components can be used to obtain the minimum necessary line-of-sight stability specifications. The relation between stability requirements and sensor resolution is discussed, with a view to improving communication between the data analyst and the control systems engineer.
It is shown here that, under certain conditions, the low-frequency accelerations on experiments being performed aboard orbiting spacecraft due to gravity gradient, atmospheric drag, and spacecraft attitude or orientation can cause sustained fluid motions which require correction by advanced mass compensation techniques. The gravity gradient tensor is derived, and an expression for the difference between the absolute accelerations of a free particle and the mass center of the spacecraft is obtained. A model for the variation of atmospheric density with altitude is discussed, the equations governing the relative motion of a drag-free particle with respect to the mass center of the spacecraft are presented, and analytical and numerical solutions are obtained. Two possible spacecraft altitudes are considered. The problem of the Stokes motion of a sphere immersed in a viscous fluid is examined. Results are presented for the motion of a steel ball in water and for a triglycine sulfate crystal freely suspended in solution.
Undefonned Structure.
Weight Matrices for Test Case Maneuve rs.
Anti-Symmetric Deformation Modes.
In this paper the problem of maneuvering a flexible spacecraft through a large angle is considered, where the disturbance-accommodating feedback control tracks a desired output state. The desired output state is provided from an open-loop solution for the linear system model. The components of the disturbance vector are assumed to be represented in terms of Fourier series. Closed-form solutions are provided for the Ricati, prefilter, state trajectory, and residual state trajectory equations which define the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index for frequency-shaping, in order to smooth both the open- and closed-loop control commands.
This paper addresses the problem of estimating the masses of Phobos and Deimos from Doppler and onboard optical measurements during the Viking extended mission. A Kalman filter is used to analyze the effects of gravitational uncertainties and nongravitational accelerations. These accelerations destroy the dynamical integrity of the orbit and multi-batch or limited memory filtering is preferred to single batch processing. Optical tracking is essential to improve the relative orbit geometry. The masses can be determined to about 10% and 25% respectively for Phobos and Deimos, assuming satellite densities of about 3 g per cu cm.
Laser range measurements are used to determine the orbit of Seasat during the period from July 28, 1978, to Aug. 14, 1978, and the influence of the gravity field, atmospheric drag, and solar radiation pressure on the orbit accuracy is investigated. It is noted that for the orbits of three-day duration, little distinction can be made between the influence of different atmospheric models. It is found that the special Seasat gravity field PGS-S3 is most consistent with the data for three-day orbits, but an unmodeled systematic effect in radiation pressure is noted. For orbits of 18-day duration, little distinction can be made between the results derived from the PGS gravity fields. It is also found that the geomagnetic field is an influential factor in the atmospheric modeling during this time period. Seasat altimeter measurements are used to determine the accuracy of the altimeter measurement time tag and to evaluate the orbital accuracy.
The tidal potential is related to small periodic variations in the geopotential which are caused by the formation of the tidal bulge and by the redistribution of masses in the earth's interior under the influence of lunisolar tidal attraction. The tidal effects in the motion of a satellite can be interpreted as the result of tidal periodic oscillations. An investigation of the tidal disturbing potential is conducted and the differential equations for the variations of the elements are considered. It is suggested that a future planning should include the tidal observations on the earth surface.
This paper addresses the problem of control synthesis for vibration suppression in large flexible structures. The control strategy employed involves a decentralized model reference adaptive approach using a variable structure, sliding mode control. Local models are formulated based on desired damping and response time in a model-following scheme for various model configurations. Variable-structure controllers are then designed employing collocated angular rate and position feedback. In this scheme local control forces the system to move on a local sliding surface in some local error space. An important feature of this approach is that the local subsystem is made insensitive to dynamical interactions with other subsystems once the sliding surface is reached. Numerical simulations are carried out using NASA's flexible grid experimental apparatus.
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
A NASA/ASEE Summer Study conducted at the University of Santa Clara in 1980 examined the feasibility of using advanced artificial intelligence and automation technologies in future NASA space missions. Four candidate applications missions were considered: (1) An intelligent earth-sensing information system, (2) an autonomous space exploration system, (3) an automated space manufacturing facility, and (4) a self-replicating, growing lunar factory. The study assessed the various artificial intelligence and machine technologies which must be developed if such sophisticated missions are to become feasible by century's end.
The feasibility of using machine intelligence, including automation and robotics, in future space missions was studied.
Three atmospheric guidance concepts proposed for an aeroassist flight experiment are presented. The flight experiment will simulate a return from geosynchronous orbit by an aeroassisted orbital transfer vehicle and is proposed to be flown on board the Space Shuttle in 1992. The three guidance concepts include an analytic predictor/corrector, a numeric predictor/corrector, and an energy controller. The algorithms for the three guidance methods are developed and performance results are presented for the nominal case and for several cases dispersed from the nominal conditions.
This paper presents the theory of optimal aeroassisted orbital transfer, with special consideration given to the transfer about a central body with an atmosphere, with propulsive maneuvers in space modeled as instantaneous changes in the velocity vector. It is shown that there are four potentially optimal transfer modes, two aeroassisted and two all-propulsive, for each point in the two-dimensional transfer space. Aeroassisted orbital transfer introduces a strong coupling between the trajectory design and the vehicle design; a trajectory that minimizes fuel mass without attention to heating may require the vehicle to have a heavy thermal protection system. It is emphasized that, if aeroassisted transfer is to be preferred to all-propulsive transfer, it must offer a reduction in fuel mass greater than the increase in thermal protection mass.
The problem of generating good nominal trajectories is considered with particular reference to an AFE type spacecraft flying with constant angle of attack and variable angle of bank. A simulated GEO-to-LEO aeroassisted orbital transfer is considered. It is shown that, for fixed control, the AFE trajectory exhibits strong intrinsic instability in the longitudinal motion and near neutrality in the lateral motion, while stability can be artificially induced via feedback control, the effectiveness of a feedback control scheme depends on control margin availability. The AFE nominal trajectory must be chosen as a compromise between good performance and good control margin.
In the present treatment of optimal control problems arising in the study of coplanar aeroassisted orbital transfer, the hybrid combination of propulsive parameters in space and aerodynamic maneuvers employing lift modulation in the sensible atmosphere indicates that the optimal energy-viewpoint solution is the grazing trajectory; this trajectory is characterized by favorable values of the peak heating rate and the peak dynamic pressure. Numerical solutions are obtained by means of the sequential gradient restoration algorithm for optimal control problems. It is found that nearly-grazing trajectories yielding the least-square value of the path inclination have desirable characteristics from the standpoints of energy, heating rate, and dynamic pressure.
Application of slightly modified off-the-shelf automatic celestial navigation systems ('star trackers') is considered for the purposes of monitoring variations in the optical depth of the stratospheric aerosol and ozone layers. The basic principle of the technique is to observe stars from an orbiting station as they are occulted by the stratospheric aerosol layer. Since molecular and refraction extinction are directly calculable, total extinction measurements using a dual-sensor (S4 and S20) approach allows us to directly solve for ozone and aerosol extinction and look for correlations between these two parameters. The technique appears promising for remotely monitoring aerosol and ozone optical depth in the 15-25 km region over selected locations and is independently accurate if aerosol composition and relative size distribution are invariant.
The navigational accuracy of an oceangoing vessel using conventional GPS p-code data is examined. The GPS signal is transmitted over two carrier frequencies in the L-band at 1575.42 and 1227.6 MHz. Achievable navigational uncertainties of differenced positional estimates are presented as a function of the parameters of the problem, with particular attention given to the effect of sea-state, user equivalent range error, uncompensated antenna motion, varying delay intervals, and reduced data rate examined in the unaided mode. The unmodeled errors resulting from satellite ephemeris uncertainties are shown to be negligible for the GPS-NDS (Navigation Development) satellites. Requirements are met in relatively calm seas, but accuracy degradation by a factor of at least 2 must be anticipated in heavier sea states. The aided mode of operation is examined, and it is shown that requirements can be met by using an inertial measurement unit (IMU) to aid the GPS receiver operation. Since the use of an IMU would mean higher costs, direct Doppler from the GPS satellites is presented as a viable alternative.
The Alfven wave excited by a long cylindrical satellite moving with a constant velocity at an angle relative to a uniform magnetic field has been calculated. Assuming a plasma with infinite conductivity, the linearized momentum equation and Maxwell's equations are applied to a cylindrical satellite carrying a variable current. The induced magnetic field is determined, and it is shown that the Alfven disturbance zone is of limited extent, depending on the satellite shape. The wave drag coefficient is calculated and shown to be small compared to the induction drag coefficient at all altitudes considered.
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) (exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics quaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.
Estimation of precise tracking station locations for deep space navigation is based on combining state estimates derived from a multitude of planetary encounter missions with planet direction information provided by the planetary ephemeris. Procedures for reducing the dimensionality of the station location estimation problem and for analytically correcting estimates for ephemeris updates have been developed. Using Householder transforms the large scale state estimation problem is decomposed into a sequence of dynamically uncoupled problems of lower dimension. The effect of an ephemeris update is shown to be adequately approximated by Brouwer-Clemence Set III perturbations for the earth-moon barycenter and the target planet for each mission.
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.
Limited word size in contemporary microprocessors causes numerical problems in autonomous satellite navigation applications. Numerical error introduced in navigation computations performed on small wordlength machines can cause divergence of sequential estimation algorithms. To insure filter reliability, square root algorithms have been adopted in many applications. The optimal navigation algorithm requires a careful match of the estimation algorithm, dynamic model, and numerical integrator. In this investigation, the relationship of several square root filters and numerical integration methods is evaluated to determine their relative performance for satellite navigation applications. The numerical simulations are conducted using the Phase I GPS constellation to determine the orbit of a LANDSAT-D type satellite. The primary comparison is based on computation time and relative estimation accuracy.
The International Sun-Earth Explorer-3 (ISEE-3) was moved from its mission halo orbit upstream of the earth's magnetosphere on June 10, 1982. Multiple lunar swingby maneuvers were then used to shape the trajectory for extensive exploration of the distant geomagnetic tail and finally to place the spacecraft on a course that will intercept the comet Giacobini-Zinner on September 11, 1985. With this new mission objective, the spacecraft was renamed the International Cometary Explorer (ICE). A double-lunar-swingby control technique involving five passes by the moon was eventually implemented to accomplish this, but in the process of finding this solution several feasible, though less optimal, alternative trajectory sequences implementing the same procedure were discovered. This paper provides a descriptive comparison of these very different orbital profiles and serves to illustrate the utility and great flexibility of this orbital control procedure. Targeting methodology for finding constrained solutions in this space is also presented.
Accurate orbit determination and the recovery of geophysical parameters are presently attempted via methodologies which use differenced height measurements at the points where the ground tracks of the altimetric satellite orbits intersect. Such 'crossover measurements' could significantly improve the earth's gravity field model. Attention is given to a novel technique employing crossover measurements from two satellites carrying altimeter instruments; this method can observe zonal harmonics of the earth's geopotential which are weakly observed through single-satellite crossovers. This dual-satellite crossover technique will be applicable to data from such future oceanographic satellites as ERS-1.
It is noted that major improvements have been made in the Goddard Space Flight Center (GSFC) geodynamic models for Seasat. It is pointed out that the dominant error source in Seasat ephemeris computation is currently the uncertainty in modeling the earth's gravity field. Attention is also given to significant errors arising from atmospheric drag and solar radiation pressure modeling. It is noted that a comparison of GSFC and Naval Surface Weapons Center (NSWC) Seasat ephemerides indicate the presence of an unexplained difference of about 4 m in the location of the center of mass along the Z axis. This difference is consistent with that obtained with earlier geoid and station coordinated comparisons performed by other investigators. It is expected that future combinations of Seasat and GEOS-3 altimeter data, together with laser and Unified S-Band tracking data, will ultimately produce a gravity field which allows computations of a global Seasat ephemeris with an rms radial accuracy of about 50 cm.
This paper describes the use of stochastic differential correction models in refining the Seasat orbit based on post-flight analysis of tracking data. The objective is to obtain orbital-height precision that is commensurate with the inherent Seasat altimetry data precision level of 10 cms. Local corrections to a mean ballistic arc, perturbed principally by atmospheric drag variations and local gravitational anomalies, are obtained by the introduction of stochastic dynamical models in conjunction with optimal estimation/smoothing techniques. Assessment of the resulting orbit with 'ground truth' provided by Seasat altimetry data shows that the orbital height precision is improved by 32% when compared to a conventional least-squares solution using the same data set. The orbital height precision realized by employing stochastic differential correction models is in the range of 73 cms to 208 cms rms.
The applications sensors of many low altitude earth satellites designed for recording surface or atmospheric data require near zero orbital eccentricities for maximum usefulness. Coverage patterns and altitude profiles require specified values of orbit semimajor axis. Certain initial combinations of semimajor axis, eccentricity, and argument of perigee can produce a so called 'frozen orbit' and minimum altitude variation which enhances sensor coverage. This paper develops information on frozen orbits and minimum altitude variation for all inclinations, generalizing previous results. In the altitude regions where most of these satellites function (between 200 and 1000 kilometers) strong atmospheric drag effects influence the evolution of the initial orbits. Active orbital maneuver control techniques to correct evolution of orbit parameters while minimizing the frequency of maneuvers are presented. The paper presents the application of theoretical techniques for control of near frozen orbits and expands upon the methods useful for simultaneously targeting several inplane orbital parameters. The applications of these techniques are illustrated by performance results from the Atmosphere Explorer (AE-3 and -5) missions and in preflight maneuver analysis and plans for the Seasat Oceanographic Satellite.
An analytic approach is used to obtain the optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous for the Clohessy-Wiltshire equations. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Motion equations of sun, moon, earth and lunar probe integrated by power series solution and analytic continuation with recursively formed derivatives
We present the conceptual design of an instrument that can provide a continuous analog measure of the pitch and yaw angles of a low altitude satellite in the frame of the neutral atmosphere. The device, which uses pressure sensor orientation to provide its signal, can function in an attitude control loop and/or be used to measure atmospheric winds or wave motions. Any arbitrary angle of attack (pitch and yaw) less than +/- 45 deg can be selected for a heading. The sensitivity of the device is 0.1 deg but this would be limited by low ambient pressure at high altitudes and by multiple particle collisions in and below the slip flow region. The development of a prototype flight unit is in progress.
Spacecraft Model.
Rigid Body Angle and Normalized Control Profiles for W B = 1.0 rad/ s.
Frequency Spectra of the Normalized Controls for Starting Guesses with WB = 0. \047 rad/ s and W B = \ .0 rad/s. digits of accuracy. The continuation parameter increments are exponential, where the kth continuation parameter is given by a l l ) = e(kin 2)/.-1 , where n = 3 is arbitrarily chosen as the number of discrete steps. Thus, the entire continuation is performed with the following set of parameters: (ah a 2) = (0, 0), (0.260, 0), (0.587,0) , (1,0) , (1,0.260), (1,0.587), and (1, 1).
The paper considers the problem of maneuvering a flexible spacecraft through large angles in finite time. The basic control problem is divided into two parts. The first part consists of generating a frequency-shaped open-loop solution for the nonlinear rigid body as the nominal solution. The resulting two-point boundary-value problem is solved by introducing a continuation method for altering the mass distribution and boundary conditions for the spacecraft. For the second part, a feedback control is designed by linearizing the flexible body response about several points along the rigid body nominal solution. The perturbation gains are designed by using a frequency-shaped cost functional approach. The gains are linearly interpolated to produce smooth control time-histories as the linear piecewise constant plant models change during the maneuver.
The Laser Interferometer Space Antenna (LISA) mission is a planned NASA-ESA gravity wave detector consisting of three spacecraft in heliocentric orbit. Lasers are used to measure distance fluctuations between the proof masses aboard the spacecraft to the picometer level over the 5 million kilometer spacing. Each spacecraft and it's two laser transmit/receive telescopes must be held stable in pointing to less than 8 nanoradians per root Hertz in the frequency band 0.1 mHz to 0.1 Hz. This is accomplished by sensing the pointing error in the received beam and controlling the spacecraft attitude with a set of micronewton thrusters. Requirements, sensors, actuators, control design, and simulations are described in this paper.
A mathematical description of the data reduction technique used in analyzing Voyager calibration data is presented. To achieve the required telecommunication link performance, highly accurate pointing of the Voyager high gain antenna boresight relative to earth is necessary. To provide the optimum pointing, in-flight calibrations of the high gain antenna pointing mechanism are regularly made, and the design of the calibration and the antenna error models is delineated. It is shown that due to the use of wide angle sun sensors for celestial attitude control, the Voyager antenna error model differs from those of previous missions. Results of the in-flight calibrations and their implementation in improving the antenna pointing are also presented.
This paper deals with the application of linear optimal control and filtering theory to control a spinning spacecraft with movable telescoping appendages. The equations of motion are linearized about the desired final state. A feedback control system is designed to maintain this final state, with plant noise and measurement noise present in the system. Analytic results are obtained for special cases and numerical results are presented for the general case.
The control of a spin-stabilized spacecraft consisting of a rigid central hub and one or two movable offset telescoping booms (with end masses) is considered. The equations of rotational motion are linearized about either of two desired final states. A control law for the boom end mass position is sought such that a quadratic cost functional involving the weighted components of angular velocity plus the control is minimized when the final time is unspecified and involves the solution of the matrix Riccati algebraic equation. For three axis control more than one offset boom (orthogonal to each other) is required. For two-axis control with a single boom offset from a symmetrical hub, an analytic solution is obtained; when this system is used for nutation decay the time constant is one order of magnitude smaller than previously achieved using nonoptimal control logic. For the general case results are obtained numerically.
Dimensionless Error Coefficients for a Circular Orbit.
Dimensionless Error Coefficients for an Elliptic Orbit, Epoch at Perigee.
Dimensionless Error Coefficients for an Elliptic Orbit, Epoch at Apogee.
Based on a Taylor series expansion, an easily-computed approximation to the Cartesian state transition matrix is presented for a general velocity-independent force field. Suitable for the short time intervals encountered in onboard navigation applications of the extended Kalman filter, it provides approximately five decimal digits of accuracy for earth orbiting spacecraft with update intervals of one minute, and better accuracy for shorter intervals.
The accurate determination of the geocentric coordinates of a tracking station is essential for most geodetic and geophysical satellite applications. Since most of these satellites are close to the earth, the geopotential model is a dominant source of error which significantly influences station coordinate determinations. Other sources, such as GM error and drag, also influence the accuracy of the station coordinate determination. One technique for reducing the effect of these errors is to use short-arcs consisting of a few passes of the satellite over the tracking station. This paper analyzes the sensitivity of short-arc station coordinate estimates to various errors in the physical model, to the number of observations, and to the station-satellite geometry using simulated as well as real data.
A numerical method to find suitable Mars parking orbits is developed which takes into account geometries associated with the asymptotes, along with the nodal precession caused by the oblateness of Mars. A selected orbital plane which contains the arrival asymptote precesses through the stay time to the plane also containing the departure asymptote. The parking orbit is co-planar with both the arrival and departure asymptotes and only in-plane burns are required at both Mars arrival and departure. The need for a plane change at Mars departure to achieve the proper velocity vector for earth return is eliminated. The method requires very little computation time to determine a set of all possible inclinations and right ascensions of the ascending nodes.
An attempt is made to develop a method for realistic estimation of the initial LEO mass. The method takes into account the actual geometry between the inbound and outbound hyperbolic asymptotes and the parking orbit, along with precession effects caused by the oblateness of Mars, in calculating the arrival and departure Delta V values. Three mission scenarios alternative to the arbitrarily assumed two tangential periapsis burns are described: a tangential periapsis arrival and an in-plane departure; an in-plane arrival and in-plane departure; and a tangential periapsis arrival and a 3D departure. Results obtained by the method under consideration compared well with a trajectory integration code, where the differences in the initial LEO orbit mass were within one percent, for all three cases. The method is considered to be an ideal tool for preliminary mission design, since it reduces the analysis computation time with minimal loss in accuracy.
Top-cited authors
John Junkins
  • Texas A&M University
Landis Markley
Hanspeter Schaub
  • University of Colorado Boulder
Kathleen Howell
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D. Mortari
  • Texas A&M University