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In this paper, we present a tensorial derivation of the equations of motion of a formation consisting of N spacecraft each modeled as a rigid body.
The Terrestrial Planet Finder Interferometer (TPF-I) is a large space telescope consisting of four 4 meter diameter telescopes flying in formation in space together with a fifth beam combiner spacecraft.
In this paper we present a solution to the formation initialization (FI) problem for N distributed spacecraft located in deep space. Our solution to the FI problem is based on a three-stage sky search procedure that reduces the FI problem for N spacecraft to the simpler problem of initializing a set of sub-formations.
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In this paper, we consider various classes of constrained attitude control (CAC) problem in single and multiple spacecraft settings. After categorizing attitude constraints into four distinct types, we provide an overview of the existing approaches to this problem. We then proceed to further expand on a recent algorithmic approach to the CAC problem. The paper concludes with an example demonstrating the viability of the proposed algorithm for a multiple spacecraft constrained attitude reconfiguration scenario.
In a precious paper the authors developed a formation initialization (FI) algorithm for a deep space, N-spacecraft formation. It was demonstrated analytically that this FI contribution of this paper is to extend this planar guarantee to deep space formations with arbitrary initial conditions. As part of the guarantee of initialization, a bound on the time-to-initialize is obtained. The guaranteed FI algorithm is then demonstrated for a two-spacecraft formation with realistic deep space mission constraints (e.g. limited field-of-view relative sensors and attitude constraints). The two-spacecraft scenario is challenging in that it has the least relative sensor field-of-view overlap. Finally, for this scenario, the distribution of time-to-initialize is characterized through a 150,000-case Monte Carlo analysis.
In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.
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This paper describes the profiles and requirements of the ST-3 and ST-5 missions, and discusses the unique technological challenges each of them presents. Bothe the AFF and CCNT trace their heritage to GPS receivers, using measurements of both RF carrier phase and a ranging code. They will operate, however, at very different frequency bands; the ADD at Ka-band, and the CCNT at S-band.
The interferometric version of the Terrestrial Planet Finder (TPF-I) has the potential to find and characterize earth-sized planets in the habitable zones of over 250 nearby stars and to search for life using biomarkers in the atmospheres of any planets found. The scientific case for such a mission continues to be strengthened by on-going progress in the detection of planets via indirect means. This paper summarizes the status of TPF-I, illustrative scientific requirements for the mission, and its enabling technologies.
An effective technique for real-time differential orbit determination with GPS bias fixing is formulated. With this technique, only real-time GPS orbits and clocks are needed (available from the NASA Global Differential GPS System with 10-20 cm accuracy). The onboard, realtime orbital states of user satellites (few meters in accuracy) are used for orbit initialization and integration. An extended Kalman filter is constructed for the estimation of the differential orbit between the two satellites as well as a reference orbit, together with their associating dynamics parameters. Due to close proximity of the two satellites and of similar body shapes, the differential dynamics are highly common and can be tightly constrained which, in turn, strengthens the orbit estimation. Without explicit differencing of GPS data, double-differenced phase biases are formed by a transformation matrix. Integer-valued fixing of these biases are then performed which greatly strengthens the orbit estimation. A 9-day demonstration between GRACE orbits with baselines of approx.200 km indicates that approx.80% of the double-differenced phase biases can successfully be fixed and the differential orbit can be determined to approx.7 mm as compared to the results of onboard K-band ranging.
The Earth Observatory Formation at L2, a Lagrange libration point, is a unique large aperture (25 m diameter) space telescope concept that will improve the knowledge and understanding of dynamic, chemical and radiative mechanisms that cause changes in the atmosphere, and can lead to the development of models and techniques to predict short and long-term climate changes. The results of this concept definition study show that the telescope concept is feasible, and can have technology readiness in the 2020 time frame. Further advanced development in several subsystems is needed, such as higher efficiency Xenon ion thrusters with throttling, and optical quality large membrane mirror with active shape control. It presents an analysis and solution of guidance, sensing, control, and propulsion problems for a formation of two spacecraft on the Sun-Earth line in the neighborhood of the Sun-Earth L2 point, that observes Earth s atmosphere during continuous solar occultation by the Earth. A system architecture is described for the observatory, and its components that include unique mission specific metrology. The formation must follow a powered trajectory with strictly limited fuel use to observe solar occultation. A configuration of ion thrusters and reaction wheels for translation and attitude control is designed along with algorithms for orbit following and formation control. Simulation results of the orbital and formation dynamics are presented that verify performance of the control systems.
We have developed an algorithm to retrieve scattering cloud pressures and other cloud properties with the Aura Ozone Monitoring Instrument (OMI). The scattering cloud pressure is retrieved using the effects of rotational Raman scattering (RRS). It is defined as the pressure of a Lambertian surface that would produce the observed amount of RRS consistent with the derived reflectivity of that surface. The independent pixel approximation is used in conjunction with the Lambertian-equivalent reflectivity model to provide an effective radiative cloud fraction and scattering pressure in the presence of broken or thin cloud. The derived cloud pressures will enable accurate retrievals of trace gas mixing ratios, including ozone, in the troposphere within and above clouds. We describe details of the algorithm that will be used for the first release of these products. We compare our scattering cloud pressures with cloud-top pressures and other cloud properties from the Aqua Moderate-Resolution Imaging Spectroradiometer (MODIS) instrument. OMI and MODIS are part of the so-called A-train satellites flying in formation within 30 min of each other. Differences between OMI and MODIS are expected because the MODIS observations in the thermal infrared are more sensitive to the cloud top whereas the backscattered photons in the ultraviolet can penetrate deeper into clouds. Radiative transfer calculations are consistent with the observed differences. The OMI cloud pressures are shown to be correlated with the cirrus reflectance. This relationship indicates that OMI can probe through thin or moderately thick cirrus to lower lying water clouds.
The MASSIM (Milli-Arc-Second Structure Imager) mission will use a set of achromatic diffractive-refractive Fresnel lenses to achieve imaging in the X-ray band with unprecedented angular resolution. It has been proposed for study within the context of NASA's "Astrophysics Strategic Mission Concept Studies" program. Lenses on an optics spacecraft will focus 5-11 keV X-rays onto detectors on a second spacecraft flying in formation 1000 km away. It will have a point-source sensitivity comparable with that of the current generation of major X-ray observatories (Chandra, XMM-Newton) but an angular resolution some three orders of magnitude better. MASSIM is optimized for the study of jets and other phenomena that occur in the immediate vicinity of black holes and neutron stars. It can also be used for studying other phenomena on the milli-arc-second scale, such as those involving proto-stars, the surfaces and surroundings of nearby active stars and interacting winds.
MASSIM, the Milli-Arc-Second Structure Imager, is a mission that has been proposed for study within the context of NASA's "Astrophysics Strategic Mission Concept Studies" program. It uses a set of achromatic diffractive-refractive Fresnel lenses on an optics spacecraft to focus 5-11 keV X-rays onto detectors on a second spacecraft flying in formation 1000 km away. It will have a point-source sensitivity comparable with that of the current generation of major X-ray observatories (Chandra, XMM-Newton) but an angular resolution some three orders of magnitude better. MASSIM is optimized for the study of jets and other phenomena that occur in the immediate vicinity of black holes and neutron stars. It can also be used for studying other astrophysical phenomena on the milli-arc-second scale, such as those involving proto-stars, the surfaces and surroundings of nearby active stars and interacting winds. After introducing the principle of diffractive imaging in the x-ray/gamma-ray regime, the MASSIM mission concept and baseline design will be described along with a discussion of the options and trade-offs within the X-ray optics design.
Virtual Satellite (VirtualSat) is a computer program that creates an environment that facilitates the development, verification, and validation of flight software for a single spacecraft or for multiple spacecraft flying in formation. In this environment, enhanced functionality and autonomy of navigation, guidance, and control systems of a spacecraft are provided by a virtual satellite that is, a computational model that simulates the dynamic behavior of the spacecraft. Within this environment, it is possible to execute any associated software, the development of which could benefit from knowledge of, and possible interaction (typically, exchange of data) with, the virtual satellite. Examples of associated software include programs for simulating spacecraft power and thermal- management systems. This environment is independent of the flight hardware that will eventually host the flight software, making it possible to develop the software simultaneously with, or even before, the hardware is delivered. Optionally, by use of interfaces included in VirtualSat, hardware can be used instead of simulated. The flight software, coded in the C or C++ programming language, is compilable and loadable into VirtualSat without any special modifications. Thus, VirtualSat can serve as a relatively inexpensive software test-bed for development test, integration, and post-launch maintenance of spacecraft flight software.
A computer program called "42" simulates the attitudes and trajectories of multiple spacecraft flying in formation anywhere in the Solar System.