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In this paper we discuss the four classes of constellation/formation support with emphasis of DSMS current status (technology and implementation) and plans in each area.
The last 15 years has seen considerable progress in the conception and development of ideas for multi-spacecraft optical interferometers.
This paper gives a characterization of the equivalent topologies and uses this approach to show that there exists a control topology which achieves a global tracking objective using only local controllers.
This paper compares autonomous relative navigation performance for formations in eccentric, medium and high-altitude Earth orbits using Global Positioning System (GPS) Standard Positioning Service (SPS), crosslink, and celestial object measurements. For close formations, the relative navigation accuracy is highly dependent on the magnitude of the uncorrelated measurement errors. A relative navigation position accuracy of better than 10 centimeters root-mean-square (RMS) can be achieved for medium-altitude formations that can continuously track at least one GPS signal. A relative navigation position accuracy of better than 15 meters RMS can be achieved for high-altitude formations that have sparse tracking of the GPS signals. The addition of crosslink measurements can significantly improve relative navigation accuracy for formations that use sparse GPS tracking or celestial object measurements for absolute navigation.
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. We demonstrate our FI algorithm in simulation using NASA’s five spacecraft Terrestrial Planet Finder mission as an example.
Some simple guidelines based on the accuracy in determining a satellite formation s semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member's semi-major axis are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or vice versa. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver we, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
Several techniques are used to synthesize the formation-keeping control law for a three-satellite formation in low-earth orbit. The objective is to minimize maneuver cost and position tracking error. Initial reductions are found for a one-satellite case by tuning the state-weighting matrix within the linear-quadratic-Gaussian framework. Further savings come from adjusting the maneuver interval. Scenarios examined include cases with and without process noise. These results are then applied to a three-satellite formation. For both the one-satellite and three-satellite cases, increasing the maneuver interval yields a decrease in maneuver cost and an increase in position tracking error. A maneuver interval of 8-10 minutes provides a good trade-off between maneuver cost and position tracking error. An analysis of the closed-loop poles with respect to varying maneuver intervals explains the effectiveness of the chosen maneuver interval.
Spacecraft formations enable a variety of mission concepts, from gravity reconstruction to extrasolar planet detection to heliophysics observatories. In particular, space-based radio interferometers can detect signals in frequency ranges that are absorbed by Earth’s ionosphere or atmosphere. Furthermore, such formation missions are now feasible under constrained cost caps due to the growing availability of SmallSat components with spaceflight heritage that are compatible the CubeSat formfactor. Accordingly, we analyze a mission concept operating multiple SmallSats in a passive cluster to establish a space-based interferometer. The goal of this array is to reconstruct radio emissions associated with Coronal Mass Ejections (CMEs) from the Sun, giving us insight into the particle acceleration occurring during these events. This low-cost mission concept presents a number of unique challenges in regards to mission design and navigation, particularly the configuration of the spacecraft to optimize science return and the reconstruction of precise spacecraft-spacecraft separation values. After providing a brief overview of the mission concept, this paper presents several key features of the mission design and orbit determination strategy that enable this potential heliophysics mission.
The problem of coordination and control of multiple spacecraft (MS) moving in formation is considered. Here, each MS is modeled by a rigid body with fixed center of mass. First, various schemes for generating the desired formation patterns are discussed, Then, explicit control laws for formation-keeping and relative attitude alignment based on nearest neighbor-tracking are derived. The necessary data which must be communicated between the MS to achieve effective control are examined. The time-domain behavior of the feedback-controlled MS formation for typical low-Earth orbits is studied both analytically and via computer simulation. The paper concludes with a discussion of the implementation of the derived control laws, and the integration of the MS formation coordination and control system with a proposed inter-spacecraft communication/computing network.
In this paper, we describe the mission design for TPF assuming a distributed spacecraft concept using formation flight around both a halo orbit around L2 as well as a heliocentric orbit. Although the mission architecture is still under study, the next two years will include study of four design cncepts and a downselect to two concepts around 2005.
Goddard Space Flight Center is currently developing advanced spacecraft systems to provide autonomous navigation and control of formation flyers. This paper discusses autonomous relative navigation performance for formations in eccentric, medium, and high-altitude Earth orbits using Global Positioning System (GPS) Standard Positioning Service (SPS) and intersatellite range measurements. The performance of several candidate relative navigation approaches is evaluated. These analyses indicate that the relative navigation accuracy is primarily a function of the frequency of acquisition and tracking of the GPS signals. A relative navigation position accuracy of 0.5 meters root-mean-square (RMS) can be achieved for formations in medium-attitude eccentric orbits that can continuously track at least one GPS signal. A relative navigation position accuracy of better than 75 meters RMS can be achieved for formations in high-altitude eccentric orbits that have sparse tracking of the GPS signals. The addition of round-trip intersatellite range measurements can significantly improve relative navigation accuracy for formations with sparse tracking of the GPS signals.
The Goddard Space Flight Center is currently developing advanced spacecraft systems to provide autonomous navigation and control of formation flyers. This paper discusses autonomous relative navigation performance for a formation of four eccentric, medium-altitude Earth-orbiting satellites using Global Positioning System (GPS) Standard Positioning Service (SPS) and "GPS-like " intersatellite measurements. The performance of several candidate relative navigation approaches is evaluated. These analyses indicate that an autonomous relative navigation position accuracy of 1meter root-mean-square can be achieved by differencing high-accuracy filtered solutions if only measurements from common GPS space vehicles are used in the independently estimated solutions.
This paper discusses the development of a linear control algorithm for formations in the vicinity of the L2 sun-Earth libration point. The development of a simplified extended Kalman filter is included as well. Simulations are created for the analysis of the stationkeeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. For formation maneuvering, the formation spacecraft track to within 4 meters of their desired position and within 1.5 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the formation spacecraft tracking to within several micrometers. Each spacecraft uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.
Weak Stability regions serve as superior locations for interferometric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observing efficiency. Design of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of WSB solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in WSB regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numerical methods for attaining constrained formation geometries and controlling their dynamical evolution. This paper presents a survey of formation missions in the WSB regions and a brief description of the formation design using numerical and dynamical techniques.
The literature offers a number of approximations for analytically and/or efficiently computing the probability of collision between two space objects. However, only one of these techniques is a completely analytical approximation that is suitable for use in the preliminary design phase, when it is more important to quickly analyze a large segment of the trade space than it is to precisely compute collision probabilities. Unfortunately, among the types of formations that one might consider, some combine a range of conditions for which this analytical method is less suitable. This work proposes a simple, conservative approximation that produces reasonable upper bounds on the collision probability in such conditions. Although its estimates are much too conservative under other conditions, such conditions are typically well suited for use of the existing method.
The Guidance, Navigation, and Control Center (GNCC) at Goddard Space Flight Center (GSFC) has successfully developed high-accuracy autonomous satellite navigation systems using the National Aeronautics and Space Administration's (NASA's) space and ground communications systems and the Global Positioning System (GPS). In addition, an autonomous navigation system that uses celestial object sensor measurements is currently under development and has been successfully tested using real Sun and Earth horizon measurements.The GNCC has developed advanced spacecraft systems that provide autonomous navigation and control of formation flyers in near-Earth, high-Earth, and libration point orbits. To support this effort, the GNCC is assessing the relative navigation accuracy achievable for proposed formations using GPS, intersatellite crosslink, ground-to-satellite Doppler, and celestial object sensor measurements. This paper evaluates the performance of these relative navigation approaches for three proposed missions with two or more vehicles maintaining relatively tight formations. High-fidelity simulations were performed to quantify the absolute and relative navigation accuracy as a function of navigation algorithm and measurement type. Realistically-simulated measurements were processed using the extended Kalman filter implemented in the GPS Enhanced Inboard Navigation System (GEONS) flight software developed by GSFC GNCC. Solutions obtained by simultaneously estimating all satellites in the formation were compared with the results obtained using a simpler approach based on differencing independently estimated state vectors.