Background

apsynsim simulation results for a spacecraft constellation Successive output from APSYNSIM interferometry simulation showing improving image reconstruction (bottom) as baseline coverage increases (top).
Radio frequency interferometry works by extracting information from the small phase differences among simultaneous observations by multiple spatially-distributed radio telescopes. Each distinct planar-projected vector between telescope locations (called a baseline) improves the quality of images that can be reconstructed from the joint data. A few small radio telescopes can thus be combined into a single instrument that approximates the capabilities of a giant radio dish the size of the largest baseline.

Terrestrial radio telescope arrays have been constructed that span tens of kilometers with dozens of antennas, and international collaborations have joined a handful of individual telescopes together to span multiple continents, with baselines up to ~8,000km. In order to allow capturing the best selection of baselines for different targets throughout the sky, reconfigurable arrays have telescopes mounted on mobile platforms that are repositioned between observations. In addition, the rotation of the Earth helps to sweep a ground-based array through a range of aspect angles with respect to fixed targets in the sky, providing additional baseline variety even within a single long-duration observation. The choice of telescope layouts for terrestrial interferometers has been carefully studied, yielding recommendations of special irregular patterns that depend on the target's celestial position and shape. This helps avoid duplicate distances and angles in the baselines between telescopes pairs that might occur with a more regular layout, and which do not contribute much to the array's imaging capability.

composite Hubble/VLA image of Hercules A galaxy with radio jets Radio-bright jets of the Hercules A galaxy. NASA, ESA, S. Baum and C. O'Dea (RIT), R. Perley and W. Cotton (NRAO/AUI/NSF), and the Hubble Heritage Team (STScI/AURA)
Astronomers are able to use ground-based radio interferometer arrays to resolve structural details of objects much too distant to be directly imaged by even the largest single telescopes. The ideal targets for radio interferometry are radio-bright objects with complex extended geometry, such as the relativistic jet lobes emanating from active galactic nuclei. A super-massive black hole at the heart of such a galaxy is thought to harvest the gravitational potential energy of in-falling matter from its accretion disc to power perpendicular jets of ionized material. These jets are initially highly collimated and can then extend to form vast lobes of synchrotron-illuminated material well beyond the host galaxy itself. Due to the immense luminosity of these sources, they can be detected from across the universe, but often at such huge distances that teasing out any structural detail requires extremely long baseline interferometry.

A constellation of small spacecraft, each equipped with a radio-frequency sensor, can leverage interferometry to combine their individually modest detection capabilities into a synthetic aperture instrument with much greater resolving power. A space-based array could access baseline distances that are unachievable on the Earth's surface, and could do so from a privileged vantage above the obscuring effects of the atmosphere, terrestrial noise sources, and the horizon. Furthermore, the relative orbital motions of the spacecraft would continuously change the constellation geometry and thus sample a large variety of baseline distances and angles.

Problem

While ground-based interferometer design has been well studied, space-based interferometer constellations introduce many more additional degrees of freedom. The mission design for such a constellation must balance among many competing variables: science quality, number of craft, total launch mass, data storage, communication topology, fuel costs, target coverage, mission operability, fault tolerance, etc. In particular, the details of the orbital geometry selected for each member craft directly impact the detection capabilities of the whole constellation, as well as the later data communication loads. Even more, the geometry of the constellation may be modified during the mission by expending maneuvering propellent to boost individual spacecraft to different orbits, further magnifying the range of possible mission scenarios. The problem faced is how to select high quality spacecraft orbits and other constellation features within such a vast mission design space so as to focus further human attention on only the most promising possibilities.

Impact

Automated analysis and trade space exploration has the potential to significantly improve the mission design process by focusing human creativity on the highest quality solutions. This is particularly true for interferometry missions where there are an even higher number of design variables under consideration. In addition, effective modeling of future mission operability is becoming more important as mission data volumes increase amid constrained communication resources.

Status

The RELIC mission study utilized the automated operability modeling to assist in communication hardware selection and data management analysis in 2016. The study then leveraged the automated orbit parameter optimization techniques to narrow down candidate constellation configurations in 2017.

Description

data flow diagram Process data flow, showing significant offline precomputation to speed heuristic optimization among possible orbit selections.
The RELIC mission study is using automated heuristic-guided orbit optimization and mission scheduling algorithms to assist in the mission design process. The constellations studied took the form of a set of concentric rings of radio telescope spacecraft flanking a single communications mothership that serves as the data relay to Earth. Constellation geometry is automatically tuned to improve image reconstruction quality and cost effectiveness of the constellation by searching among myriad possible orbital configurations. Mission design parameters, including instrument data acquisition rates and communication capabilities, are then evaluated via automated scheduling and simulation software to gauge the potential science return and overall operability of the mission. Initial results have shown impressive speed ups in design evaluation as well as relative improvements over orbit ensembles selected manually by experts.

The first step involves significant pre-computation of the geometric relationships of the spacecraft constellation and potential targets in order to accelerate later search steps. A set of provided ranges for constellation ring parameters such as number of spacecraft, orbital inclination, total fuel mass, etc is first discretized to a reasonable density for search. For example, the relative inclinations of the daughter-craft rings may range from 0 to 90 degrees above the mother-ship's orbital plane in increments of 10 degrees. Each term of the cartesian product of discretized constellation parameters are used to generate a set of coherent constellation orbits, in the form of SPICE kernels. The SPICE kernels are used to calculate the projective baselines between all pairs of orbits with respect to a set of evaluation targets for each candidate constellation. These baselines are then loaded into an efficient histogram baseline-coverage cache that efficiently answers future queries about the contribution of each orbit to different constellation configurations. This cache forms the basis of the baseline-coverage heuristic that guides future search steps.

Subsequently, the ideal constellation for a given set of constraints is "grown" via heuristic-guided iterative search. Several separate search strategies were evaluated, including hybrid combinations of such strategies. Forward-Greedy : score each possible next orbit based on how much it improves the current constellation if added, and then add the single maximum-scoring orbit as a new member of the constellation Reverse-Greedy : score each current orbit based on how much the constellation suffers if it is removed, and then remove the single least-damaging orbit from the constellation Accordion-Greedy : alternate between forward and reverse greedy phases of search with a specified cadence, eventually arriving at a target constellation size Risk-Aware : additionally accounts for a given probability of spacecraft loss during the mission by sampling across possible loss scenarios when scoring orbit contributions Fuel-Aware : accounts for the propellant mass expended in order to achieve different spacecraft orbits (e.g. higher inclination rings require much more fuel) by weighting alongside baseline coverage Throughout the search process, the baseline-coverage cache is kept updated to allow fast access to scoring queries relevant to the current constellation.

screenshot of communication plan Screenshot of ASPEN data communication plan for a small constellation, showing initial observation period, variable data-rate relay cross-link to mothership, and final downlink to earth ground stations.
Once a high-quality candidate constellation has been selected, it is submitted to a set of automated scheduling algorithms that optimize the communication operations of the constellation. The scheduling algorithms leverage additional heuristics regarding the relative communication bandwidths and observation opportunities available at different times during the mission. The best times for two spacecraft to communicate is when they are at their closest range, since data rates diminish as the square of distance between nodes. Thus, the best communication schedules typically involve collecting data locally until another craft comes within close range, then stopping observation in order to transfer data during the favorable data rate window. Eventually the data must reach the central mothership and be relayed to ground stations.

Different parameters of the constellation beyond geometry are also evaluated during this operations simulation step, including relative sizing of communication equipment on the mothership versus daughter-ships. A final reporting is made of the required mission lifetime and consumable resources necessary to support a given observation campaign using each candidate constellation, as well as final image quality measures that might be expected. Human mission designers can then use the output of the automated analysis to help trade capabilities versus equipment costs, operational costs, launch costs, etc.

Applications

Assistive mission design techniques in general apply widely to the early development phases of many missions. The RELIC mission analysis software is well suited to the growing number of missions that exploit the advantages of multiple spacecraft, and in particular interferometric observatories. The automated scheduling technology also readily applies to the operational phase of such missions, transforming operational strategies into complex command orchestration among many spacecraft.

Publications