Scheduling algorithms for rapid imaging using agile Cubesat constellations
Introduction
Earth-science processes are intrinsically dynamic, complex, and interactive. To achieve an all-embracing understanding of the emergence and evolution of these processes requires the collection and assimilation of enormous amounts of data, using complementary measurements in space and time. Spatial measurements from multiple vantage points – space, air, ground and water – help resolve measurement and model uncertainties. Distributed Space Missions (DSMs) such as formation flight and constellations are being recognized as important solutions to increase measurement samples over space and time (D’Errico, 2012), especially when augmented with aircraf. The National Research Council (NRC), in its mid-term assessment of NASA’s implementation of the 2007 Decadal Survey recommended a “more agile and cost-effective replacement of individual sensors… moving away from a single parameter and sensor-centric approach toward a systems approach that ties observations together to study processes important to understanding Earth-system feedbacks” (National Research Council, 2012). DSMs also minimize launch and operational risks by adding redundancy in numbers, and allow for deploying evolved technology as they become available. However, they carry a risk unexpected failures in case of poorly understood interdependencies. Continued effort for creating and maintaining an interoperable environment for a diverse set of sensors (land, marine, air, space) using software and internet is underway in NASA Sensor Webs (Mandl et al., 2006). The goal is to allow sensors to operate in a semi-automated, collaborative manner for scientific investigation, disaster management, resource management and environmental intelligence. The development of software tools to design DSMs, in keeping with customizable science objectives for rapid pre-PhaseA trade studies is currently underway at NASA Goddard Space Flight Center (LeMoigne et al., 2017). While this initiative is expected to foster innovation on multi-satellite solutions in the Earth Science community, it does not model operational planning, scheduling or autonomy.
Response and revisit requirements for Earth Observation (EO) vary significantly by application, ranging from less than an hour to monitor disasters, to daily for meteorology, to weekly for land cover monitoring (Sandau et al., 2010). Geostationary satellites provide frequent revisits, but at the cost of coarse spatial resolution, extra launch costs and no polar access. Lower Earth Orbit (LEO) satellites overcome these shortcomings, but need numbers and coordination to to match GEO's responsiveness. While adding satellites to a constellation or optimizing their orbits can significantly improve revisit/response, adding agility to the satellites and autonomy to the constellation can improve the revisit/response for the same number of satellites in given orbits. Moreover, human operators are expected to scale linearly with constellation nodes (Eickhoff, 2011) and as satellites and ground stations scale to hundreds or more, operations staffing may become cost prohibitive. Deployment, maintenance, imaging, downlink, maneuver, de-orbit and other satellite operations within scarce resources are complex scheduling problems (Lin et al., 2005), and NP-hard unless formulated and bounded very carefully to make the design space tractable (Arkali et al., 2008). Scaling the problem to multiple satellites and including uncertainty of control subsystems adds complexity even further. Early investment in autonomy will increase management efficiency of the inevitably numerous space nodes, including better fault detection and isolation.
Large, single satellites with agile attitude control capabilities have demonstrated rapid image collection from space, mostly individually but also sometimes as an ad-hoc constellation. Fig. 1 (not to scale) shows six images of interest that are imaged by a single satellite by pointing appropriately over three orbits, which would not have been possible with a fixed viewing sensor. Autonomous, agile steering of the spacecraft body allows image acquisition over a much larger field of regard, thereby improving coverage and revisit. Planning and scheduling algorithms have been successfully developed for single large satellite missions, examples being Automated Scheduling and Planning Environment (ASPEN) for EO-1 (Sherwood et al., 1998), scheduling for the Advanced Spaceborne Thermal Emission and Reflectance Radiometer (ASTER) (Muraoka et al., 1998) on the Terra satellite, high resolution imagery from the IKONOS commercial satellite (Martin, 2002) and scheduling observations for the geostationary GEO-CAPE satellite (Frank et al., 2016). Scheduling image strips over Taiwan by ROCSAT-II was formulated as an integer programming problem and Lagrangian relaxation is used to decompose it into separable sub-problems (Lin et al., 2005). The hyperspectral instrument CHRIS, carried on the Proba spacecraft, demonstrated dynamic pointing for multi-angle imaging of specific ground spots that it is commanded to observe (Barnsley et al., 2004).
The problem of tasking multiple, diverse sensors was preliminarily addressed for aerial flight paths using the orienteering algorithm and demonstrated on NASA’s INTEX-B flight data (Oza et al., 2008). Scheduling resource-constrained observations for large satellite constellations has been formulated in detail for the French PLEIADES project (Damiani et al., 2005, Lemaître et al., 2002) with recommendations dependent on weak to strong coordination between the space agents. Scheduling for the COSMO-SkyMed constellation of synthetic aperture radars was proposed using a deterministic constructive algorithm with look-ahead and back-tracking capabilities to allow for updates on resources and changes to requests (Bianchessi and Righini, 2008). Evolutionary algorithms have been proposed and computationally simulated for single spacecraft (Xhafa et al., 2012), multiple payloads (Jian and Cheng, 2008) and comparative merits documented for satellite fleets (Globus et al., 2002), but they are very limited in mission applications. Algorithms for agent-based autonomous scheduling have been implemented on NASA’s Deep Space 1, and simulated for a cluster on a real-time testbed (Schetter et al., 2003). (Abramson et al., 2013, Robinson et al., 2017) have developed a coordinated planner that can handle a continuous stream of image requests from users, by finding opportunities of collection and scheduling air or space assets to maximize collected utility.
In the last decade, Cubesats have increased in size (27U or ∼40 kg standard in formulation) and emerged as increasingly capable platforms for Earth observation (Space Studies Board, 2016). Small satellites with one or few instruments provide a cost effective way to deploying a large constellation, thereby leveraging economies of scale and redundancy in numbers. In comparison, large bus-sized satellites with many instruments need redundancy in their components and higher reliability because the cost of their failure is higher. Simulation studies have optimized the scheduling for single Cubesat downlink to a network of ground stations (Spangelo and Cutler, 2012) or multiple payloads’ downlink to existing stations (Jian and Cheng, 2008), within available storage, energy and access time constraints. Studies have also combined single satellite scheduling (using integer programming applied to greedy search) with information sharing across satellites for a weak consensus on feasible charging, downlink and observation schedules (Kennedy and Cahoy, 2015) using fixed view imagers. Theoretical studies have shown that multiple satellites when downlinking to ground stations with overlapping visibility can be scheduled in polynomial time only for special cases when station reconfiguration time is near zero (Arkali et al., 2008), and greedy and linear programming algorithms suggested.
Given the increasingly precise attitude control systems emerging in the commercial market for Cubesats (ARC Mission Design Center, 2016), small spacecraft now have the ability to slew and point as per command, within few minutes of notice. While academic literature addresses satellite scheduling/coordination for large, steerable satellites and small, fixed view satellites, we found very little work reported on algorithms for controlled pointing and distributed target observation for imaging constellations, given current Cubesat maneuverability, accurate pointing and image angular constraints. Assuming a known Cubesat, small satellite constellation or Sensor Web structure (in terms of orbits, sensors, ground stations, images of interest, etc.), this paper demonstrates a scheduling algorithm that steers each spacecraft attitude in a manner that maximizes collected images and/or imaging time. The goal is to inform design studies of agile constellation operations because agility comes at the cost of ground segment complexity and associated schedule optimization. (Morris and Dungan, 2007, Morris et al., 2009) has simulated a workflow model and a model-based observation based planner, which adapts to changes in its own configuration, recognizes opportunities for modifying data acquisition plans to improve overall performance and coordinates resources and tasks accordingly. (Witt et al., 2008) demonstrated the planner on NASA’s ST-5 mission for lights-out operations. Our proposed, ground-based planner will also be model-based and adaptive, however, for the purpose of scheduling steering and imaging operations for multiple spacecraft.
Section snippets
Proposed methodology
This section proposes a scheduling framework for the attitude control of multiple Cubesats, so that they can (together) image as many given targets as possible, given constraints from orbital mechanics (OM) and attitude control systems (ACS), and summarizes a review of relevant scheduling literature used to inform this framework. The innovative aspects are the modularity of the OM, ACS and optimization modules, which allows independent numerical solution, uncertainty modeling and innovation
Results using dynamic programming
We applied the DP algorithm described in Section 2.3 to both case studies in Section 2.5, and found a large improvement in the number of unique images seen, compared to a static sensor. The case studies are different in that the Landsat case has globally distributed coarse images that need to be observed with a wider sensor, while the coral case has sparsely distributed but fine images that need to be observed with a narrow sensor. The Landsat case is a rapid imaging mode while the coastal case
Verification using integer programming
We implemented the MILP formulation of Section 2.4 using the General Algebraic Modeling System (GAMS), with subsequent solution by the CPLEX 12.7 solver. The model was solved on the Stanford Sherlock Computing Cluster using the 16 threads of a dual socket Intel(R) Xeon(R) CPU E5-2650 v2 @ 2.60 GHz (8 core/socket) with 64 GB RAM. The full problem comprises 9 million constraints and over 800,000 binary variables, with Eq. (7) being the major source of rows, necessitating high RAM availability.
Summary and future work
This article proposed a simple, modular framework for scheduling the attitude control operations for a constellation of small satellites to maximize the observation of requested images around the globe. The orbital mechanics and ACS modules can be simulated independently, as a function of satellite and image request specifications, and their outputs applied to a DP algorithm and the solution schedule improved upon by the MILP algorithm. Independence of the different modules allows for numerical
Acknowledgements
The Quick Response System Grant, awarded by NASA’s Earth Science Technology Office, funded the presented work. The authors are grateful to Dr. Jeremy Frank at the NASA Ames Research Center, and Prof. Marco Pavone and Stefan Jorgensen at Stanford University for very useful discussions that have improved the quality of this paper. The integer programming portion of the computing for this research was performed on the Sherlock cluster at Stanford University, where we would like to thank the
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