Skip to main content
Search
Search
Quick Search anywhere
Quick Search fdjslkfh
Advanced search
Cart
Join AIAA Institution Login
Skip main navigationClose Drawer MenuOpen Drawer Menu
Journal of Spacecraft and Rockets logo
Skip to article control options
No AccessFull-Length Paper

Optimization of CubeSat Constellations for Uncued Electrooptical Space Object Detection and Tracking

Published Online:23 Mar 2016https://doi.org/10.2514/1.A33386

Abstract

The proliferation of onorbit debris has motivated much of the recent space situational awareness missions and related research. Space-based missions are typically carried out by large spacecraft, yet the emerging and improving technology for CubeSat-class satellites offers a potential new platform for space situational awareness. This paper formally defines space object detectability for a given electrooptical sensor and applies an optimization problem approach to mission design for a CubeSat space situational awareness constellation. The optimization of the design parameters for this constellation is separated into a formal description of the concept of operations, an optimization of the electrooptical sensor payload itself, and an optimization of the constellation parameters via the number of satellites and traditional orbital parameters. A Pareto frontier of mission design points in terms of object detection capability and lifecycle cost is presented.

References

  • [1] Whitlock D. O., History of On-Orbit Satellite Fragmentations, 13th ed., NASA Lyndon B. Johnson Space Center, Houston, TX, 2004, pp. 1–10. Google Scholar

  • [2] Chatters E. P. and Crothers B. J., “Space Surveillance Network,” Air University Space Primer, U.S. Air Force, 2009, pp. 249–258, Chap. 19. Google Scholar

  • [3] Shoots D., “International Space Station Performs Fourth and Fifth Debris Avoidance Maneuvers of 2014,” Orbital Debris Quarterly, Vol. 19, No. 1, 2015, p. 9. Google Scholar

  • [4] Morton M. and Roberts T., “Joint Space Operations Center (JSPOC) Mission System (JMS),” AMOS Technologies Conference, Maui Economic Development Board, Inc., Maui, HI, 2011, p 6. Google Scholar

  • [5] Gleghorn G., “Orbital Debris: A Technical Assessment,” Committee on Space Debris, National Research Council, National Academy Press, Washington, D.C., 1995, pp. 35–37. Google Scholar

  • [6] Bauer W., Romberg O., Wiedemann C., Drolshagen G. and Vörsmann P., “Development of In-Situ Space Debris Detector,” Advances in Space Research, Vol. 54, No. 9, 2014, pp. 1858–1869. doi:https://doi.org/10.1016/j.asr.2014.07.035 ASRSDW 0273-1177 CrossrefGoogle Scholar

  • [7] McKnight D. S. and Di Pentino F. R., “New Insights on the Orbital Debris Collision Hazard at GEO,” Acta Astronautica, Vol. 85, April–May 2013, pp. 73–82. doi:https://doi.org/10.1016/j.actaastro.2012.12.006 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [8] Kan S., “China’s Anti-Satellite Weapon Test,” Congressional Research Service Rept.  RS22652, Washington, D.C., 2007. Google Scholar

  • [9] Wang T., “Analysis of Debris from the Collision of the Cosmos 2251 and the Iridium 33 Satellites,” Science and Global Security, Vol. 18, No. 2, 2010, pp. 87–118. doi:https://doi.org/10.1080/08929882.2010.493078 SGSEE8 CrossrefGoogle Scholar

  • [10] Kelso T. S., “Analysis of the Iridium 33-Cosmos 2251 Collision,” Astrodynamics, Vol. 135, Nos. 1–3, 2010, pp. 1099–1112. Google Scholar

  • [11] Murray C., “China Missile Launch May Have Tested Part of a New Anti-Satellite Capability,” Report to Congress of the U.S.-China Economic and Security Review Commission, US Government Printing Office, 2013, pp. 219–220. Google Scholar

  • [12] Heimerdinger D. J., “Orbital Debris and Associated Space Flight Risks,” Reliability and Maintainability Symposium, IEEE Publ., Piscataway, NJ, 2005, pp. 508–513, doi:https://doi.org/10.1109/RAMS.2005.1408413 Google Scholar

  • [13] Shoots D., “Update on 3 Major Debris Clouds,” Orbital Debris Quarterly, Vol. 14, No.2, 2010, pp. 1–3. Google Scholar

  • [14] Christiansen E., Hyde J. and Bernhard R., “Space Shuttle Debris and Meteoroid Impacts,” Advances in Space Research, Vol. 34, No. 5, 2004, pp. 1097–1103. doi:https://doi.org/10.1016/j.asr.2003.12.008 ASRSDW 0273-1177 CrossrefGoogle Scholar

  • [15] Kessler D. J. and Cour-Palais B. G., “Collision Frequency of Artificial Satellites: The Creation of a Debris Belt,” Journal of Geophysical Research, Vol. 83, No. A6, 1978, pp. 2637–2646. doi:https://doi.org/10.1029/JA083iA06p02637 JGREA2 0148-0227 CrossrefGoogle Scholar

  • [16] “National Space Policy of the United States of America,” Office of the President of the United States, Washington, D.C., 2010, pp. 7–8. Google Scholar

  • [17] Scaparotti C. M., “Joint Publication 3-14, Space Operations,” Defense Technical Information Center, Washington, D.C., 2013, Chap. II. Google Scholar

  • [18] Technology Horizons, Vol. 1, Air Univ. Press, Maxwell AFB, AL, 2011, pp. 95–96. Google Scholar

  • [19] Hale R. F., “United States Department Of Defense Fiscal Year 2016 Budget Request,” U.S. Dept. of Defense, Office of the Under Secretary of Defense, Chief Financial Officer, 2015, p. 15. Google Scholar

  • [20] “Report of the Scientific and Technical Subcommittee on its Fifty-Second Session,” Vol. 10, No. 19, United Nations, Committee on the Peaceful Uses of Outer Space, 2015, pp. 17–20. Google Scholar

  • [21] Potter A. E., Ground-Based Optical Observations of Orbital Debris—A Review, Vol. 16, Advances in Space Research, Pergamon, New York, 1995, pp. 35–45. doi:https://doi.org/10.1016/0273-1177(95)98751-9 Google Scholar

  • [22] Grometstein A. A., “MIT Lincoln Laboratory Technology in Support of National Security,” Lincoln Lab., Massachusetts Inst. of Technology, Lexington, MA, 2011, pp. 45–49. Google Scholar

  • [23] Foster J. L., Benbrook J. R. and Stansbery E. G., Detection of Small Radar Cross-Section Orbital Debris with the Haystack Radar, Vol. 35, Advances in Space Research, Pergamon, New York, 2005, pp. 1210–1213. doi:https://doi.org/10.1016/j.asr.2005.05.041 Google Scholar

  • [24] Thompson T. W., Goldstein R. M., Campbell D. B., Stansbery E. G. and Potter A. E., “Radar Detection of Centimeter-Sized Orbital Debris - Preliminary Arecibo Observations at 12.5-cm Wavelength,” Geophysical Research Letters, Vol. 19, No. 3, 1992, pp. 257–259. doi:https://doi.org/10.1029/91gl02772 GPRLAJ 0094-8276 CrossrefGoogle Scholar

  • [25] Gruntman M., “Passive Optical Detection of Submillimeter and Millimeter Size Space Debris in Low Earth Orbit,” Acta Astronautica, Vol. 105, No. 1, 2014, pp. 156–170. doi:https://doi.org/10.1016/j.actaastro.2014.08.022. AASTCF 0094-5765 CrossrefGoogle Scholar

  • [26] Flury W., Massart A., Schildknecht T., Hugentobler U., Kuusela J. and Sodnik Z., “Searching for Small Debris in the Geostationary Ring,” ESA Bulletin, Vol. 104, 2000, pp. 92–100. ESABD8 0376-4265 Google Scholar

  • [27] Monet D., Axelrod T., Claver C., Blake T., Lupton R., Pearce E., Shah R. and Woods D., “Rapid Cadence Collections with the Space Surveillance Telescope,” Maui Economic Development Board, Inc., Maui, HI, 2012, pp. 1–4. Google Scholar

  • [28] Malek K., Batsch T., Cwiok M., Dominik W., Kasprowicz G., Majcher A., Majczyna A., Mankiewicz L., Nawrocki K., Pietrzak R., Piotrowski L. W., Ptasinska M., Siudek M., Sokolowski M., Uzycki J., Wawer P., Wawrzaszek R., Wrochna G., Zaremba M. and Zarnecki A. F., “General Overview of the ‘Pi of the Sky’ System,” Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments, Vol. 7502, May 2009, Paper 75020D, doi:https://doi.org/10.1117/12.837741 CrossrefGoogle Scholar

  • [29] Wawrzaszek R., Wawer P., Sokolowski M., Nawrocki K., Pietrzak R., Malek K., Zaremba M. and Piotrowski L. W., “Possible Use of the ‘Pi of the Sky’ System in a Space Situational Awareness Program,” Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments, Vol. 7502, 2009. doi:https://doi.org/10.1117/12.838751 CrossrefGoogle Scholar

  • [30] Beskin G., Bondar S., Karpov S., Plokhotnichenko V., Guarnieri A., Bartolini C., Greco G., Piccioni A. and Shearer A., “From TORTORA to MegaTORTORA—Results and Prospects of Search for Fast Optical Transients,” Advances in Astronomy, Vol. 2010, 2010, pp. 1–9. doi:https://doi.org/10.1155/2010/171569 AAYAAK 0065-2180 CrossrefGoogle Scholar

  • [31] Pollacco D., Skillen I., Cameron A., Christian D., Hellier C., Irwin J., Lister T., Street R., West R., Anderson D., Clarkson W., Deeg H., Enoch B., Evans A., Fitzsimmons A., Haswell C., Hodgkin S., Horne K., Kane S., Keenan F., Maxted P., Norton A., Osborne J., Parley N., Ryans R., Smalley B., Wheatley P. and Wilson D., “The WASP Project and the SuperWASP Cameras,” Publications of the Astronomical Society of the Pacific, Vol. 118, Oct. 2006, pp. 1407–1418. doi:https://doi.org/10.1086/508556 PASPAU 0004-6280 CrossrefGoogle Scholar

  • [32] Shell J. R., “Optimizing Orbital Debris Monitoring with Optical Telescopes,” AMOS Technologies Conference, Maui Economic Development Board, Inc., Maui, HI, 2010, pp. 10–13. Google Scholar

  • [33] “Meteoroid and Debris Impact Features Documented on the Long Duration Exposure Facility,” M.o.t.L.M. Group and D.S. Investigation, NASA Lyndon B. Johnson Space Center, Publication 84, JSC 24608, Houston, TX, 1990. Google Scholar

  • [34] Mandeville J. C., Maag C. R. and Durin C., In-Situ Detection of Micrometeoroids and Orbital Debris: The PIE Experiment on MIR, Vol. 25, Advances in Space Research-Series, Pergamon, Oxford, 2000,, pp. 329–334. doi:https://doi.org/10.1016/s0273-1177(99)00949-7. Google Scholar

  • [35] Fu X. J., Liu G. M. and Gao M. G., “Overview of Orbital Debris Detection Using Spaceborne Radar,” Iciea 2008: 3rd IEEE Conference on Industrial Electronics and Applications, Proceedings, Vols. 1–3, IEEE Publ., New York, 2008, pp. 1071–1074. Google Scholar

  • [36] Gaposchkin M. E., von Braun C. and Sharma J., “Space-Based Space Surveillance with the Space-Based Visible,” Journal of Guidance, Control, and Dynamics, Vol. 23, No. 1, 2000, pp. 148–152. doi:https://doi.org/10.2514/2.4502 JGCDDT 0162-3192 LinkGoogle Scholar

  • [37] Maskell P. and Oram L., “Sapphire: Canada’s Answer to Space-Based Surveillance of Orbital Objects,” AMOS Technologies Conference, Maui Economic Development Board, Inc., Maui, HI, 2008, pp. 3–4. Google Scholar

  • [38] Simms L. M., De Vries W., Riot V., Olivier S. S., Pertica A., Bauman B. J., Phillion D. and Nikolaev S., “Space-Based Telescopes for Actionable Refinement of Ephemeris Pathfinder Mission,” Optical Engineering, Vol. 51, No. 1, 2012, Paper 011004. doi:https://doi.org/10.1117/1.OE.51.1.011004. CrossrefGoogle Scholar

  • [39] Teehan R. F., “Responsive Space Situation Awareness in 2020,” U.S. Air Force, Maxwell AFB, Montgomery, AL, 2007, pp. 5–9. Google Scholar

  • [40] Sharma J., Stokes G. H., von Braun C., Zollinger G. and Wiseman A. J., “Toward Operational Space-Based Space Surveillance,” Lincoln Laboratory Journal, Vol. 13, No. 2, 2002, pp. 309–334. LLJ0EJ 0896-4130 Google Scholar

  • [41] Simms L. M., Riot V., De Vries W., Olivier S. S., Pertica A., Bauman B. J., Phillion D. and Nikolaev S., “Optical Payload for the STARE Mission,” SPIE Defense and Security Conference, Soc. of Photographic Instrumentation Engineers, Bellingham, WA, 2011, pp. 4–14. Google Scholar

  • [42] O’Brien T. E., “Space Situational Awareness Cubesat Concept of Operations,” M.S. Thesis, Naval Postgraduate School, Monterey, CA, 2011. Google Scholar

  • [43] Larson W. J. and Wertz J. R., Space Mission Analysis and Design, 3rd ed., Space Technology Library, Microcosm, Cleveland, OH, 1999, Chap. 19. Google Scholar

  • [44] Boshuizen C. R., Mason J., Klupar P. and Spanhake S., “Results from the Planet Labs Flock Constellation,” AIAA Conference on Small Satellites, Logan, UT, 2014. Google Scholar

  • [45] Ferringer M. P., Spencer D. B., Reed P. M., Clifton R. S. and Thompson T. G., “Pareto-Hypervolumes for the Reconfiguration of Satellite Constellations,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper  2008-6611, 2008, doi:https://doi.org/10.2514/6.2008-6611 LinkGoogle Scholar

  • [46] Ely T. A., Crossley W. A. and Williams E. A., “Satellite Constellation Design for Zonal Coverage Using Genetic Algorithms,” Journal of the Astronautical Sciences, Vol. 47, Nos. 3–4, 1999, pp. 207–228. JALSA6 0021-9142 CrossrefGoogle Scholar

  • [47] Frayssinhes E., “Investigating New Satellite Constellation Geometries with Genetic Algorithms,” AIAA/AAS Astrodynamics Specialists Conference, AIAA Paper  1996-3636, 1996, pp. 582–586. LinkGoogle Scholar

  • [48] Mason W. J., Coverstone-Carroll V. and Hartmann J. W., “Optimal Earth Orbiting Satellite Constellations Via a Pareto Genetric Algorithm,” AIAA Paper  1998-4381, 1998, doi:https://doi.org/10.2514/6.1998-4381. Google Scholar

  • [49] Kiremitci H., “Satellite Constellation Optimization for Turkish Armed Forces,” M.S. Thesis, Naval Postgraduate School, Monterey, CA, 2013. Google Scholar

  • [50] Hutchison M., Kolarik K. M. and Water J., “Joint Space Operations Center (JSPOC) Mission System (JMS) Common Data Model: Foundation for Interoperable Data Sharing for Space Situational Awareness,” The Aerospace Corporation, Ground System Architectures Workshop, The Aerospace Corporation, El Segundo, CA, 2013, pp. 6–7. Google Scholar

  • [51] Walker J. G., “Circular Orbit Patterns Providing Continuous Whole Earth Coverage,” Royal Aircraft Establishment, TR-77044, Farnborough, England, 1970. Google Scholar

  • [52] Beste D. C., “Design of Satellite Constellations for Optimal Continuous Coverage,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 14, No. 3, 1978, pp. 466–473. doi:https://doi.org/10.1109/TAES.1978.308608 CrossrefGoogle Scholar

  • [53] Ballard A., “Rosette Constellations of Earth Satellites,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 16, No. 5, 1980, pp. 656–673. doi:https://doi.org/10.1109/TAES.1980.308932 IEARAX 0018-9251 CrossrefGoogle Scholar

  • [54] Ulybyshev Y. P., “Design of Satellite Constellations with Continuous Coverage on Elliptic Orbits of Molniya Type,” Cosmic Research, Vol. 47, No. 4, 2009, pp. 310–321. doi:https://doi.org/10.1134/S0010952509040066 CSCRA7 0010-9525 CrossrefGoogle Scholar

  • [55] Draim J. E., “Three- and Four-Satellite Continuous-Coverage Constellations,” Journal of Guidance, Control, and Dynamics, Vol. 8, No. 6, 1985, pp. 725–730. doi:https://doi.org/10.2514/3.20047 JGCDDT 0162-3192 LinkGoogle Scholar

  • [56] Draim J. E., “A Common-Period Four-Satellite Continuous Global Coverage Constellation,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 5, 1987, pp. 492–499. doi:https://doi.org/10.2514/3.20244 JGCDDT 0162-3192 LinkGoogle Scholar

  • [57] Mortari D. and Wilkins M. P., “Flower Constellation Set Theory. Part I: Compatibility and Phasing,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 3, 2008, pp. 953–962. IEARAX 0018-9251 CrossrefGoogle Scholar

  • [58] Wilkins M. P. and Mortari D., “Flower Constellation Set Theory Part II: Secondary Paths and Equivalency,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 3, 2008, pp. 964–976. IEARAX 0018-9251 CrossrefGoogle Scholar

  • [59] Draim J. E., “Lightsat Constellation Designs,” AIAA Satellite Communications Conference, AIAA Paper  1992-1998, 1992, pp. 1361–1369. doi:https://doi.org/10.2514/6.1992-1988 LinkGoogle Scholar

  • [60] Worthy J. L., Holzinger M. J. and Fujimoto K., “Optical Sensor Constraints on Space Object Detection and Admissible Regions,” AAS/AIAA Astrodynamics Specialist Conference, Univelt, Inc., San Diego, CA, 2013, pp. 12–16. Google Scholar

  • [61] Coder R. D. and Holzinger M. J., “Multi-Objective Design of Optical Systems for Space Situational Awareness,” Acta Astronautica, submitted for publication. Google Scholar

  • [62] Holzinger M. J., Alfriend K. T., Wetterer C. J., Luu K. K., Sabol C. and Hamada K., “Photometric Attitude Estimation for Agile Space Objects with Shape Uncertainty,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 3, 2014, pp. 912–932, doi:https://doi.org/10.2514/1.58002 JGCDDT 0162-3192 LinkGoogle Scholar

  • [63] Milani A., Gronchi G. F., Vitturi M. D. and Knezevic Z., “Orbit Determination with Very Short Arcs. I Admissible Regions,” Celestial Mechanics and Dynamical Astronomy, Vol. 90, Nos. 1–2, 2004, pp. 57–85. doi:https://doi.org/10.1007/s10569-004-6593-5. CrossrefGoogle Scholar

  • [64] Stansbery E. G., Matney M. J., Krisko P. H., Anz-Meador P. D., Horstman M. F., Opiela J. N., Hillary E., Hill N. M., Kelley R. L., Vavrin A. B. and Jarkey D. R., “NASA Orbital Debris Engineering Model ORDEM 3.0–Users Guide,” NASA Rept. TP-2014-217370, NASA Johnson Space Center, Houston, TX, 2012. Google Scholar

  • [65] Bonami P., Kilinc M. and Linderoth J., “Algorithms and Software for Convex Mixed Integer Nonlinear Programs,” Mixed Integer Nonlinear Programming, Vol. 154, edited by Lee J. and Leyffer S., Springer Science and Business Media, New York, 2011, pp. 1–40. doi:https://doi.org/10.1007/978-1-4614-1927-31. Google Scholar

  • [66] Schildknecht T., Optical Astrometry of Fast Moving Objects Using CCD Detectors, Inst. fur Geodasie und Photogrammetrie, Zurich, 1994. Google Scholar

  • [67] de Feo M., Graziano A., Miglioli R. and Farina A., “IMMJPDA Versus MHT and Kalman Filter with NN Correlation: Performance Comparison,” IEE Proceedings: Radar, Sonar and Navigation, Vol. 144, No. 2, 1997, pp. 49–56. doi:https://doi.org/10.1049/ip-rsn:19970976 CrossrefGoogle Scholar

  • [68] Danchick R. and Newnam G., “Reformulating Reid’s MHT Method With Generalised Murty K-Best Ranked Linear Assignment Algorithm,” IEEE Proceedings—Radar, Sonar and Navigation, Vol. 153, No. 1, 2006, doi:https://doi.org/10.1049/ip-rsn:20050041 CrossrefGoogle Scholar

  • [69] Liou J. C., “Modeling the Large and Small Orbital Debris Populations for Environment Remediation,” Orbital Debris Program Office, NASA TR, June 2014. Google Scholar

  • [70] Walker J. G., “Some Circular Patterns Providing Continuous Whole Earth Coverage,” Journal of the British Interplanetary Society, Vol. 24, No. 7, 1971, pp. 369–384. JBISAW 0007-084X Google Scholar

  • [71] Broder M., Mahr E., Barkmeyer D., Burgess E., Alvarado W., Toas S. and Hogan G., “Review of Three Small-Satellite Cost Models,” AIAA SPACE Conference and Exposition, AIAA Paper  2009-6689, 2009. LinkGoogle Scholar

  • [72] Boghosian M. and Valerdi R., “Cost Estimating Methodology for Very Small Satellites,” COCOMO Forum, Univ. of Southern California, Los Angeles, CA, 2011, pp. 3–12. Google Scholar

  • [73] Mahr E. and Richardson G., Development of the Small Satellite Cost Model (SSCM), Vol. 8-3832, The Aerospace Corporation, Los Angeles, CA, 2002, pp. 1–8. Google Scholar

  • [74] Larson W. J. and Wertz J. R., Space Mission Analysis and Design, 3rd ed., Space Technology Library, Microcosm, Cleveland, OH, 1999, Appendix. Google Scholar

  • [75] Wang L., Wang Y., Chen K. and Zhang H., “Optimization of Regional Coverage Reconnaissance Satellite Constellation by NSGA-II Algorithm,” 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA), IEEE Publ., Piscataway, NJ, 2008, pp. 660–684, doi:https://doi.org/10.1109/ICICTA.2008.322 Google Scholar

  • [76] Mavrotas G., “Effective implementation of the Epsilon-constraint method in Multi-Objective Mathematical Programming problems,” Applied Mathematics and Computation, Vol. 213, No. 2, 2009, pp. 455–465. doi:https://doi.org/10.1016/j.amc.2009.03.037 AMHCBQ 0096-3003 CrossrefGoogle Scholar

  • [77] Goldberg D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., Boston, 1989. Google Scholar

Previous article
Next article