[en] This paper addresses the computation of Delta-V-optimal, safe, relative orbit reconfigurations for satellite formations in a centralized fashion. The formations under consideration comprise an uncontrolled chief spacecraft flying with an arbitrary number, N, of deputy satellites, where each deputy is equipped with a single electric thruster. Indeed, this represents a technological solution that is becoming widely employed by the producers of small-satellite platforms. While adopting a single electric thruster does reduce the required power, weight, and size of the orbit control system, it comes at the cost of rendering the satellite under-actuated. In this setting, the satellite can provide a desired thrust vector only after an attitude maneuver is carried out to redirect the thruster nozzle opposite to the desired thrust direction. In order to further extend the applicability range of such under-actuated platforms, guidance strategies are developed to support different reconfiguration scenarios for N-satellite formations. This paper starts from a classical non-convex quadratically constrained trajectory optimization formulation, which passes through multiple simplifications and approximations to arrive to two novel convex formulations, namely a second-order cone programming formulation, and a linear programming one. Out of five guidance formulations proposed in this article, the most promising three were compared through an extensive benchmark analysis that is applied to fifteen of the most widely-used solvers. This benchmark experiment provides information about the key distinctions between the different problem formulations, and under which conditions each one of them can be recommended.
Research center :
Interdisciplinary Centre for Security, Reliability and Trust (SnT) > ARG - Automation & Robotics
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
MAHFOUZ, Ahmed ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Automation
Gaias, Gabriella ; Department of Aerospace Science and Technology, Politecnico di Milano, Milan, Italy
Dalla Vedova, Florio; LuxSpace, Betzdorf, Luxembourg
VOOS, Holger ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Automation
External co-authors :
yes
Language :
English
Title :
Delta-V-optimal centralized guidance strategy for under-actuated N-satellite formations
FNR14302465 - Development Tool For Autonomous Constellation And Formation Control Of Microsatellites, 2019 (01/09/2020-31/08/2023) - Holger Voos
Name of the research project :
Development Tool For Autonomous Constellation And Formation Control Of Microsatellites - AuFoSat
Funders :
Fonds National de la Recherche Luxembourg
Funding number :
BRIDGES/19/MS/ 14302465
Funding text :
This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR) , grant reference BRIDGES/19/MS/14302465 . For the purpose of open access, and in fulfilment of the obligations arising from the grant agreement, the author has applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission.This research was funded in whole, or in part, by the Luxembourg National Research Fund (FNR), grant reference BRIDGES/19/MS/ 14302465. For the purpose of open access, and in fulfillment of the obligations arising from the grant agreement, the author has applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission.
Pelton, J.N., Madry, S., Introduction to the small satellite revolution and its many implications. Handbook of Small Satellites: Technology, Design, Manufacture, Applications, Economics and Regulation, 2020, Springer International Publishing, Cham, 3–31, 10.1007/978-3-030-36308-6_1 URL https://doi.org/10.1007/978-3-030-36308-6_1.
Miller, S., Walker, M.L.R., Agolli, J., Dankanich, J., Survey and performance evaluation of small-satellite propulsion technologies. J. Spacecr. Rockets 58:1 (2021), 222–231, 10.2514/1.A34774.
O'Reilly, D., Herdrich, G., Kavanagh, D.F., Electric propulsion methods for small satellites: A review. Aerospace, 8(1), 2021, 10.3390/aerospace8010022 URL https://www.mdpi.com/2226-4310/8/1/22.
Stanzione, V., Sabbatinelli, B., PLATiNO project: A new Italian multi-application small satellite platform for highly competitive missions. 69th International Astronautical Congress (IAC), 2018, International Astronautical Federation, Bremen, Germany.
Helmeid, E., Buursink, J., Poppe, M., Ries, P., Gales, M., The integrated avionics unit - performance, innovation and application. 2022 Poster presentation at The 4S Symposium, Vilamoura, Portugal, 2022.
Larsson, R., Noteborn, R., Bodin, P., Simone, D., Karlsson, T., Carlsson, A., Autonomous formation flying in LEO - seven months of routine formation flying with frequent reconfigurations. 4th International Conference on Spacecraft Formation Flying Missions & Technologies, 2011 URL https://elib.dlr.de/74364/.
Gaias, G., D'Amico, S., Impulsive maneuvers for formation reconfiguration using relative orbital elements. J. Guid. Control Dyn. 38:6 (2015), 1036–1049, 10.2514/1.G000189.
Di Mauro, G., Bevilacqua, R., Spiller, D., Sullivan, J., D'Amico, S., Continuous maneuvers for spacecraft formation flying reconfiguration using relative orbit elements. Acta Astronaut. 153 (2018), 311–326, 10.1016/j.actaastro.2018.01.043.
Chernick, M., D'Amico, S., New closed-form solutions for optimal impulsive control of spacecraft relative motion. J. Guid. Control Dyn. 41:2 (2018), 301–319, 10.2514/1.G002848.
Scala, F., Gaias, G., Colombo, C., Martín-Neira, M., Design of optimal low-thrust manoeuvres for remote sensing multi-satellite formation flying in low Earth orbit. Adv. Space Res. 68:11 (2021), 4359–4378, 10.1016/j.asr.2021.09.030.
De Vittori, A., Palermo, M.F., Lizia, P.D., Armellin, R., Low-thrust collision avoidance maneuver optimization. J. Guid. Control Dyn. 45:10 (2022), 1815–1829, 10.2514/1.G006630.
Gaias, G., Ardaens, J.-S., Flight demonstration of autonomous noncooperative rendezvous in low Earth orbit. J. Guid. Control Dyn. 41:6 (2018), 1337–1354, 10.2514/1.G003239.
Gaias, G., D'Amico, S., Ardaens, J.-S., Generalised multi-impulsive manoeuvres for optimum spacecraft rendezvous in near-circular orbit. Int. J. Space Sci. Eng. 3:1 (2015), 68–88, 10.1504/IJSPACESE.2015.069361.
Belloni, E., Silvestrini, S., Prinetto, J., Lavagna, M., Relative and absolute on-board optimal formation acquisition and keeping for scientific activities in high-drag low-orbit environment. Adv. Space Res. 73:11 (2024), 5595–5613, 10.1016/j.asr.2023.07.051 Recent Advances in Satellite Constellations and Formation Flying. URL https://www.sciencedirect.com/science/article/pii/S0273117723006002.
Mahfouz, A., Gaias, G., Vedova, F.D., Voos, H., Fuel-optimal formation reconfiguration by means of unidirectional low-thrust propulsion system. J. Guid. Control Dyn., 2024, 10.2514/1.G008214 in press.
D. Menzio, A. Mahfouz, D. Vedova, et al., Formation design of an inter-satellite link demonstration mission, in: Proceedings of the 11th International Workshop on Satellite Constellations & Formation Flying, Milan, IT, 2022.
A. Mahfouz, D. Mezio, F. Dalla-Vedova, H. Voos, Relative State Estimation for LEO Formations with Large Inter-satellite Distances Using Single-Frequency GNSS Receivers, in: Proceedings of the 11th International Workshop on Satellite Constellations & Formation Flying, Milan, IT, 2022.
Mahfouz, A., Mezio, D., Dalla-Vedova, F., Voos, H., GNSS-based baseline vector determination for widely separated cooperative satellites using L1-only receivers. Adv. Space Res., 2023, 10.1016/j.asr.2023.06.037.
Vallado, D.A., Fundamentals of Astrodynamics and Applications. Vol. 12. 2001, Springer Science & Business Media.
Gaias, G., Colombo, C., Lara, M., Analytical framework for precise relative motion in low Earth orbits. J. Guid. Control Dyn. 43:5 (2020), 915–927, 10.2514/1.G004716.
Morgan, D., Chung, S.-J., Hadaegh, F.Y., Model predictive control of swarms of spacecraft using sequential convex programming. J. Guid. Control Dyn. 37:6 (2014), 1725–1740, 10.2514/1.G000218.
T. Pippia, V. Preda, S. Bennani, T. Keviczky, Reconfiguration of a satellite constellation in circular formation orbit with decentralized model predictive control, in: Proceedings of the 2022 CEAS EuroGNC Conference, Berlin, Germany, 2022, CEAS-GNC-2022-027.
Gaias, G., Lovera, M., Trajectory design for proximity operations: The relative orbital elements’ perspective. J. Guid. Control Dyn. 44:12 (2021), 2294–2302, 10.2514/1.G006175.
Ross, I.M., Space trajectory optimization and L1-optimal control problems. Gurfil, P., (eds.) Modern Astrodynamics Elsevier Astrodynamics Series, vol. 1, 2006, Butterworth-Heinemann, 155–VIII, 10.1016/S1874-9305(07)80008-2.
Venkateswara Rao, D., Go, T.H., Optimization of aircraft spin recovery maneuvers. Aerosp. Sci. Technol. 90 (2019), 222–232, 10.1016/j.ast.2019.04.046 URL https://www.sciencedirect.com/science/article/pii/S1270963818329092.
Abdelkarim, A., Jia, Y., Gorges, D., Optimization of vehicle-to-grid profiles for peak shaving in microgrids considering battery health. IECON 2023-49th Annual Conference of the IEEE Industrial Electronics Society, 2023, IEEE, 1–6, 10.1109/IECON51785.2023.10312094.
Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H., Applications of second-order cone programming. Linear Algebra Appl. 284:1 (1998), 193–228, 10.1016/S0024-3795(98)10032-0 International Linear Algebra Society (ILAS) Symposium on Fast Algorithms for Control, Signals and Image Processing. URL https://www.sciencedirect.com/science/article/pii/S0024379598100320.
Elble, J.M., Sahinidis, N.V., Scaling linear optimization problems prior to application of the simplex method. Comput. Optim. Appl. 52:2 (2012), 345–371, 10.1007/s10589-011-9420-4.
Fasano, G., Renga, A., D'Errico, M., Formation geometries for multistatic SAR tomography. Acta Astronaut. 96 (2014), 11–22, 10.1016/j.actaastro.2013.11.024 URL https://www.sciencedirect.com/science/article/pii/S009457651300427X.
Wang, W., Wu, D., Sun, R., Baoyin, H., Optimal projected circular orbit for spacecraft formation flying near a slowly rotating asteroid. IEEE Trans. Aerosp. Electron. Syst. 58:6 (2022), 5483–5493, 10.1109/TAES.2022.3173247.
Makhorin, A., GNU linear programming kit (GLPK). 2012 URL https://www.gnu.org/software/glpk/. (Accessed 21 May 2024).
Forrest, J., Vigerske, S., Ralphs, T., Hafer, L., Santos, H.G., Jan-Willem, A., Saltzman, M., Kristjansson, B., King, A., Bonami, P., Luies, R., Brito, S., et al. coin-or/Clp: Release releases/1.17.9. 2023, Zenodo, 10.5281/zenodo.10041272.
Stellato, B., Banjac, G., Goulart, P., Bemporad, A., Boyd, S., OSQP: An operator splitting solver for quadratic programs. Math. Program. Comput. 12:4 (2020), 637–672, 10.1007/s12532-020-00179-2.
O'Donoghue, B., Chu, E., Parikh, N., Boyd, S., Conic optimization via operator splitting and Homogeneous self-dual embedding. J. Optim. Theory Appl. 169:3 (2016), 1042–1068 URL http://stanford.edu/~boyd/papers/scs.html.
Domahidi, A., Chu, E., Boyd, S., ECOS: An SOCP solver for embedded systems. European Control Conference, ECC, 2013, 3071–3076.
Wächter, A., Biegler, L.T., On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106:1 (2006), 25–57, 10.1007/s10107-004-0559-y URL https://doi.org/10.1007/s10107-004-0559-y.
Gleixner, A., Eifler, L., Gally, T., Gamrath, G., Gemander, P., Gottwald, R.L., Hendel, G., Hojny, C., Koch, T., Miltenberger, M., Müller, B., Pfetsch, M.E., Puchert, C., Rehfeldt, D., Schlösser, F., Serrano, F., Shinano, Y., Viernickel, J.M., Vigerske, S., Weninger, D., Witt, J.T., Witzig, J., The SCIP Optimization Suite 5.0: Technical report., 2017, Optimization Online URL http://www.optimization-online.org/DB_HTML/2017/12/6385.html.
MOSEK ApS, A., The MOSEK optimization toolbox for MATLAB manual. Version 10.0. 2024 URL https://docs.mosek.com/10.0/toolbox/index.html.
Gurobi Optimization, LLC, A., Gurobi optimizer reference manual. Version 11.0. 2024 URL https://www.gurobi.com/documentation/current/refman/index.html.
CPLEX, IBM ILOG, A., V12. 1: User's manual for CPLEX. Int. Bus. Mach. Corp., 46(53), 2009, 157.
Ge, D., Huangfu, Q., Wang, Z., Wu, J., Ye, Y., Cardinal optimizer (COPT) user guide. 2023 https://guide.coap.online/copt/en-doc.
Fair Isaac Corporation, FICO, R.H., FICO xpress optimizer reference manual. Version 9.4. 2024 URL https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/HTML/GUID-3BEAAE64-B07F-302C-B880-A11C2C4AF4F6.html.
The MathWorks Inc., R.H., Optimization Toolbox version: 9.2 (R2021b). 2021, The MathWorks Inc., Natick, Massachusetts, United States URL https://www.mathworks.com/products/optimization.html.
G. Borelli, G. Gaias, C. Colombo, Safe guidance scheme for proximity operations forced motion, J. Guid. Control Dyn., 1–18, http://dx.doi.org/10.2514/1.G008179.
J. Currie, D.I. Wilson, OPTI: Lowering the Barrier Between Open Source Optimizers and the Industrial MATLAB User, in: N. Sahinidis, J. Pinto (Eds.), Foundations of Computer-Aided Process Operations, Savannah, Georgia, USA, 2012.
