Volume 24, Issue 4 No AccessImpulsive Feedback Control to Establish Specific Mean Orbit Elements of Spacecraft FormationsHanspeter Schaub and Kyle T. AlfriendHanspeter Schaub Sandia National Laboratories, Albuquerque, New Mexico 87185-1003Search for more papers by this author and Kyle T. Alfriend Texas A&M University, College Station, Texas 77843-3141Search for more papers by this authorPublished Online:23 May 2012https://doi.org/10.2514/2.4774SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookXLinked InRedditEmail About Previous article Next article FiguresReferencesRelatedDetailsSee PDF for referencesCited byLinear Time/Parameter-Varying Models with Relative Orbit Elements Considering Continuous ControllabilityTakahiro Sasaki 22 November 2024 | Journal of Guidance, Control, and Dynamics, Vol. 48, No. 1Near-optimal maneuver design for high-accuracy trans-lunar injection with highly elliptical phasing loops9 August 2024 | Astrodynamics, Vol. 8, No. 4Fuel-optimal acquisition and control of a cartwheel formation in Earth displaced heliocentric orbit1 Nov 2024 | Advances in Space Research, Vol. 74, No. 10Impulsive Maneuvers Sequencer for Abort-Safety of Formation Flying1 Oct 2024 | IEEE Transactions on Aerospace and Electronic Systems, Vol. 60, No. 5Practical Gain Tuning Using Bayesian Optimization with Input Constraints for Low-Thrust Satellite Rendezvous *21 Aug 2024Modified Filter for Mean Elements Estimation with State Jumping1 Aug 2024 | Journal of Systems Engineering and Electronics, Vol. 35, No. 4Optimal Control Laws Considering Controllability Properties in Linear Time/Parameter-Varying Models for Spacecraft Relative Motion in Perturbed OrbitsTakahiro Sasaki4 January 2024Attitude Control of Satellites with Reaction Wheels and Its Formation Keeping15 May 2024Simplified Maneuvering Strategies for Rendezvous in Near-Circular Earth Orbits12 December 2023 | Aerospace, Vol. 10, No. 12Evaluation and Comparison of Three Fuel Optimal Impulsive Control Strategies for Satellite Formation Reconfiguration8 May 2023Optimized relative phase maintenance for heterogeneous area-to-mass ratio microsatellite constellations1 May 2023 | Journal of Physics: Conference Series, Vol. 2472, No. 1Design and optimization of stable initial heliocentric formation on the example of LISA1 Jan 2023 | Advances in Space Research, Vol. 71, No. 1Nonlinear Model Predictive Control of J2-perturbed impulsive transfer trajectories in long-range rendezvous missions1 Jan 2023 | Aerospace Science and Technology, Vol. 132Decentralized Formation and Constellation Stability Design Requirements Using Differential Mean Orbit ElementsMarcus J. 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Arantes Gilz, Mioara Joldes, Christophe Louembet and Frédéric Camps16 June 2019 | Journal of Guidance, Control, and Dynamics, Vol. 42, No. 8Relative Sensing, Control Precision, and Mission Delta-V Trade-Offs for Precision Formation Flying in Planetary OrbitKai Matsuka, Daniel Scharf, Nuno Filipe, Carl Seubert and David Bayard25 February 2019 | Journal of Guidance, Control, and Dynamics, Vol. 42, No. 5Autonomous Orbital Rendezvous Using a Coordinate-Free, Nonsingular Orbit Representation1 Mar 2019Approximate analytic solution of motion for spacecraft around an oblate planet18 January 2018 | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 233, No. 4Second-Order Integral-Form Gauss’s Variational Equations Under Impulsive ControlGang Zhang and Daniele Mortari30 September 2018 | Journal of Guidance, Control, and Dynamics, Vol. 42, No. 2Nonlinear Analytical Equations of Relative Motion on J2-Perturbed Eccentric OrbitsBradley Kuiack and Steve Ulrich15 October 2018 | Journal of Guidance, Control, and Dynamics, Vol. 41, No. 12Overview and GNC design of the CubeSat Proximity Operations Demonstration (CPOD) mission1 Dec 2018 | Acta Astronautica, Vol. 153On frequency distribution of impulsive feedback control times1 Sep 2018 | Journal of the Franklin Institute, Vol. 355, No. 14Analytical Mechanics of Space Systems, Fourth EditionHanspeter Schaub and John L. Junkins19 January 2018Spacecraft Formation Flying10 August 2022Spacecraft formation control using analytical finite-duration approaches24 June 2017 | CEAS Space Journal, Vol. 10, No. 1Dynamics and offset control of tethered space-tug system1 Jan 2018 | Acta Astronautica, Vol. 142Comprehensive Survey and Assessment of Spacecraft Relative Motion Dynamics ModelsJoshua Sullivan, Sebastian Grimberg and Simone D’Amico17 April 2017 | Journal of Guidance, Control, and Dynamics, Vol. 40, No. 8Robustness analysis method for orbit control1 Aug 2017 | Acta Astronautica, Vol. 137Debris Avoidance Maneuvers for Spacecraft in a ClusterElad Denenberg and Pini Gurfil8 March 2017 | Journal of Guidance, Control, and Dynamics, Vol. 40, No. 6Formation flying and position determination for a space-based interferometer in GEO graveyard orbit1 Mar 2017Real-Time On-board Estimation & Optimal Control of Autonomous Micro-Satellite Proximity OperationsDylan Thomas, Katherine Mott, Kristen Tetreault, Kevin M. Nastasi, Ian Elliott, Robert Scheible, Ethan Ohriner and Jonathan Black5 January 2017Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation25 October 2016Continuous-Time Modeling and Control Using Nonsingular Linearized Relative-Orbit ElementsTrevor Bennett and Hanspeter Schaub7 October 2016 | Journal of Guidance, Control, and Dynamics, Vol. 39, No. 12Establishing a Formation of Small Satellites in a Lunar Flower Constellation12 September 2016 | The Journal of the Astronautical Sciences, Vol. 63, No. 4Real-Time Optimal Control, & Tracking of Autonomous Micro-Satellite Proximity OperationsKevin M. Nastasi, Dylan Thomas, Kristen Tetreault, Ian Elliott and Jonathan Black9 September 2016Fuel-/Time-Optimal Relative Trajectories for a Satellite near a Perturbed, Elliptical OrbitAndrew Rogers, Craig Woolsey, Jonathan Black and Robert McGwier18 July 2016 | Journal of Spacecraft and Rockets, Vol. 53, No. 5Spacecraft Rendezvous by Differential Drag Under UncertaintiesLeonel Mazal, David Pérez, Riccardo Bevilacqua and Fabio Curti17 April 2016 | Journal of Guidance, Control, and Dynamics, Vol. 39, No. 8Optimal impulsive closed-form control for spacecraft formation flying and rendezvous1 Jul 2016Fuel efficient control strategy for constellation orbital deployment4 Jan 2016 | Aircraft Engineering and Aerospace Technology, Vol. 88, No. 1Orbit Data Processing29 July 2016Orbit and Formation Control for the Next Generation Gravity Mission**Part of this research was carried out within the study Next Generation Gravity Mission (NGGM): AOCS Solutions and Technologies study and within the ESA Networking Partner Initiative (NPI) PhD project Laser Metrology Spacecraft Formation (Ref. 4000109653/13/NL/MH) funded by the European Space Agency; Thales Alenia Space Italy (Turin) being the prime contractor1 Jan 2016 | IFAC-PapersOnLine, Vol. 49, No. 17Impulsive Spacecraft Formation Maneuvers with Optimal Firing TimesLudwik A. Sobiesiak and Christopher J. Damaren8 September 2015 | Journal of Guidance, Control, and Dynamics, Vol. 38, No. 10Lyapunov-Floquet control of satellite relative motion in elliptic orbits1 Oct 2015 | IEEE Transactions on Aerospace and Electronic Systems, Vol. 51, No. 4Formation Establishment and Reconfiguration Using Differential Elements in J2-Perturbed OrbitsChristopher W. T. Roscoe, Jason J. Westphal, Jacob D. Griesbach and Hanspeter Schaub23 July 2015 | Journal of Guidance, Control, and Dynamics, Vol. 38, No. 9Impulsive Maneuvers for Formation Reconfiguration Using Relative Orbital ElementsG. Gaias and S. D’Amico25 April 2014 | Journal of Guidance, Control, and Dynamics, Vol. 38, No. 6Stability notions for a class of nonlinear systems with measure controls6 February 2015 | Mathematics of Control, Signals, and Systems, Vol. 27, No. 2Autonomous Guidance for Rendezvous Phasing Based on Special-Point-Based ManeuversJing-Rui Zhang, Shu-Ge Zhao and Yao Zhang27 May 2014 | Journal of Guidance, Control, and Dynamics, Vol. 38, No. 4Impulsive Spacecraft Formation Maneuvers with Optimal Firing TimesLudwik A. Sobiesiak and Chris J. Damaren2 January 2015Lorentz-Augmented Spacecraft Formation Reconfiguration1 Jan 2015 | IEEE Transactions on Control Systems Technology, Vol. 52Orbital estimation of spacecraft under unknown low-thrust acceleration (Second report: estimation of osculating orbital elements)1 Jan 2015 | Transactions of the JSME (in Japanese), Vol. 81, No. 826Optimal impulsive maneuvers for formation reconfiguration using relative orbit elements1 Dec 2014Model predictive orbit control of a Low Earth Orbit satellite using Gauss’s variational equations11 December 2013 | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 228, No. 13Optimal tracking and formation keeping near a general Keplerian orbit under nonlinear perturbations1 Sep 2014 | Advances in Space Research, Vol. 54, No. 6Model predictive control of passive and periodic satellite formation based on linear programming approach1 Aug 2014Stability and Performance of Orbital Elements Feedback for Cluster Keeping Using Differential Drag10 December 2014 | The Journal of the Astronautical Sciences, Vol. 61, No. 2N-Impulse Formation Flying Feedback Control Using Nonsingular Element DescriptionPaul V. Anderson and Hanspeter Schaub21 February 2014 | Journal of Guidance, Control, and Dynamics, Vol. 37, No. 2Formation establishment and reconfiguration using differential elements in J2-perturbed orbits1 Mar 2014Analytical Derivation of Single-Impulse Maneuvers Guaranteeing Bounded Relative Motion Under J2Vladimir Martinusi and Pini Gurfil10 January 2014 | Journal of Guidance, Control, and Dynamics, Vol. 37, No. 1Determination and Estimation of Differential Mean Orbital Elements for Formation-Flying MissionsKai Wang, Tong Chen and Shijie Xu10 January 2014 | Journal of Guidance, Control, and Dynamics, Vol. 37, No. 1A Delayed Impulse Control Strategy for Spacecraft Formations1 October 2015 | The Journal of the Astronautical Sciences, Vol. 60, No. 3-4Elliptical formation control based on relative orbit elements1 Dec 2013 | Chinese Journal of Aeronautics, Vol. 26, No. 6Analytical mathematical feedback guidance scheme for low-thrust orbital plane change maneuvers1 Dec 2013 | Mathematical and Computer Modelling, Vol. 58, No. 11-12Mean Orbital Elements Estimation for Autonomous Satellite Guidance and Orbit ControlWeichao Zhong and Pini Gurfil29 October 2013 | Journal of Guidance, Control, and Dynamics, Vol. 36, No. 6Long-Term Cluster Flight of Multiple Satellites Using Differential DragOhad Ben-Yaacov and Pini Gurfil29 October 2013 | Journal of Guidance, Control, and Dynamics, Vol. 36, No. 6Stability of an impulsive control scheme for spacecraft formations in eccentric orbits10 October 2012 | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 227, No. 10A Comparison of Algorithms for Computing Differential Mean Orbital Elements in Formation Flying MissionsKai Wang, Tong Chen and Shijie Xu15 August 2013Optimal Hybrid Control for Lorentz-Augmented Formation FlyingLudwik A. Sobiesiak and Chris J. Damaren15 August 2013Fuel Optimal Maneuver of Passive and Periodic Satellite Formation: Linear Programming Approach1 Aug 2013Nonlinear Adaptive Feedback Control for Spacecraft Proximity Formation Flying1 August 2013 | Applied Mechanics and Materials, Vol. 376Decentralized mean orbit element formation stability for uncoordinated maneuvers1 Jun 2013Controllers' design and verification based on the method of undetermined coefficients for satellite formation1 Jun 2013A Robust Adaptive Control Law for Satellite Formation Flying1 Feb 2013 | Acta Automatica Sinica, Vol. 39, No. 2Online Estimation of Mean Orbital Elements with Control Inputs1 Jan 2013Fuel-Optimal Low-Thrust Reconfiguration of Formation- Flying Satellites via Homotopic Approach Jing Li and Xiao-ning Xi 25 October 2012 | Journal of Guidance, Control, and Dynamics, Vol. 35, No. 6Decentralized Mean Orbit-Element Formation Guidance, Navigation, and Control: Part 1Marcus Holzinger and Jay McMahon6 September 2012Decentralized Mean Orbit-Element Formation Guidance, Navigation, and Control: Part 2Jay McMahon and Marcus Holzinger6 September 2012Hybrid Periodic Differential Element Control Using the Geomagnetic Lorentz ForceLudwik Sobiesiak and Christopher Damaren6 September 2012Analytic Solution to Optimal Reconfigurations of Satellite Formation Flying in Circular Orbit under $J_2$ Perturbation1 Jul 2012 | IEEE Transactions on Aerospace and Electronic Systems, Vol. 48, No. 3Optimal Multi-Impulse Orbit Transfer Using Nonlinear Relative Motion Dynamics16 March 2014 | The Journal of the Astronautical Sciences, Vol. 59, No. 1-2Spaceborne Autonomous Formation-Flying Experiment on the PRISMA Mission S. D'Amico , J.-S. Ardaens and R. Larsson 28 August 2012 | Journal of Guidance, Control, and Dynamics, Vol. 35, No. 3Impulsive Control for Formation Flight About Libration Points Rui Qi , Shijie Xu and Ming Xu 28 August 2012 | Journal of Guidance, Control, and Dynamics, Vol. 35, No. 2A Hierarchical Evolutionary Trajectory Planner for Spacecraft Formation Reconfiguration1 Jan 2012 | IEEE Transactions on Aerospace and Electronic Systems, Vol. 48, No. 1Autonomous Low-Earth-Orbit Station-Keeping with Electric Propulsion Andrea Garulli , Antonio Giannitrapani , Mirko Leomanni and Fabrizio Scortecci 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 34, No. 6Satellite formation reconfiguration and station-keeping using state-dependent Riccati equation technique1 Sep 2011 | Aerospace Science and Technology, Vol. 15, No. 6Spaceborne Autonomous Formation Flying Experiment on the PRISMA MissionSimone D'Amico, Jean-Sebastien Ardaens and Robin Larsson14 June 2012Nonlinear Adaptive Control for Low Earth Orbit Formation Flying1 Aug 2011Approach Guidance with Double-Line-of-Sight Measuring Navigation Constraint for Autonomous Rendezvous Tong Chen and Shijie Xu 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 34, No. 3System test results from the GNC experiments on the PRISMA in-orbit test bed1 Apr 2011 | Acta Astronautica, Vol. 68, No. 7-8A New Control Scheme for Satellite Formation Reconfiguration1 Jan 2011 | TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, Vol. 53, No. 182Hardware-in-the-loop simulations of GPS-based navigation and control for satellite formation flying1 Dec 2010 | Advances in Space Research, Vol. 46, No. 11Impulsive formation control using orbital energy and angular momentum vector1 Sep 2010 | Acta Astronautica, Vol. 67, No. 5-6References1 Jan 2010Impulsive Control of Satellite Formation Flying using Orbital Period Difference1 Jan 2010 | IFAC Proceedings Volumes, Vol. 43, No. 15Spacecraft formation flying: A review and new results on state feedback control1 Dec 2009 | Acta Astronautica, Vol. 65, No. 11-12Orbital corrections by a single-input impulsive control applied along the geomagnetic field1 Dec 2009 | Acta Astronautica, Vol. 65, No. 11-12Spaceborne Autonomous Relative Control System for Dual Satellite Formations Jean-Sébastien Ardaens and Simone D'Amico 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 32, No. 6Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation: Legendre Pseudospectral Approach Baolin Wu , Danwei Wang , Eng Kee Poh and Guangyan Xu 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 32, No. 4PRISMA: An In-Orbit Test Bed for Guidance, Navigation, and Control Experiments Per Bodin , Robin Larsson , Fredrik Nilsson , Camille Chasset , Ron Noteborn and Matti Nylund 23 May 2012 | Journal of Spacecraft and Rockets, Vol. 46, No. 3Satellite formation flying using variable structure model reference adaptive control20 February 2009 | Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 223, No. 3Analytical Mechanics of Space Systems, Second Edition John L. Junkins and Hanspeter Schaub 22 August 2012Spacecraft Formation Flying22 August 2012Autonomous guidance and control of Earth-orbiting formation flying spacecraft: Closing the loop1 Dec 2008 | Acta Astronautica, Vol. 63, No. 11-12Fundamental Frequencies of Satellite Relative Motion and Control of Formations Srinivas R. Vadali , Prasenjit Sengupta , Hui Yan and Kyle T. Alfriend 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 31, No. 5PRISMA: An In-Orbit Test Bed for GNC ExperimentsPer Bodin, Robin Larsson, Fredrik Nilsson, Camille Chasset, Ron Noteborn and Matti Nylund15 June 2012Formation Maintenance and Fuel Balancing for Satellites with Implusive ControlHui Yan, Srinivas Vadali and Kyle Alfriend15 June 2012Fuel-Equivalent Relative Orbit Element Space Jean-Francois Hamel and Jean de Lafontaine 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 31, No. 1Orbit and attitude control of spacecraft formation flying1 Jan 2008 | Applied Mathematics and Mechanics, Vol. 29, No. 1Satellite formation flying using along-track thrust1 Oct 2007 | Acta Astronautica, Vol. 61, No. 7-8Optimal Microsatellite Cluster Design for Space-Based Tracking MissionsJohn Griffith, Leena Singh and Jonathan How15 June 2012Relative Motion Control for Autonomous Rendezvous Based on Classical Orbital Element Differences Chen Tong , Xu Shijie and Wang Songxia 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4Gauss's Variational Equation-Based Dynamics and Control for Formation Flying Spacecraft Louis Breger and Jonathan P. How 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 30, No. 2μ Control for Satellites Formation Flying1 Jan 2007 | Journal of Aerospace Engineering, Vol. 20, No. 1Autonomous Guidance & Control of Earth-Orbiting Formation Flying Spacecraft Jean-François Hamel29 November 2012Classical Orbit Element Differences Determination Using Relative Position Coordinates Zhe Dong , Zheng You and Xiaomin Zhang 23 May 2012 | Journal of Spacecraft and Rockets, Vol. 43, No. 4Cooperative Spacecraft Formation Flying: Model Predictive Control with Open- and Closed-Loop Robustness1 Jan 2006Control Strategies for Formation Flight In the Vicinity of the Libration Points B. G. Marchand and K. C. Howell 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 28, No. 6Optimal Invariant Spacecraft Formation Deployment with Collision Risk Management A. Boutonnet , V. Martinot , A. Baranov and B. Escudier 23 May 2012 | Journal of Spacecraft and Rockets, Vol. 42, No. 5Optimal Single-Impulse FormationkeepingPini Gurfil19 June 2012Design of Spacecraft Formation Orbits Relative to a Stabilized Trajectory F. Y. Hsiao and D. J. Scheeres 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 28, No. 4Relative Motion between Elliptic Orbits: Generalized Boundedness Conditions and Optimal Formationkeeping Pini Gurfil 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 28, No. 4Formation Establishment and Reconfiguration Using Impulsive Control S. S. Vaddi , K. T. Alfriend , S. R. Vadali and P. Sengupta 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 28, No. 2Natural and non-natural spacecraft formations near the L 1 and L 2 libration points in the Sun–Earth/Moon ephemeris system1 October 2010 | Dynamical Systems, Vol. 20, No. 1Formation flying control for the MMS mission using GVE-based MPC1 Jan 2005Relative Orbit Geometry Through Classical Orbit Element Differences Hanspeter Schaub 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 27, No. 5Formation Control of the MAXIM L2 Libration Orbit MissionDavid Folta, Kathy Hartman, K. Howell and B. Marchand22 June 2012Formation Control of Satellites Subject to Drag Variations and J2 Perturbations David Mishne 23 May 2012 | Journal of Guidance, Control, and Dynamics, Vol. 27, No. 4Solar Wing Steering Law for Satellite Formation Flight23 August 2020 | The Journal of the Astronautical Sciences, Vol. 51, No. 2Analytical Mechanics Of Space Systems Hanspeter Schaub and John L. Junkins 22 August 2012Spacecraft Formation Flying22 August 2012A survey of spacecraft formation flying guidance and control (part 1): guidance1 Jan 2003The Dynamics of Formation Flight About a Stable Trajectory23 August 2020 | The Journal of the Astronautical Sciences, Vol. 50, No. 3Nonlinear Considerations In Satellite Formation FlyingKyle Alfriend25 June 2012 What's Popular Volume 24, Number 4July 2001 Metrics Crossmark TopicsControl TheoryFeedback ControlGlobal Positioning SystemGuidance, Navigation, and Control SystemsOptimal Control TheorySatellite Navigation SystemsSatellitesSpace Systems and VehiclesSpacecraft GuidanceSpacecraft Guidance and ControlSpacecrafts KeywordsSpacecraft FormationNonlinear FeedbackPeriapsisOsculating OrbitOptimal ControlSatellite ClustersNumerical SimulationGPSFuel ConsumptionEarthDigital Published online23 May 2012