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 onFacebookTwitterLinked InRedditEmail About Previous article Next article FiguresReferencesRelatedDetailsSee PDF for referencesCited byEvaluation and Comparison of Three Fuel Optimal Impulsive Control Strategies for Satellite Formation ReconfigurationOptimized relative phase maintenance for heterogeneous area-to-mass ratio microsatellite constellationsJournal of Physics: Conference Series, Vol. 2472, No. 1Design and optimization of stable initial heliocentric formation on the example of LISAAdvances in Space Research, Vol. 71, No. 1Nonlinear Model Predictive Control of J2-perturbed impulsive transfer trajectories in long-range rendezvous missionsAerospace Science and Technology, Vol. 132Onboard Estimation of Mean Orbital Elements Extended to State Jumping CaseYanjun Yu, Chengfei Yue, Ning Li, Feng Wang and Huayi Li21 July 2022 | Journal of Guidance, Control, and Dynamics, Vol. 45, No. 11Decentralized Formation and Constellation Stability Design Requirements Using Differential Mean Orbit ElementsMarcus J. Holzinger, Jay W. McMahon , Karina Rivera and Jillian Yuricich29 July 2022 | Journal of Spacecraft and Rockets, Vol. 59, No. 6A planning tool for optimal three-dimensional formation flight maneuvers of satellites in VLEO using aerodynamic lift and drag via yaw angle deviationsActa Astronautica, Vol. 198A satellite formation to display pixel images from the sky: Mission design and control algorithmsAdvances in Space Research, Vol. 69, No. 11A parametric constellation using relative critical inclination of satellitesAdvances in Space Research, Vol. 69, No. 9Delta-V and ground metric investigations for responsive satellite formation flyingActa Astronautica, Vol. 193Relative Transfer Singularities and Multi-Revolution Lambert UniquenessJackson Kulik and Dmitry Savransky29 December 2021Orbital Rendezvous via a General Nonsingular MethodMatthew T. Walsh and Mason A. Peck5 November 2021 | Journal of Guidance, Control, and Dynamics, Vol. 45, No. 1Geometric perspectives on fundamental solutions in the linearized satellite relative motion problemActa Astronautica, Vol. 190Time suboptimal formation flying manoeuvres through improved magnetic charged system searchAdvances in Space Research, Vol. 67, No. 11Dynamics and Optimal Control for Free-Flight and Tethered Arrays in Low Earth OrbitOptimal Multi-Target Overflight Using Ground-Track Adjustment2 February 2021 | The Journal of the Astronautical Sciences, Vol. 68, No. 1Energy-optimal reconfiguration of satellite formation flying in the presence of uncertaintiesAdvances in Space Research, Vol. 67, No. 5An in-plane $$J_2$$-invariance condition and control algorithm for highly elliptical satellite formations10 February 2021 | Celestial Mechanics and Dynamical Astronomy, Vol. 133, No. 2Distributed Game Strategy for Formation Flying of Multiple Spacecraft With Disturbance RejectionIEEE Transactions on Aerospace and Electronic Systems, Vol. 57, No. 1Closed-Form Optimal Impulsive Control of Spacecraft Formations Using Reachable Set TheoryMichelle Chernick and Simone D’Amico11 November 2020 | Journal of Guidance, Control, and Dynamics, Vol. 44, No. 1Practical Optimization of Low-Thrust Minimum-Time Orbital Rendezvous in Sun-Synchronous OrbitsComputer Modeling in Engineering & Sciences, Vol. 126, No. 2Perturbed ISL Analysis in LEO Satellite ConstellationIn-Plane Formation Reconfiguration with Radial ManeuversYeerang Lim and Sung-Hoon Mok10 August 2020 | Journal of Guidance, Control, and Dynamics, Vol. 43, No. 10Solar Radiation Pressure–Based Orbit Control with Application to Small-Body LandingKenshiro Oguri and Jay W. McMahon28 November 2019 | Journal of Guidance, Control, and Dynamics, Vol. 43, No. 2Impulsive orbit correction using second-order Gauss’s variational equations10 February 2020 | Celestial Mechanics and Dynamical Astronomy, Vol. 132, No. 2Analytical Results to Fuel-optimal Spacecraft Formation ManeuverJournal of Physics: Conference Series, Vol. 1449, No. 1Quasi-impulsive maneuvers to correct mean orbital elements in LEO28 March 2019 | CEAS Space Journal, Vol. 11, No. 3New Solutions to Impulsive Correction for Argument of Perigee Using Gauss’s Variational EquationsJournal of Aerospace Engineering, Vol. 32, No. 5Stable Model Predictive Strategy for Rendezvous Hovering Phases Allowing for Control SaturationPaulo R. 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 RepresentationApproximate 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) missionActa Astronautica, Vol. 153On frequency distribution of impulsive feedback control timesJournal 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 systemActa 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 controlActa 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 orbitReal-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 rendezvousFuel efficient control strategy for constellation orbital deploymentAircraft 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 contractorIFAC-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 orbitsIEEE 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 ReconfigurationIEEE Transactions on Control Systems TechnologyOrbital estimation of spacecraft under unknown low-thrust acceleration (Second report: estimation of osculating orbital elements)Transactions of the JSME (in Japanese), Vol. 81, No. 826Optimal impulsive maneuvers for formation reconfiguration using relative orbit elementsModel 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 perturbationsAdvances in Space Research, Vol. 54, No. 6Model predictive control of passive and periodic satellite formation based on linear programming approachStability 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 orbitsAnalytical 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 elementsChinese Journal of Aeronautics, Vol. 26, No. 6Analytical mathematical feedback guidance scheme for low-thrust orbital plane change maneuversMathematical 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 ApproachNonlinear Adaptive Feedback Control for Spacecraft Proximity Formation Flying1 August 2013 | Applied Mechanics and Materials, Vol. 376Decentralized mean orbit element formation stability for uncoordinated maneuversControllers' design and verification based on the method of undetermined coefficients for satellite formationA Robust Adaptive Control Law for Satellite Formation FlyingActa Automatica Sinica, Vol. 39, No. 2Online Estimation of Mean Orbital Elements with Control InputsFuel-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 $J_2$ PerturbationIEEE 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 ReconfigurationIEEE 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 techniqueAerospace 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 FlyingApproach 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 bedActa Astronautica, Vol. 68, No. 7-8A New Control Scheme for Satellite Formation ReconfigurationTRANSACTIONS 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 flyingAdvances in Space Research, Vol. 46, No. 11Impulsive formation control using orbital energy and angular momentum vectorActa Astronautica, Vol. 67, No. 5-6ReferencesImpulsive Control of Satellite Formation Flying using Orbital Period DifferenceIFAC Proceedings Volumes, Vol. 43, No. 15Spacecraft formation flying: A review and new results on state feedback controlActa Astronautica, Vol. 65, No. 11-12Orbital corrections by a single-input impulsive control applied along the geomagnetic fieldActa 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 loopActa 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 flyingApplied Mathematics and Mechanics, Vol. 29, No. 1Satellite formation flying using along-track thrustActa 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 FlyingJournal 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 RobustnessControl 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. 1Relative 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 2012The 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 2012A survey of spacecraft formation flying guidance and control (part 1): guidanceFormation flying control for the MMS mission using GVE-based MPC What's Popular Volume 24, Number 4July 2001 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 ConsumptionEarthPDF Published online23 May 2012