• Massachusetts Institute of Technology• Space Systems Laboratory• Lockheed Martin Corporation• Advanced Technology CenterElectromagnetic Formation FlightElectromagnetic Formation FlightNRO DII Final ReviewFriday, August 29, 2003National Reconnaissance OfficeHeadquartersChantilly, VADII EMFF Final ReviewAug. 29, 2003OutlineOutline• Motivation• Fundamental Principles– Governing Equations– Trajectory Mechanics– Stability and Control• Mission Applicability– Sparse Arrays– Filled Apertures– Other Proximity Operations• Mission Analyses– Sparse Arrays– Filled Apertures– Other Proximity Operations• MIT EMFFORCE Testbed–Design–Calibration–Movie• Space Hardware Design Issues– Thermal Control– Power System Design– High B-Field Effects• ConclusionsDII EMFF Final ReviewAug. 29, 2003MotivationMotivation• Traditional propulsion uses propellant as a reaction mass• Advantages– Ability to move center of mass of spacecraft(Momentum conserved when propellant is included)– Independent (and complete) control of each spacecraft• Disadvantages– Propellant is a limited resource– Momentum conservation requires that the necessary propellant mass increase exponentially with the velocity increment (∆V)– Propellant can be a contaminant to precision opticsDII EMFF Final ReviewAug. 29, 2003Question I:Question I:• Is there an alternative to using propellant?• Single spacecraft: – Yes, If an external field exists to conserve momentum– Otherwise, not that we know of…• Multiple spacecraft– Yes, again if an external field exists– OR, if each spacecraft produces a field that the others can react against– Problem: Momentum conservation prohibits control of the motion of the center of mass of the cluster, since only internal forces are presentDII EMFF Final ReviewAug. 29, 2003Question II:Question II:• Are there missions where the absolute position of the center of mass of a cluster of spacecraft does not require control?• Yes! In fact most of the ones we can think of…– Image construction• u-v filling does not depend on absolute position– Earth coverage• As with single spacecraft, Gravity moves the mass center of the cluster as a whole, except for perturbations…– Disturbance (perturbation) rejection• The effort to control perturbations affecting absolute cluster motion (such as J2) is much greater than that for relative motion• Only disturbances affecting the relative positions (such as differential J2) NEED controlling to keep a cluster together– Docking• Docking is clearly a relative position enabled maneuverDII EMFF Final ReviewAug. 29, 2003Example: Image ConstructionExample: Image Construction• Image quality is determined by the point spread function of aperture configuration()211)(2expsinsin)cos1(,⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡∑⎟⎠⎞⎜⎝⎛ψ+ψλπ−⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛λθπ⎟⎠⎞⎜⎝⎛λθπ⎟⎠⎞⎜⎝⎛λθ+π=ψψ=NnnjnijiyxiDDJDI• The geometry dependence can be expanded into terms which only depend on relative positionAperture dependenceGeometry dependenceIψi()= IApψi()N + cos2πλψi(x1− x2)⎛ ⎝ ⎞ ⎠ + cos2πλψi(x1− x3)⎛ ⎝ ⎞ ⎠ + ...⎡ ⎣ ⎢ ⎤ ⎦ ⎥DII EMFF Final ReviewAug. 29, 2003Comparison Comparison --GolayGolayConfigurationsConfigurationsPSFs for the Golay configurations shown here will not change if the apertures are shifted in any directionDII EMFF Final ReviewAug. 29, 2003Question III:Question III:• What forces must be transmitted between satellites to allow for all relative degrees of freedom to be controlled?– In 2-D, N spacecraft have 3N DOFs, but we are only interested in controlling (and are able to control) 3N-2 (no translation of the center of mass)– For 2 spacecraft, that’s a total of 4:• All except case (4) can be generated using axial forces (such as electrostatic monopoles) and torques provided by reaction wheels• Complete instantaneous control requires a transverse force, which can be provided using either electrostaticor electromagnetic dipoles1234DII EMFF Final ReviewAug. 29, 2003What is it NOT good for?What is it NOT good for?• Orbit Raising• Bulk Plane Changes•De-Orbit• All these require rotating the system angular momentum vector or changing the energy of the orbit• None of these is possible using only internal forcesDII EMFF Final ReviewAug. 29, 2003Forces and Torques: ConceptualForces and Torques: ConceptualNSSNNSSNBAAB• In the Far Field, the dipole field structure for electrostatic and electromagnetic dipoles are the same• The electrostatic analogy is useful in getting a physical feel for how the transverse force is applied• Explanation …DII EMFF Final ReviewAug. 29, 2003EMFF Vehicle Conceptual ModelEMFF Vehicle Conceptual Model• In the Far Field, Dipoles add as vectors• Each vehicle will have 3 orthogonal electromagnetic coils– These will act as dipole vector components, and allow the magnetic dipole to be created in any direction• Steering the dipoles electronically will decouple them from the spacecraft rotational dynamics• A reaction wheel assembly with 3 orthogonal wheels provides counter torques to maintain attitudeDII EMFF Final ReviewAug. 29, 2003OutlineOutline• Motivation• Fundamental Principles– Governing Equations– Trajectory Mechanics– Stability and Control• Mission Applicability– Sparse Arrays– Filled Apertures– Other Proximity Operations• Mission Analyses– Sparse Arrays– Filled Apertures– Other Proximity Operations• MIT EMFFORCE Testbed–Design– Calibration–Movie• Space Hardware Design Issues– Thermal Control– Power System Design– High B-Field Effects• ConclusionsDII EMFF Final ReviewAug. 29, 2003Magnetic Dipole ApproximationMagnetic Dipole Approximation• The interaction force between two arbitrary magnetic circuits is given by the Law of Biot and SavartI1I2O• In general, this is difficult to solve, except for cases of special symmetry• Instead, at distances far from one of the circuits, the magnetic field can be approximated as a dipole[]011 11153 3()ˆˆˆ ˆ 3 3()44orBr rrrr rµµµµ µµµππ⋅⎡⎤⎛⎞=−=⋅−⎜⎟⎢⎥⎣⎦⎝⎠ where its dipole strength µ1is given by the product of the total current around the loop (Amp-turns) and the area enclosedDII EMFF Final ReviewAug. 29, 2003DipoleDipole--Dipole InteractionDipole Interaction• Just as an