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Formation Flight, Dynamics

Formation Flight, Dynamics. Josep Masdemont, UPC. Outline. Introduction Natural Motions Near the Lagrange Points Formations and Constellations Definitions of Basic Concepts & Orbital Strategies TPF Simulations Approaches to Transfer, Reconfig., Pattern Maint. Conclusions.

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Formation Flight, Dynamics

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  1. Formation Flight, Dynamics Josep Masdemont, UPC

  2. Outline • Introduction • Natural Motions Near the Lagrange Points • Formations and Constellations • Definitions of Basic Concepts & Orbital Strategies • TPF Simulations • Approaches to Transfer, Reconfig., Pattern Maint. • Conclusions

  3. Introduction (1) • Historical Perspective • Newton (1665) • Euler (1753) • Lagrange (1772) • Poincaré (1892) • Moulton (1920) ... • Recent Advances • Dynamical Systems Theory • Fast Modern Computers • Great Amount of New Analytical, Numerical, & Graphical Procedures

  4. LOW PRECISION REQUIREMENTS YESTERDAY HIGH PRECISION REQUIREMENTS TODAY More Missions Available • Human Role • Accurate Measurements • Complex Missions (Genesis, TPF) New Demands Introduction (2)

  5. Natural Motions Near the Lagrange Points • Very Nonlinear Behaviour • Gravity Field Is Complex, But Well Known • Orbital Families: • Periodic: Halo, Liapunov, Vertical • Quasiperiodic: Lissajous, Quasihalos • Use of Natural Motion Makes Mission Design Easier, Cheaper, and Safer

  6. HORIZONTAL LYAPUNOV Orbit NORTHERN QUASIHALO Orbits SOUTHER Orbits NORTHERN HALO Orbit VERTICAL LYAPUNOV Orbit LISSAJOUS Orbits The Map of the Orbital Families JMS- 6

  7. Formations and Constellations • Highly Dependent on Requirements and Mission Context • Different Regimes Offer Different Uses • Classic Near Earth Constellations (GPS, Cluster) • Not Suitable for IR Observatories • Expensive to Maintain, May Be Infeasible • Highly Variable Geometry and Environment • Lagrange Points Offer Unique Applications • Ideal Observatory Location, Cheap to Maintain • Constant Geometry & Cold Environment, Easy Access • Dynamics Permit Formation Control

  8. Formation Classification • According to Type • Constellation & Loose Formations • Precise Formations • Large Diameter Formations: > 1000 km • Small Diameter Formations: < 100 km • According to Location and Attitude • Avoid Certain Zones • Stay in Certain Zones • Requirements in Angular Distances • Orientation of Orbital Planes

  9. Launch & Transfer Deployment Reformation / Reconfiguration Pattern Maintenance Station Keeping Contingency Plan Definitions of Basic Concepts

  10. Earth Basic Orbital Strategies • Base Orbit Strategy • Each S/C Follows an Orbit Relative to a Predefined One Known as the Base Orbit • Base Orbit May Have No S/C on It • Nominal Orbit Strategy • Each S/C Follows Its Own Predefined Orbit, Known as Its Nominal Orbit Base Orbit

  11. TPF Simulations: Dynamical Aspects 6-GON • Very Small Diameter N-gon • Different Scales • Distance From Earth to S/C: 1,500,000 km Aprox. • Distances Between S/C: Order of 20-100 m • Relative Position Accuracy : Better Than 20 cm

  12. TPF Simulations: Assumptions Formation Objective: Satellites Spinning in an Inertial Plane About a Selected Base Libration Orbit • 6 S/C Configuration as in TPF Book • 20-sided N-gon, 100 M Diameter • 3 Revolutions/Day • 10 Hr Initial Deployment from Base Orbit • Impulsive Burns at Vertex for Reconfiguration • Not Optimized • Fully Integrated Orbits With Full JPL Ephemeris

  13. TPF Simulation Animation Sequence • Halo Base Orbit (Results Independent of Orbit Type) • Transfer to Halo Using Its Stable Manifold • Deploy from Base Orbit into 20-gon Formation • Pattern Maintenance Maneuvers, With Station Keeping • Reconfiguration to Next 20-gon Formation • Pattern Maintenance Maneuvers

  14. TPF Simulation: 10 Year DV Budget (m/s) Maneuvers Per S/C 20-Gon Diameter, 3 Rev/Day m/s 50m 100m • Halo Insertion 5 5 • Initial Deployment (10h) 0.009 0.018 • Formation Maintenance 0.1/Day 0.2/Day • Station Keeping (Z-Axis) 3/Yr (TBD) 3/Yr (TBD) • Reconfiguration (est.) 0.05/Day 0.1/Day • 10 Year DV Budget (m/s) apr. 585 1135

  15. TPF Simulations: Performance Scaling D=Diameter of Ngon (m) N=Revolutions/Day • Formation Maintenance DV/Day = 2.3 e-2 cm/s * D * N * N Linear in D, Quadratic in N. • Deployment DV (Est. Of Reconfigurations) • Approx linear in D, asymptotic in N. Suitable rules: N=1 N=3 1 Hr Transfer: 5.5e-2 * D 5.6e-2 * D cm/s 3 Hr Transfer: 1.9e-2 * D 2.7e-2 * D cm/s 5 Hr Transfer: 1.3e-2 * D 2.2e-2 * D cm/s 10 Hr Transfer: 0.9e-2 * D 1.8e-2 * D cm/s 100 Hr Transfer: 0.5e-2 * D 1.5e-2 * D cm/s

  16. TPF Simulations: Issues • Feasibility of Frequent Accurate Small DV´s • 60 / Day, at 1 mm/s • Are There High Precision Small Thursters at This Level ? • Use Continuous Low Thust Control Instead ? • Development of Control Algorithm • Linear Controller (Around Nonlinear Base Orbit) Will Work • Need Nonlinear Trajectory Computations • Feasibility of Autonomous On-Board Control • Need New Analysis Tools

  17. Transfer Approach • Need to Augment Traditional Transfers • Transfers to Small Diameter Formation • Need to Develop Deployment • Transfers to Large Diameter Formation • Need Detail “Dynamical Map” of the L1/L2 Regime • Need Trajectory Timing, Phasing, & Synchronization • By Product: Contingency Plans

  18. Reformation Approach • Reformation of Small Diameter Formations • Linear Control Around Nonlinear Base Orbit • Reformation of Large Diameter Formations • Same as Classical Transfers Between Libration Orbits • Same Analysis Provides Local Contingency Plans

  19. Pattern Maintenance & Control Approach • Pattern Maint. of Small Diameter Formations • Linear Control Around Nonlinear Base Orbit • Station Keeping Absorbed by Pattern Maint. Maneuvers • Pattern Maint. of Large Diameter Formations • Classical Station Keeping to Nominal Orbits • Muli-Scale Station Keeping & Control • Transfers Between Libration Orbits • Autonomous On-Board Trajectory Computations • Applicable to Loose Constellation Control

  20. Conclusions • Formation Flight Near L1/L2 Very Close at Hand • What We Know Now • Formation Flight Is Dynamically Possible Near L1/L2 • Base Orbit Dynamics and Methodologies • Station Keeping and Transfer Procedures • What Needs More Development • Detail “Dynamical Map” of the L1/L2 Regime • Trajectory Timing, Phasing, & Synchronization • Precision Formation Control • Autonomous On-Board Trajectory Computations & Control • Mission Design Tools with Advanced Visualization

  21. General Procedures: Transfer Transfer to Large Diameter Formations Transfer to Small Diameter Formations Traditional Transfer + Deployment Timing Better Knowledge of the “Roads” Contingency Plans

  22. Station Keeping and Control Approaches Station Keeping of Large Diameter Formations Station Keeping of Small Diameter Formations Pattern Maintenance Manouvres Autonomous Navigation ( Low Thrust / BB) Classical Nominal Orbit Maintenance Loose Constellations

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