1. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 1 Formation Flight, Dynamics Josep Masdemont, UPC

2. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 3 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 Introduction (1)

4. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 4 Introduction (2) LOW PRECISION REQUIREMENTS YESTERDAY HIGH PRECISION REQUIREMENTS TODAY More Missions Available New Demands Human Role Accurate Measurements Complex Missions (Genesis, TPF)

5. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00 The Map of the Orbital Families NORTHERN HALO Orbit HORIZONTAL LYAPUNOV Orbit LISSAJOUS Orbits NORTHERN QUASIHALO Orbits VERTICAL LYAPUNOV Orbit SOUTHER Orbits JMS- 6

7. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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 Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 9 Definitions of Basic Concepts Launch & Transfer Deployment Reformation / Reconfiguration Pattern Maintenance Station Keeping Contingency Plan

10. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 10 Basic Orbital Strategies Earth Nominal Orbit Strategy –Each S/C Follows Its Own Predefined Orbit, Known as Its Nominal Orbit Base Orbit 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

11. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 11 TPF Simulations: Dynamical Aspects 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 6-GON

12. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 14 TPF Simulation: 10 Year  V Budget (m/s) Maneuvers Per S/C 20-Gon Diameter, 3 Rev/Day m/s50m100m Halo Insertion55 Initial Deployment (10h)0.0090.018 Formation Maintenance0.1/Day0.2/Day Station Keeping (Z-Axis)3/Yr (TBD)3/Yr (TBD) Reconfiguration(est.)0.05/Day0.1/Day 10 Year  V Budget (m/s) apr. 5851135

15. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 15 TPF Simulations: Performance Scaling Formation Maintenance  V/Day = 2.3 e-2 cm/s * D * N * N Linear in D, Quadratic in N. Deployment  V (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 D=Diameter of Ngon (m) N=Revolutions/Day

16. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 16 TPF Simulations: Issues Feasibility of Frequent Accurate Small  V´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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 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. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 21 Traditional Transfer + Deployment General Procedures: Transfer Transfer to Small Diameter Formations Transfer to Large Diameter Formations Timing Better Knowledge of the “Roads” Contingency Plans

22. Formation Flight, Dynamics Josep Masdemont UPC 10/19/00JMS- 22 Station Keeping and Control Approaches Station Keeping of Small Diameter Formations Station Keeping of Large Diameter Formations Autonomous Navigation ( Low Thrust / BB) Pattern Maintenance Manouvres Loose Constellations Classical Nominal Orbit Maintenance