Formation Flight, Dynamics
10/19/00 JMS- 1
Josep Masdemont
UPCFormation Flight, DynamicsJosep Masdemont, UPC
Formation Flight, Dynamics
10/19/00 JMS- 2
Josep Masdemont
UPCOutline
• 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
Formation Flight, Dynamics
10/19/00 JMS- 3
Josep Masdemont
UPC
• 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)
Formation Flight, Dynamics
10/19/00 JMS- 4
Josep Masdemont
UPCIntroduction (2)
LOW PRECISION
REQUIREMENTS
YESTERDAY
HIGH PRECISION
REQUIREMENTS TODAY
More Missions Available
New Demands
• Human Role
• Accurate Measurements
• Complex Missions (Genesis, TPF)
Formation Flight, Dynamics
10/19/00 JMS- 5
Josep Masdemont
UPC
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
Formation Flight, Dynamics
10/19/00
Josep Masdemont
UPCThe Map of the Orbital Families
NORTHERN HALO Orbit
HORIZONTAL LYAPUNOV Orbit
LISSAJOUS Orbits
NORTHERN QUASIHALO
Orbits
VERTICAL LYAPUNOV Orbit
SOUTHER Orbits
JMS- 6
Formation Flight, Dynamics
10/19/00 JMS- 7
Josep Masdemont
UPCFormations 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
Formation Flight, Dynamics
10/19/00 JMS- 8
Josep Masdemont
UPCFormation 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
Formation Flight, Dynamics
10/19/00 JMS- 9
Josep Masdemont
UPCDefinitions of Basic Concepts
• Launch & Transfer
• Deployment
• Reformation / Reconfiguration
• Pattern Maintenance
• Station Keeping
• Contingency Plan
Formation Flight, Dynamics
10/19/00 JMS- 10
Josep Masdemont
UPCBasic 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
Formation Flight, Dynamics
10/19/00 JMS- 11
Josep Masdemont
UPC
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
Formation Flight, Dynamics
10/19/00 JMS- 12
Josep Masdemont
UPCTPF 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
Formation Flight, Dynamics
10/19/00 JMS- 13
Josep Masdemont
UPC
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
Formation Flight, Dynamics
10/19/00 JMS- 14
Josep Masdemont
UPC
TPF Simulation: 10 YearV 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 V Budget (m/s) apr. 585 1135
Formation Flight, Dynamics
10/19/00 JMS- 15
Josep Masdemont
UPC
TPF Simulations: Performance Scaling
• Formation Maintenance V/Day= 2.3 e-2 cm/s * D * N * NLinear 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
Formation Flight, Dynamics
10/19/00 JMS- 16
Josep Masdemont
UPCTPF 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
Formation Flight, Dynamics
10/19/00 JMS- 17
Josep Masdemont
UPCTransfer 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
Formation Flight, Dynamics
10/19/00 JMS- 18
Josep Masdemont
UPCReformation 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
Formation Flight, Dynamics
10/19/00 JMS- 19
Josep Masdemont
UPC
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
Formation Flight, Dynamics
10/19/00 JMS- 20
Josep Masdemont
UPCConclusions
• 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
Formation Flight, Dynamics
10/19/00 JMS- 21
Josep Masdemont
UPC
Traditional Transfer + Deployment
General Procedures: Transfer
Transfer to Small Diameter Formations
Transfer to Large Diameter Formations
Timing
Better Knowledge of the “Roads”
Contingency Plans
Formation Flight, Dynamics
10/19/00 JMS- 22
Josep Masdemont
UPC
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 ConstellationsClassical Nominal Orbit Maintenance
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