Formation Flight, Dynamics

Formation Flight, Dynamics

10/19/00 JMS- 1

Josep Masdemont

UPCFormation Flight, DynamicsJosep Masdemont, UPC


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


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)


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)


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


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


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


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


10/19/00 JMS- 9

Josep Masdemont

UPCDefinitions of Basic Concepts

• Launch & Transfer

• Deployment

• Reformation / Reconfiguration

• Pattern Maintenance

• Station Keeping

• Contingency Plan


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


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


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


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


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


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





D=Diameter of Ngon (m)

N=Revolutions/Day


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


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


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


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


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


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


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

Formation Flight, Dynamics

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