a sw suite for formation flying mission analysis and gnc...

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3nd European Workshop on Astrodynamic Tools and Techniques

October 2006

© 2006 DEIMOS Space S.L. – www.deimos-space.com

© 2006 DEIMOS Engenharia, S.A. – www.deimos.com.pt

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FF ToolboxA SW Suite for Formation

Flying Mission Analysis and

GNC Design

Luis F. PeñínAugusto Caramagno

Space Systems Engineering DivisionDEIMOS Space S.L. & DEIMOS Engenharia

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Toolbox DefinitionToolbox Definition

• Objectives:– Analysis and Design of Formation Flying Missions– Evaluation of GNC system design– Testbench for Guidance & Control algorithm evaluation– Performance assessment through Monte Carlo simulation

campaigns• Target User:

– Mission Analysis– GNC System Analyst

• Results of ESA, national and internal projects

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DEIMOS FF ActivitiesDEIMOS FF Activities

• Formation Flying Roadmap

2002 2003 2004 2005

STIFF

DICOFF

PCOS

FEMDIS

· Formation Transfer L2 · Planetocentric FF · FF Topology definition · Trajectory optimisation · FF Relative GNC · FF Transfer L2

· FF Deployment in L2· FF Operations in L2 · Topology definition · FF Relative GNC

· Formation Reconfiguration in L2

· FF trajectory planning · Formation coordination · FF Relative GNC

· Formation in GTO · Formation design· GNC modes · Optimal profiles

LODATO

· Transfer to L2 · Transfer with RV - Formation maneuvers

ICC-2

FF Algorithms for S3 (Alcatel-Scisys)FF RT Test-Bench (DEIMOS)

2006

GNCO

- Formation design in HEO - Robust Control

2007

PROBA3

- Mission Analysis - FF management

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Toolbox ContextToolbox Context

FF Toolbox

GNC analyst

System Studies

Performance indexes and budgets)

)

Technology development programs

Autocoding process

C-code Version

Autocoded simulatorsource files

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• Scope of functions

FF FF Toolbox Scope Toolbox Scope (1/2)(1/2)

Orbital environment

(mission phase selection)

Mission requirements

and constraints

Mis

sion

Ana

lysi

s

Absolute trajectory definition

Formation topology definition

GNC modes definition

iterative optimisation

Absolute trajectory

requirements

Relative trajectory

requirementsGNC

Formation GNC

S/C G&C Navigation

GNC architecture

definition Budget

allocation

Control Algorithms

Actuators Sensors

Navigation Algorithms

Allocation of requirements to GNC functions

GNC architecture

GNC Functions

Requirements definition

Mission Analysis & GNC design

Avionics definition

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FF FF Toolbox Scope Toolbox Scope (2/2)(2/2)

• Scope of analysis and design capabilities

Closed-loop Design

Closed-loop Analysis

Closed-loop Simulation

Performance Analysis

Dispersion Analysis

Open-loop Simulation

Collision Risk Assessment

OK?

No

YesOpen-loop operation

Closed-loop operation

System Budgets

Requirements and Constraints Verification

OK?

No

Yes

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Mission design toolsMission design tools

– Environment• Gravitational perturbations

– Central field– High order harmonics

• Solar radiation pressure• Third body perturbation

– Sun– Moon

– Orbits• Earth arbitrary orbit• Mars arbitrary orbit• Transfer orbit to L2• Halo orbit on L2

Orbital environment



and constraints

Mis

sion

Ana

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GNC modes definition


Absolute trajectory

requirements

Relative trajectory

requirementsGNC

Formation GNC

S/C G&C Navigation

GNC architecture

definition Budget

allocation

Control Algorithms

Actuators Sensors



GNC architecture

GNC Functions

– Formation topologies• Space & time oriented• Target & orbit oriented• Forced and natural formations• Tight and loose formations

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-16 -14 -12 -10 -8 -6 -4 -2 0 2

x 105

-1

-0.5

0

0.5

1x 10

6 Transfer trajectory (low thrust arcs in red)

x synodic axes, km

y sy

nodi

c ax

es, k

m

Earth L2

-14 -12 -10 -8 -6 -4 -2 0 2

x 105

-2

-1

0

1

2

x 105

x synodic axes, km

z sy

nodi

c ax

es, k

m

Earth L2

-2

0

2

4

x 105

-1-0.5

0

0.51

x 106

-1.5

-1

-0.5

0

0.5

1

1.5

x 105

x axis , kmy axis , km

z ax

is, k

m

Low thrust transfer to L2 design

L2 halo orbit design

Arbitrary planetocentric orbit design

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Formation Formation planning planning toolstools

– Formation manoeuvres design• Resizing (nominal & optimal)• Rotating (nominal & optimal)• Slewing (nominal & optimal)

– Formation coordination• Nominal coordination• Optimal coordination

– Formation deployment in L2• Lyapunov functions with

continuous thrust • Lyapunov functions with

on/off control • Hybrid strategy deployment• Deployment by layers

Orbital environment



and constraints

Mis

sion

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GNC modes

definition


Absolute trajectory

requirements

Relative trajectory

requirementsGNC

Formation GNC

S/C G&C Navigation

GNC architecture

definition Budget

allocation

Control Algorithms

Actuators Sensors



GNC architecture

GNC Functions

In collaboration with University of Barcelona - IEEC

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Reconfiguration manoeuvresReconfiguration manoeuvres

Resize from 100 to 200 m, initial fuel unbalance, optimal planning

Rotation of 45º, initial fuel unbalance, optimal planning & coordination

Slew of 45º, fuel unbalance, optimal planning & coordination

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Deployment manoeuvresDeployment manoeuvres

Formation deployment with Lyapunov functions from a random disposition in L2

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Spacecraft Spacecraft GNC GNC functionsfunctions

– Spacecraft guidance & control• Relative reference traj.design

– Based on position/velocity– Based on time

• Gravity gradient FFW• MIMO controllers design

– Two-body problem– Three-body problem

– Formation navigation• Peer-to-peer navigation• Least squares estimation• Performance models

Orbital environment



and constraints

Mis

sion

Ana

lysi

s



GNC modes

definition


Absolute trajectory

requirements

Relative trajectory

requirementsGNC

Formation GNC

S/C G&C Navigation

GNC architecture

definition Budget

allocation

Control Algorithms

Actuators Sensors



GNC architecture

GNC Functions

– Actuators• FEEPs thrusters• Optimal Thrust

Assignment Unit

– Sensors• RF-based relative navigation • Laser-based relative navigation• Inertial Measurement Unit• Star tracker

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S/C S/C Guidance and Guidance and ControlControl

Centralbody

Master (C)

Flyer

rvδ

rv

Crv

θ

Pericenter

we

ue

ve

Inertial frame (0)

Intermediate frame (S)

General formulation for relative state definition of FF topologies

TargetReferenced

OrbitalFrame

InertialFrame

OrbitalReference

SpaceOriented

ReferenceAhead

ReferenceBehind

TimeOriented

Formation Topologies

-0.2503 -0.2502 -0.2501 -0.25

-2

-1

0

1

2

x 10-4

xaxis (km)

zaxi

s (k

m)

f(x,z)=0guidance

-0.25 -0.2499 -0.2498 -0.2497

-2

-1

0

1

2

x 10-4

xaxis (km)

zaxi

s (k

m)

f(x,z)=0guidance

LMO post-homing station keeping: guidance relative position for a time-SK guidance scheme (left) and true anomaly SK guidance scheme (right)

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Control error Control error exampleexample

LMO post-homing SK: Time-SK closed-loop simulation (ideal GNC).

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8Control Error (RF)

no. orbits

erro

r(m)

lqr1lqr2

0 0.5 1 1.5 20

0.5

1

1.5

2x 10

-5 Control (RF)

no. orbits

Con

trol a

ccel

erat

ion(

m/s

2 ) lqr1lqr2

0 0.5 1 1.5 20

0.05

0.1

0.15

0.2Budgets (FEEP+RF)

no. orbits

ΔV(

m/s

)

lqr1lqr2

HMO close holding at -20 m: performances of different controllers (FEEP + RF)

LQR1: minimise consumption; LQR2: minimise control error

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Controller design toolsController design tools

– Controller design• Scenarios

– Two body problem– Three body problem

• Controllers– SISO controller– MIMO SVF controller– MIMO LQR controller

– Controller analysis• Nominal stability• Nominal performance• Robust stability• Robust performance

Closed-loop Design




Dispersion Analysis



OK?

No



System Budgets


OK?

No

Yes

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Controllers AnalysisControllers Analysis

10-5

10-4

10-3

10-2

10-1

100

101

102

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10Maximum singular values of the sensitivity (S)

Frequency (rad(s)

Sin

gula

r val

ues

(db)

siso0svf0lqr1lqr3lqr5Wp

10-5

10-4

10-3

10-2

10-1

100

101

102

-40

-20

0

20

40

60

80

100Robus t performance upon diagonal input uncertainty

Frequency (rad(s )

Sin

gula

r val

ues

(db)

s is o0s vf0lqr1lqr3lqr5

Bode Magnitude Diagram

Frequency (rad/s ec)

Mag

nitu

de (a

bs)

10-5

100

10-20

100



Mag

nitu

de (a

bs)

10-5

100

10-20

100 Bode Magnitude Diagram


Mag

nitu

de (a

bs)

10-5

100

10-20

100



Mag

nitu

de (a

bs)

10-5

100

10-20



Mag

nitu

de (a

bs)

10-5

100

10-20

10-10



Mag

nitu

de (a

bs)

10-5

100

10-20

100



Mag

nitu

de (a

bs)

10-5

100

10-20

100


Frequency (rad/s ec)M

agni

tude

(abs

)

10-5

100

10-20

10-10



Mag

nitu

de (a

bs)

10-5

100

10-20

100

Nominal and robust performance analysis of different controllers

Uncertainty definition

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Simulation and analysis toolsSimulation and analysis tools

– Simulations• Scenarios

– Mars planetocentric– Earth planetocentric– Transfer to L2– Halo orbit around L2

• Types– Open-loop– Closed-loop– Selective perturbations

– Performance Analysis• Monte-Carlo analysis• Parametric analysis• Time domain analysis• Control effort analysis• Communication analysis

Closed-loop Design




Dispersion Analysis



OK?

No



System Budgets


OK?

No

Yes

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Transfer Transfer L2 L2 OpenOpen--loop Simloop Sim

0 0.5 1-20

0

20

40

60

80

100Relative position

% transfer

xrot

(km

)Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m

0 0.5 1-80

-60

-40

-20

0

20Relative position

% transfer

yrot

(km

)

Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m

0 0.5 1-20

-15

-10

-5

0

5Relative position

% transfer

zrot

(km

)

Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m

0.999 0.9995 1

3.14

3.15

3.16

3.17

3.18

3.19

3.2x 10

4 Relative position

% transfer

xrot

(km

)

Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m

(with radiation pressure)

0.997 0.998 0.999 1

-2.24

-2.23

-2.22

-2.21

-2.2

x 104

Relative position

% transfer

yrot

(km

)

Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m


0.999 0.9995 1

-5495

-5490

-5485

-5480

-5475

-5470

-5465

-5460

Relative position

% transfer

zrot

(km

)

Δx(t0)=100mΔy(t0)=100mΔz(t0)=100m


Comparison of relative position evolution for different initial deltas in position. Upper row with no SRP, lower row with SRP.

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Communication AnalysisCommunication Analysis

Parametric analysis of the effect of communication latency (s) in different parameters of a resize manoeuvre.

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Parametric AnalysisParametric Analysis

Parametric analysis of the effect of reducing the manoeuvre time (s) in different parameters of a rotation manoeuvre.

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MonteMonte--Carlo SimulationCarlo Simulation

-26.8 -26.6 -26.4 -26.2 -26 -25.8-2576.6

-2576.5

-2576.4

-2576.3

-2576.2

-2576.1

xaxis , km

yaxi

s, k

m

-26.8 -26.6 -26.4 -26.2 -26 -25.8-2573.2

-2573.15

-2573.1

-2573.05

-2573

-2572.95

-2572.9

-2572.85

xaxis , km

zaxi

s, k

m

-2573.2-2573.15-2573.1-2573.05 -2573 -2572.95-2572.9-2572.85-2576.6

-2576.5

-2576.4

-2576.3

-2576.2

-2576.1

zaxis , km

yaxi

s, k

m

Final 1-sigma and 2-sigma position dispersion ellipsoid and Monte-Carlo absolute trajectory

points for SK in Mars Orbit

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Analysis toolsAnalysis tools

– Dispersion analysis• Analytical propagation• Numerical propagation

– Without perturbations– Extended with air drag

– Collision risk Assessment• Based on dispersion matrix

– System budgets• Total formation ΔV • Spacecraft ΔV • Required control bandwidth• Communication effort

Closed-loop Design




Dispersion Analysis



OK?

No



System Budgets


OK?

No

Yes

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Dispersion and Collision RiskDispersion and Collision Risk

Evolution of position dispersion ellipsoid of satellite 1 after 1 orbit in an InSAR C-Band

formation

(initial dispersion 10 cm in position and 0.1 mm/s in velocity)

(40x40 m baseline)

0 2000 4000 6000 8000 10000 120000

0.01

0.02

0.03

0.04

0.05

0.06

0.07Collis ion ris k as s es s ment validation

Pro

babi

lity

of c

ollis

ion

S amples

ComputedMonte-Carlo

Monte-Carlo validation of the algorithm for computing the probability of collision

0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028-0.03

-0.02

-0.01

0

0.01

0.02

0.03Relative pos ition

xaxis , km

yaxi

s, k

m

0.014 0.016 0.018 0.02 0.022 0.024 0.026 0.028-1.5

-1

-0.5

0

0.5

1

1.5x 10

-3

xaxis , km

zaxi

s, k

m

-1.5 -1 -0.5 0 0.5 1 1.5

x 10-3

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

zaxis , km

yaxi

s, k

m

0.01

0.02

0.03

-0.04-0.020

0.020.04

-2

-1

0

1

2

x 10-3

xaxis , kmyaxis , km

zaxi

s, k

m

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System budgetsSystem budgets

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2Budgets (ideal)

no. orbits

ΔV(

m/s

)

lqr2lqr3lqr4sisosvf

Example of total ΔV with different controllers

Example of DV consumed by each S/C during a resizing manoeuvre

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Common infrastructure (1/2)Common infrastructure (1/2)

Dynamics & Kinematics

On-Board Systems

Rea

l Wor

ld

MAN MACHINE INTERFACE

MONTE CARLO SIMULATION

Environment

GNC Algorithms

SIMULATION CORE

Sensors

SIMULATION ENGINE

Mission Definition Core Driver

Model Configuration

Actuators

Raw Data Logging

VISUALIZATION

Post-Processed

Data Raw Data

POST−PROCESSING

Configuration Data Files

COVARIANCE ANALYSIS TOOL

Fault Injection

AMM

FDIR

AUXILIARY TOOLS

Control analysis

Dispersion analysis

Auto-coding Mission profile design

S/C modeling tool

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Common infrastructure Common infrastructure (2/(2/2)2)• XML Input Files

File Data

Structure

Data Elements

Replications of theData Structure

Replication of DataElements

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Common Infrastructure Common Infrastructure (3/3)(3/3)

• Man-machine interface– Matlab command-line– Menu based

• Operational Environment– Matlab– Simulink– ANSI-C, (embedded in Simulink S-functions)

1. Closed-loop Design & Analysis 2. OL/CL Simulation 3. Performance Analysis 4. Open-loop Analysis Make a selection from the list above (0=Back)(default=1):

Simulation file selection OL/CL Simulation ------------------------------------------------------------- 1. simulation-mars.txt 2. simulation-tlp.txt 3. simulation.txt Make a selection from the list above (0=Back)(default=1): Simulation selection Performance Analysis

------------------------------------------------------------- 1. SimID: OL MissID: MARS Date: 20030304 Time: 1231337 2. SimID: OL MissID: MARS Date: 20030304 Time: 1251249 Make a selection from the list above (0=Back)(default=1):

a sw suite for formation flying mission analysis and gnc...

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