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Generalized Multi-Impulsive Maneuvers

for Optimum Spacecraft Rendezvous

G. Gaias, S. DAmico, J.-S. Ardaens

5th International Conference on SpacecraftFormation Flying Missions and Technologies

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Contents

Objectives and Motivations

Overall Concept of the Maneuvers Planner

Description of the Planner

Example of a Rendezvous

Conclusions and Way Forward

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Objectives

Generation of theopen-loop,impulsive maneuvers profilefor formation

reconfiguration

Realistic operational conditions:fuel efficiency

safe approach during rendezvous

time constraints

Autonomy:

simplicity, closed-form solutions

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Motivations

Autonomous Vision Approach Navigation and Target IdentificationAVANTI

experiment, DLR FireBird Mission

Background

Spaceborne Autonomous Formation Flying ExperimentSAFE, PRISMAmission

TanDEM-X Autonomous Formation FlyingTAFFsystem

Advanced Rendezvous Demonstration using GPS and Optical Navigation

ARGON, PRISMA mission - extended phase

(ground-in-the-loop, man-in-the-loop)

Autonomous strategy: on-board guidance, constraints handling

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Motivations



Background







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Motivations



Background







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Motivations



Background







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Overall Concept

Relative Orbital ElementsROEas state variables

= {a,,ex, ey, ix, iy}T

P = a description of each possible configuration

Layered approach

P0 PF through intermediate Pi, tooptimizea criterion

operatives modes: set criterionand evaluation of the relevance of some

operational conditions

Maneuvers computation and scheduling in compliance with time

constraints

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Overall Concept

Relative Orbital ElementsROEas state variables

= {a,,ex, ey, ix, iy}T

P = a description of each possible configuration

Layered approach

P0 PF through intermediate Pi, tooptimizea criterion

operatives modes: set criterionand evaluation of the relevance of some

operational conditions

Maneuvers computation and scheduling in compliance with time

constraints

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Use of Relative Orbital Elements

Along-Track

Radial

Along-Track

C

ross-Track

a e

a a

a i

2a ea

a

t

= (tt0)

a

t0

1 0 0 0 0 0 0

t 1 0 0 0 0 02

t2 t 1 0 0 t 0

0 0 0 1 t 0 00 0 0 t 1 0 00 0 0 0 0 1 0

0 0 0 0 0 t 1

differential drag meanJ2

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Planning: problem statement

Evolution of the motion through (t);effectof the maneuvers at ti:discontinuities in ROE

P1 = 1,0P0+a()1 P2 = 2,1P1+a()2

End-conditions: achievement of PF

Functionalcost, convex form of the ROE jumps overm steps:

Jplan =m

i=1()Ti ()i

ROE variations not due to the natural dynamics

describes delta-v cost

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Planning: problem solution

Optimality conditions reduce to alinear systemin ROE due to:

structure of (t)

relations between delta-v andROE

Generalization of a geometrical approach stepwise reconfiguration,

disturbances compensation

Suitable for automatic implementation

Framework for further development

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Supported Operative Modes

Modes Motivations Applicability

minimum delta-v

direct P0 PF

4maneuvers

absolute min cost small reconfigurations

accurate P0

maximum observability

user definedti Pi

4i maneuvers

intensify maneuvers activity

spread burns over horizon

maneuver execution errors

large reconfigurations

uncertainty on P0

Synergies

criterion: minimum delta-v

local control method: vT minor cost and best non-instantaneous observability

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Interfaces and Constraints Management

Guidance(Scheduling, Planning, Safety)

Control(Maneuvers placement)

Maneuvers profile

Forbidden time intervals

Minimum time to first maneuver

Minimum time spacing between maneuvers

Input:

y0, (P,t)0, (P,t)F, Mode Time constraints

time

time

P0 PFP1 P2

t0,2 t2

maneuvers

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Local control Problem, out-of-plane solution

Establishment of a (intermediate) reconfiguration over a control window

fixed time,fixed end-conditionsproblem

jump corrected by disturbances effects over the window

a =ai i,0ia0,i

Out-of-plane solution,deterministic:

uoop= arctan

iy

ix

|vn|= na

i

two options per orbit

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Local control Problem, in-plane solution

In-plane solution,underdetermined:

(minimum2 impulses required 6 unknowns in4 equations)

selection criterion: minimum delta-v tangential burns

autonomy: preference for analytical solutions 3-impulses

Multiple(finite number) feasible solutions over[t0w, tw]:

u= mod

arctan

eyex

,

uipj = u+kj, j = 1...3

k1 < k2 < k3

selection ofoneoption according to:1. preference tominordelta-vcost

2. preference towider spacingbetween burns

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Safety Concept

e/iplanning

Out-of-plane control In-plane control

optimal / sub-optimal

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Example of a Rendezvous

Scenario Input

500km high

98degrees inclination

Btarget: 0.01m

2/kg

B/B: 2%

P0 = [5,10000,50,250,30,200] m

PF = [0,3000,0,100,0,100] m

tF: 18orbits aftert0

time constraints, mode: max-observability

300 200 100 0 100 200 300300

200

100

0

100

200

300

aex ai

x[m]

aey

aiy[m]

start

target

0 2 4 6 8 10 12 14 16 18 2020

0

20

40

60

80

time [orbital periods]

aa[m]

0 2 4 6 8 10 12 14 16 18 202000

4000

6000

8000

10000

12000


a

[m]

1 1

1

1

Normalized e/i plane

0 2 4 6 8 10 12 14 16 18 200.04

0.02

0

0.02

0.04Total deltav: 0.2168 [m/s]


deltav,

vt

vn

[m/s]

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Impulsive maneuvers plannerfor formation reconfiguration

realistic operational conditions

autonomy: simplicity and determinism

AVANTI experiment, DLR FireBird Mission

inclusion of constraints of minimum and maximum realizable delta-v

consolidate interfaces of the module

flight software implementation

Further development of the concept (beyond the AVANTI application)

introduction of collision-avoidance constraints at the planning level

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Impulsive maneuvers plannerfor formation reconfiguration

realistic operational conditions

autonomy: simplicity and determinism

AVANTI experiment, DLR FireBird Mission

inclusion of constraints of minimum and maximum realizable delta-v

consolidate interfaces of the module

flight software implementation

Further development of the concept (beyond the AVANTI application)

introduction of collision-avoidance constraints at the planning level

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Generalized Multi-Impulsive Maneuvers

for Optimum Spacecraft Rendezvous

Introduction

Concept

Description

Example

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