Title: "Mission Analysis, Formation Geometry and Dynamics for the IRASSI Space Interferometer "  Abstract: Space-based interferometry has gained prominence in recent years, largely because higher spatial resolutions of celestial observations can be achieved with multi-telescope formations compared to those achieved with a fixed-aperture, single telescope. IRASSI is a space interferometer composed of five spacecraft, whose aim is to observe particular chemical and physical processes in cold regions of space, such as dust clouds and stellar disks, in the far-infrared frequencies.  Ultimately, the goal is to study the genesis of planets, star formation and evolution processes in these cold regions and to understand how prebiotic conditions in Earth-like planets are created. IRASSI will orbit the second Lagrange point, L2, of Sun-Earth/Moon system. The operating principle of IRASSI is based on free-drifting baselines, which dynamically change during the observations and measure therefore the incoming wavefront of a celestial target at different locations in space. This process relies on very accurate measurements of the baselines - at micrometre level - rather than on precise control of the formation. Naturally, a free-flying formation comes with a set of challenges, namely identifying a nominal formation geometry, that is, a suitable dispersion of the telescopes in three-dimensional space. In addition, understanding how this free-drifting geometry is expected to change is crucial, particularly if this may affect the operation of the telescope instruments and thus the quality of the final synthesized images. The presentation introduces therefore the IRASSI mission and the main driving requirements. The formation geometry and dynamics are thereafter evaluated. Finally, preliminary results concerning formation control are presented

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• Institute of Space Technology & Space Applications
o Universität der Bundeswehr (Munich)
o 4 groups:
o Space technology (Prof. R. Förstner)
o Navigation & Communication (Prof. B. Eissfeller)
o Satellite Navigation (Prof. T. Pany)
o Space Operations (Prof. F. Huber - Director GSOC, DLR)
Our Institute: ISTA

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• Key research areas
o Orbit determination (orbital debris, deep-space navigation)
o Formation flying & space-based interferometry
o Micro-distortion modeling
o Mission analysis (Earth, Mars, Asteroid Main Belt)
o Trajectory optimization
o GNC & landing systems for Saturn Moons
o Radio science
o Balloon technologies for Mars reentry
o Systems engineering
Our Institute: ISTA
Land
here

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Content Overview
I. Intro: The IRASSI Mission
II. Nominal Operations
III. Formation Concept & Performance
A) Formation Dynamics
B) Relative Positioning
IV. IRASSI Technical Challenges
V. Summary & Future Work

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I. The IRASSI Mission

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I. The IRASSI Mission

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• Objective: Observation of circumstellar disks and
protoplanetary regions with high spatial resolution
to characterize conditions of formation of Earth-like planets
Interferometry at far-infrared
frequencies (FIR)
I. The IRASSI Mission

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• Constellation of 5 spacecraft
• Halo-orbit around L2 (Sun-Earth/Moon system)
• Operational lifetime: 5 years
I. The IRASSI Mission
High-level Requirements
Observed wavelength (λ) 50 – 300 µm
Frequency range 1 – 6 THz
Angular Resolution 0.1 arcsec
Baseline knowledge accuracy 5 µm
Sun
L2
Earth
Sun-Earth line
Deputy
Chief

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• Reference Trajectory
• Visibility – Deep Space Antennas
• 1 DSA: 10 hours/day
• 2 or more DSA: 14.5 to 22 hours/day
I. The IRASSI Mission

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Phase
(Nominal Operations)
Duration
(5 years)
Formation Reconfiguration 12 hours
Formation Pointing 6 hours
Scientific Observations 22 hours
Calibration 4 hours
Uplink/Downlink 4 hours
Station-keeping (Impulsive, once per orbit)
1 Observation
cycle  48 hours
5 years  900
Observation cycle
II. Nominal Operations

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• Total Delta-V: 270 m/s
• ~90% Nominal Operations
Phase Maneuver Delta-V (m/s)
Transfer to L2
Correction near Earth 14
Correction near L2 16
Deployment of
Spacecraft
Deployment
1
Nominal Operations
Formation Reconfiguration 128
Formation Pointing:
• Momentum unload 11
Scientific Observations:
• Baseline Change
• Fine Target Acquisition
25
43
Station keeping 30
(End of Life) Decomissioning 1
II. Nominal Operations

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III.Formation Concept & Performance

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• Operational principle
• Dynamic baselines (contraction/expansion): 7 to 850 m
• Accurate knowledge of relative distances (NOT continuous
formation control)
III.Formation Concept & Performance
Ranging system

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III.Formation Concept & Performance
• Formation Geometry
• Double-sided asymmetric pyramid
• Functional, geometrical, science requirements
Deputy 3
Deputy 1
Deputy 4
Deputy 2
Chief

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III.Formation Concept & Performance
• Formation Geometry
• Double-sided asymmetric pyramid
• Functional, geometrical, science requirements
• Independent of formation size
Initial formation coordinates (m)
( 𝒙 𝟎, 𝒚 𝟎, 𝒛 𝟎)
Chief (0, 0, 0)
Deputy 1 (0, 𝒂, 0)
Deputy 2 (0, 0, -2𝒂)
Deputy 3 (
𝒂
4
,
𝒂
2
, -𝒂)
Deputy 4
(−
𝒂
4
,
𝒂
3
, −
𝟐𝒂
3
)
Deputy 3
Deputy 1
Deputy 4
Deputy 2
Chief

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V
U
W
• Image quality depends:
• # sample points
• Formation dynamics
• Baseline determination accuracy
III.Formation Concept & Performance
[Kraus et al., 2014]
Baseline

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• Metrics:
1. Drift
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
III.A) Formation Dynamics
𝚻

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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Formation coordinates (m)
( 𝒙 𝟎, 𝒚 𝟎, 𝒛 𝟎)
Small Large
Chief (0, 0, 0) (0, 0, 0)
Deputy 1 (0, 40, 0) (0, 400, 0)
Deputy 2 (0, 0, -80) (0, 0, -800)
Deputy 3 (10, 20, -40) (10, 20, -400)
Deputy 4 (-10,13,-26) (-100,130,-260)
• Simulation scenario:
→ At 𝒕 𝟎: small formation (𝑎 = 40 m)
→ Expansion to large formation (𝑎 = 400 m) over 22 hr
→ Free drift for 26 hr
→ Contraction from large to small over 22 hr
→ Collision avoidance maneuver
→ Free drift for 26 hr
Deputy 3
Deputy 1
Deputy 4
Deputy 2
Chief
III.A) Formation Dynamics
1st Observation
cycle
2nd Observation
cycle

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal Angles
5. Sky access
III.A) Formation Dynamics

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• Metrics:
1. Drift
2. Drift rate
3. Deformation & Tilt
4. Internal angles
5. Sky access
Evolution, Patterns,
(A)symmetries
III.A) Formation Dynamics
Using these metrics to identify patterns,
symmetries, their evolution in time to
understand how it translates to a good
synthesized image and optimize them.
We are also using the metrics to detect
off nominal situations and conditions.

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V
U
W
• Image quality depends:
• # sample points
• Formation dynamics
• Baseline determination accuracy
• Baseline not available
• Measurement chain
[Kraus et al., 2014]
Baseline
III.Formation Concept & Performance

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V
U
W
• Measurement chain
• Reference point inside telescopes: Baseline (5 µm)
• Ranging measurement ℓ
• Lever arm 𝒓 𝟏, 𝒓 𝟐
• Relative attitude 𝜽 𝟏, 𝜽 𝟐
baseline
Ranging measurement ℓ
Baseline
𝒓 𝟐𝒓 𝟏
relative positioning
estimation model
+ Δℓ
+ 𝜽 𝟏 + 𝜽 𝟐
𝜽 𝟐
𝜽 𝟏
+ 𝒓 𝟏 + 𝒓 𝟐
Baseline
III.B) Relative Positioning

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• Mechanical stability - Lever arm
• External: thermal microdistrotions (solar flux)
• Internal: microvibrations (reaction wheels), thermal
 Solution: Precise modeling & calibration
• Accuracy - ranging measurement / relative attitude
 Solution: Maturing of technology
IV.IRASSI Technical Challenges
baselineBaseline
𝒓 𝟐𝒓 𝟏
𝜽 𝟐
𝜽 𝟏
Ranging measurement ℓ
baselineBaseline
𝒓 𝟐𝒓 𝟏
𝜽 𝟐
𝜽 𝟏
Ranging measurement ℓ

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• Summary
• Formation flying:
• Continuously changing baselines
• Formation geometry independent of formation size
• Metrics to understand formation dynamics
• Technical challenges:
• Better modeling and mature technology required to meet science
goals  solutions investigated.
V. Summary & Future Work

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• Future Work
• Formation flying:
• Integrate (optimized) reconfiguration maneuvers based on
science performance
• Collision avoidance and escape maneuvers
V. Summary & Future Work

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Questions?
Thank you for your attention!

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Additional
Information

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• Constellation of 5 spacecraft
• Halo-orbit around L2 (Sun-Earth/Moon system)
• Operational lifetime: 5 years
The IRASSI Mission
High-level Requirements
Telescope mirror size 3.5 m
Formation configuration
Freeflying in
3D
Observed wavelength (λ) 50 – 300 µm
Frequency range 1 – 6 THz
Angular Resolution 0.1 arcsec
Telescope pointing accuracy
(APE)
0.4 arcsec
Baseline knowledge accuracy 5 µm
Sun
L2
Earth
Sun-Earth line
Deputy
Chief

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• Dimensions
• Length = 5.5 m
• Radius = 3 m (sunshield)
• Primary mirror diameter = 3.5 m
• Mass and Power Budget
• Wet mass  2402 kg
• Power peak  1780 W
The IRASSI Mission

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• Mission Phases
Phase Duration
Pre-launch 8 hours
Launch 25 minutes
Deployment of Spacecraft 12 hours
Transfer to L2
90 – 120 days
Activation & Initial Formation 3 days
Subsystem & Payload Commissioning 30 days
Nominal Operations:
• Formation Reconfiguration
• Formation Pointing
• Scientific Observations
• Calibration
• Uplink/Downlink
• Station-keeping
5 years
(12 hours)
(6 hours)
(22 hours)
(4 hours)
(4 hours)
Impulsive, once per orbit
1 Observation
cycle  48 hours
5 years  900
Observation cycle
Nominal Operations

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• Data Rates:
• Each spacecraft generates 64 Gbps (uncorrelated)
• Spacecraft – Ground
o ≈ 260 Gb/day (worst case after correlation)
o 4 hours: 18 Mbps (Ka-band, 26 GHz)
• Spacecraft – Spacecraft:
o High data rate: same ranging laser link (distribution of science data)
o Low data rate: 2 omni X-band antennas (collision avoidance and
distributed clock)
Nominal Operations

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Navigation Concept
• Absolute Positioning
• Earth-based tracking and navigation (DSA):
• Range 𝜌, range-rate ሶ𝜌 and Delta-DOR
• Square Root Information Filter (SRIF) for orbit
determination (𝜌, ሶ𝜌)
• Simulation data
• SPICE Toolkit & Matlab
• Dynamic model: SRP, gravitation acceleration major
bodies
DSA 1
New Norcia, Australia
DSA 2
Cebreros, Spain
DSA 3
Malargüe, Argentina

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Navigation Concept
• Absolute Positioning - Results

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Navigation Concept
• Relative Positioning
• Geometric approach (snapshot)
• 15 variables to be estimated ( 𝑖, 𝑖, 𝑖)
• Step 1: transform distance measurements to the
telescope ref. (𝜃𝑖, 𝑖)
• Step 2: define local ref. frame (6 DOF resolved)
• Step 3: trilateration (9 DOF resolved)
Deputy 3
Deputy 1
Deputy 4
Deputy 2
Chief

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Navigation Concept
• Relative Positioning
• Geometric approach (snapshot)
1. True trajectories of satellites are generated (GMAT)
(true satellite positions, true ranging sensor positions and true
baselines)
2. Measurement errors added
3. Relative positioning estimation:
i. Transformation
ii. Trilateration
4. Comparison between computed and true
baselines
Error assumptions
Measurement error 1 µm
Attitude error Normal distribution, µ = 0, σ = 0.4 arcsec
Angular measurement error
(ranging system)
Normal distribution, µ = 0, σ = 0.1 arcsec
Lever arm error 0 µm

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• Relative Positioning - Results
- With transformation
Navigation Concept
baselineBaseline
𝒓 𝟐𝒓 𝟏
𝜽 𝟐
𝜽 𝟏
Ranging measurement ℓ
Error assumptions
Measurement error 1 µm
Attitude error Normal distribution, µ = 0, σ = 0.4 arcsec
Angular measurement error
(ranging system)
Normal distribution, µ = 0, σ = 0.1 arcsec
Lever arm error 0 µm

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• Relative Positioning - Results
- Without transformation
Navigation Concept
Error assumptions
Measurement error 1 µm
Attitude error Normal distribution, µ = 0, σ = 0.4 arcsec
Angular measurement error
(ranging system)
Normal distribution, µ = 0, σ = 0.1 arcsec
Lever arm error 0 µm
baselineBaseline
Ranging measurement ℓ

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IRASSI Technical Challenges
• Relative positioning estimation – Baseline
• Real-time solution
• BUT sensitive to outliers
 Solution: Extension with a dynamical model for
robustness
baselineBaseline
𝒓 𝟐𝒓 𝟏
𝜽 𝟐
𝜽 𝟏
Ranging measurement ℓ