ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER

ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITERFederico Zuiani

Alison Gibbings, Daniel Novak, Cesar Martinez, Francesco RizziSpace Advanced Research TeamDept. of Aerospace EngineeringUniversity of Glasgow, UK

IAC-2010 – 40th Student Conference

04/19/2023

S P A C E A R TSpace Advanced Research Team

Agenda

Orbit Determination

Navigation Analysis

Baseline Option

RemarksBackground on ESMO

ESMO

NAVIG

ATION

ANALYSIS &

MAN

OEU

VRES DESIG

N04/19/2023

● 2


BA

CK

GR

OU

ND

European Student Moon Orbiter (ESMO)Fourth mission within ESA’s Education Office Satellite Programme

Over 200 UG/PG students from 19 universities in 10 countries are currently participating in the ESMO mission

First student-designed microsatellite mission to the moonSpaceART is the lead team for both Mission Analysis, Flight Dynamics subsystems

Successfully completed Phase A Feasibility Study, proceeding with preliminary design activities in Phase B

04/19/2023

● 3


2009 Baseline for Mission Analysis

Launch window anytime between 2011-2012ESMO would be injected into a GTOAll-day-launch requirement

Final operational orbit: Highly elliptical, inclined lunar polar orbitrperi = 250 km, rapo = 3600 kmUncontrolled stability requirement of minimum 6 months

Low ∆v WSB transfer with multi-revolutions departure from Earth

Requirement on max ∆v ≤ 1.35 km/s4x bi-propellant engines with thrust of 22 N and Isp of 285 s

BA

CK

GR

OU

ND

04/19/2023

● 4

Multi-revolution WSB transfer in Earth centred, equatorial reference frame


New Baseline Requirements

ProblemCut down the nominal Dv budget to below 1 km/s

Estimate the required OD accuracy to reach the Moon and be captured into an orbit with a lifetime of 6 months

Devise a navigation and trajectory control strategy to reach the Moon and be captured into an orbit with a lifetime of 6 months.

Extended 1 month parking orbit before Trans Lunar Injection (TLI)

Proposed SolutionDv savings at the Earth is not possible without making operations more complicated (e.g. with a swing-by of the Moon)We started the analysis from the Moon, going backwardOD analysis first, because if we do not know where we are, we do not know where we are going

BA

CK

GR

OU

ND

04/19/2023

● 5


Sensitivity of Lunar Orbit to LOI errors

Random errors were introduced into the Keplerian orbital elements after the injection manoeuvre

Error values ranged from 1%-5% of nominal valueOrbit was propagated forward for a maximum of 6 months using STK

OR

BIT

DE

TE

RM

INA

TIO

N

Perilune lifetime with 1% error on initial orbital elements Plot showing effect of errors for 10 sample orbits For 1% error, max

lifetime reduction of lunar orbit of 20 days

For 5% error, max lifetime reduction of lunar orbit of 90 days

Error of 1% is an acceptable compromise between mission objectives and orbit determination requirements

04/19/2023

● 6





Plot showing effect of errors for 10 sample orbits For 1% error, max

lifetime reduction of lunar orbit of 20 days

For 5% error, max lifetime reduction of lunar orbit of 90 days

Error of 1% is an acceptable compromise between mission objectives and orbit determination requirements

OR

BIT

DE

TE

RM

INA

TIO

N

Perilune lifetime with 5% error on initial orbital elements

04/19/2023

● 7





For 1% error case: Relative error in position and

velocity projected along radial, transversal and out-of-plane reference frame Origin represents the

nominal solution Relative to Earth to show the

required OD capabilities of ground stations

OR

BIT

DE

TE

RM

INA

TIO

NVELOCITY

POSITION

04/19/2023

● 8


Capture Corridor

Data from 1% error case was used to define a region in the state space (position and velocity) at different times prior to lunar orbit insertionThe region, or corridor, defines the set of positions and velocities that ESMO must have at Δt prior to LOI to be correctly captured at the MoonDisplacements in position δr and velocity δv were randomly generated within a given range

The perturbed state vector [r, v] was then propagated backward for Δt

OR

BIT

DE

TE

RM

INA

TIO

N

r

h

t

v

Nominal trajectory

dr

dv

r

h

t

v

Nominal trajectory

drdv

Corridor at tinsertion--Dt

r-h plane

r

r

04/19/2023

● 9

r-h plane


Position and Velocity Dispersion

10000 perturbed state vectors were propagated backwards for: one week, two weeks and up to the WSB point (farthest point from the Earth)Max error of magnitude: δr ± 5 km and δv ± 10 m/s

OR

BIT

DE

TE

RM

INA

TIO

N04/19/2023

● 10


Position and Velocity Dispersion

10000 perturbed state vectors were propagated backwards for: one week, two weeks and up to the WSB point (farthest point from the Earth)Max error of magnitude: δr ± 5 km and δv ± 10 m/s

OR

BIT

DE

TE

RM

INA

TIO

N04/19/2023

● 11


OD Accuracy Requirements

Trajectories corresponding to the curl will not reach the WSB region and do not represent feasible transfersCorridor tends to be thinner in the normal and transversal directions while it seems to stretch along the radial directionNote, listed accuracies in position are particularly conservative compared to generated results

100% margin was applied to account for current state of maturity of the project.

Orbit determination accuracy requirements

Position Velocity

25 km, radial (range) 5 m/s, radial (range rate)

10 km, along track 1 m/s, along track

10 km, out of plane 1 m/s, out of plane

OR

BIT

DE

TE

RM

INA

TIO

N04/19/2023

● 14


Trajectory Correction ManoeuvresBased on corridor analysis, a series of Trajectory Correction Manoeuvres (TCM) can be inserted along the transfer after each orbit determination segment

TCMs ensure ESMO’s position and velocity remain within the trajectory corridor, with the action of each TCM to reach the nominal reference trajectory

The orbit determination process was initially simulated using the ODTK package Now we are testing an in-house Uncented Kalman FilterSources of errors used in analysis:

Trans-lunar injection burn Typical dispersion errors of the launcherError in each major Δv manoeuvres of 1 m/s (3s) in every directionError in each TCM of 0.1 m/s (3s) in every direction

First OD segment assumed to occur at +1 week from TLI, and lasts for 3 days

04/19/2023

● 15

NA

VIA

TIO

N S

TR

AT

EG

Y


Example of OD+TCM Strategy

04/19/2023

● 16

NA

VIA

TIO

N S

TR

AT

EG

Y

OD #1 19–22 Mar 2011

TCM #1 22 Mar 2011∆v = 20.9 m/s

OD #2 2–5 Apr 2011

TCM #2 15 Mar 2011∆v = 0.6 m/s

OD #3 19–22 Apr 2011

TCM #3 24 Apr 2011∆v = 0.1 m/s

TCM #4 26 Apr 2011∆v = 51.5 m/s

WSB Trajectory in Earth-centred, Earth equatorial system

Total nominal Δv = 1.1257 km/s


Example of OD+TCM Strategy

04/19/2023

● 17

NA

VIA

TIO

N S

TR

AT

EG

Y

• 8 TCM’s strategy: situation at 1w from LOI


Methods to Reduce Δv

Changes to the lunar orbit were first made by increasing the apolune altitude

All other orbital elements were kept to the existing baseline, with the altitude of perigee constrained to 100 km to comply with initial NAC requirement

The higher the apolune altitude, the quicker the orbit decayed:10000 km orbit decayed in 4 months20000 km orbit decayed after 55 days56000 km orbit decayed under 30 days

04/19/2023

● 18

NE

W B

AS

EL

INE

OP

TIO

N


Frozen ‘Ely’ Orbits

High eccentric frozen orbits offer substantial savings in Dv with long term uncontrolled orbit lifetime [Ely T, Lieb E, Constellations of Elliptical Inclined Lunar Orbits Providing Polar and Global Coverage, The Journal of the Astronautical Sciences 54(1), 2006]

High eccentric frozen orbits only occur under fixed conditions of argument of periapsis (ω = 90º or 270º) and inclination (i ≥ 39.2º)

The argument of perilune ω = 270º was selected to comply with the mission payload requirements offering perilune over the South Pole

Three test cases were propagated forward for 6 months, accounting for:3rd body effects from Earth and SunMoon’s gravitational force, using 20th degree, 20th order gravitational model (LP165P)

04/19/2023

● 19

NE

W B

AS

EL

INE

OP

TIO

N


Frozen Orbit Propagation Mission Δv considered more important than NAC resolution requirement (zp ≤ 100 km)

Good compromise between ∆v and image resolution can be obtained based on Case 2 with a slightly lower perilune altitude

Frozen orbits are sensitive to orbital injection RAAN and injection date

New frozen orbit with adapted WSB transfer and LOI gives a total mission Δv of 0.869 km/s

Total savings of 0.247 km/s over previous baseline

04/19/2023

OLD Baseline with nominal RAAN 100°

NE

W B

AS

EL

INE

OP

TIO

N

Case 1: Δv = 0.947 km/s, zp ≤ 100km only after day 145

NEW Baseline

Case 2: Δv = 0.849 km/s, min(zp) > 100 km

Case 3: Δv = 0.948 km/s, zp ≤ 100km


Frozen Orbit Stability Assessment04/19/2023

NE

W B

AS

EL

INE

OP

TIO

N

Objective: describe stability behaviour of arrival orbit according to RAAN

and arrival date to derive constraint on arrival condition for WSB

trajectory optimization.

Orbit propagated for 6 months for multiple values of RAAN and TLOI .

Example: Stability assessment for a nominally unstable arrival orbit.

RAAN range: [0, 180°]

TLOI range: [Tnominal-16days, Tnominal+16days]

Result: constraints could be introduced in the trajectory optimization

process.


Frozen Orbit Stability04/19/2023

NE

W B

AS

EL

INE

OP

TIO

N

RAAN -16 -14 -12 -10 -8 -6 -4 -2T(0) Days 2 4 6 8 10 12 14 16

0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1

40 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1

0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1

50 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1

0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1

60 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1

1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1

70 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1

1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1

80 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1

1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1

90 1 1 1 1 1 1 1 10*O 0 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0

100 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0

110 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

120 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

130 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

140 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

150 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

160 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

170 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

180 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


Extended 1 month parking before TLI

Using a MBS offers higher launch date flexibility, a reduction of the gravity losses per manoeuvre and an expected reduction of the navigation ∆vBut for 1 month MBS adds 47.2 m/s to the total cost of the transfer compared to a single direct injection burn from GTO into the WSB transfer

Due to increase in perturbing effects of atmospheric drag, J2 and 3rd body effects

04/19/2023

Earth spirals occurring during the multi-burn strategy

NE

W B

AS

EL

INE

OP

TIO

N

Direct: [1xGTO, 1xWSB, 1xLOI] ∆vtot = 869 m/s, mission length: 100 days

MBS: [4xGTO, 1xWSB, 2xLOI] ∆vtot = 916 m/s, mission length: 133 days


Direct transfer versus multi-burn strategy04/19/2023

NE

W B

AS

EL

INE

OP

TIO

N

With Multiburn Strategy

T0 (launch) [MJD2000] 4408.24

ManoeuvreEarth leg

5 (WSB)Moon leg

Total1 2 3 4 (TLI) 6 (LOI) 7

Time Interval[days] 0.44 1.20 27.95 0.42 40.76 59.14 3.92 133.81

T [MJD2000] 4408.68 4409.88 4437.83 4438.24 4479.00 4538.14 4542.06

DeltaV [m/s] 395.26 228.58 22.74 146.20 28.71 75.17 20.20 916.88

Without Multiburn Strategy

T0 (launch) [MJD2000] 4438.24

Manoeuvre TLI WSB LOI Total

Time Interval[days] 0 40.76 59.15 99.91

T [MJD2000] 4438.24 4479.00 4538.15

DeltaV [m/s] 748.40 28.71 72.22 869.33


Direct transfer versus multi-burn strategy

Total cost of the new nominal solution is 916.9 m/s, against the nominal 1116.29 m/s of the previous baseline, leading to a savings of 199.4 m/s

04/19/2023N

EW

BA

SE

LIN

E O

PT

ION


Ground Station Access

3 different ESA Ground stations have been considered: Malindi, Perth, Villafranca.

04/19/2023N

EW

BA

SE

LIN

E O

PT

ION

Ground Station Malindi Perth Villafranca

Min Access Time [secs] 11135.20 20086.70 8257.91

Max Access Time [secs] 47501.47 52555.14 48829.88

Mean Access Time [secs] 42284.18 42323.53 42439.74

Total [days] 65.0902 65.6407 65.3297

Daily average [hrs] 11.6745 11.7732 11.7175


Ground Station Access

The combination of the three Ground Stations guarantees sufficient adequate time.

04/19/2023N

EW

BA

SE

LIN

E O

PT

ION


Multiburn Strategy: errors on manoeuvres

Objective: determine error on final state due to errors on thrust level and attitude.First manoeuvre was analysed:

Largest, ∆V~400 m/sFirst to be performed, thruster calibration errors possible.

Methodology:Nominal thrust profile is perturbed with a Gaussian error.Manoeuvre is numerically propagated and error on final state is calculated.

04/19/2023N

EW

BA

SE

LIN

E O

PT

ION


Multiburn Strategy: errors on manoeuvresFirst Manoeuvre

Thrust time [sec] Thrust Magnitude [N] Total DeltaV [m/s]

831.3023 88 403.9

04/19/2023N

EW

BA

SE

LIN

E O

PT

ION

Errors on Thrust Vector (3σ for Normal distribution)

Modulus Azimuth Elevation

1 N 1 deg 1 deg

Errors on final state

Position Velocity

Total Relative error [%]

Total error [m/s]

Total Relative error [%]

Relative error on modulus [%]

Error on angle [deg]

Mean 0,0045 0,6783 0,0065 0,0028 0,0031

Variance 4,29E-08 0,0001 1,03E-07 4,06E-08 3,60E-06

Min 0,0002 0,0351 0,0003 1,13E-05 4,94E-05

Max 0,0132 2,1573 0,0206 0,0098 0,0117


2014-2015 Launch Window

Previous launch window for 2011-2012 has been shifted to 2014-2015.

SpaceART’s database is currently being updated to meet new requirement.

Given the periodicity of Earth-Sun-Moon system the basic structure of the

WSB transfer remains unchanged.

Work is in progress on refining and adding solutions.

04/19/2023N

EW

LA

UN

CH

WIN

DO

W


2014-2015 Launch Window04/19/2023

NE

W L

AU

NC

H W

IND

OW

T0 [MJD2000] TF [MJD2000] Lunar Orbit. Semimajor axis Total cost [m/s]

5183.32 5276.52 Proposed operational orbit at least 10864 km 929.93

5524.95 5631.97 Stable at 10084 km (as per baseline) 934.15





5146.69 5248.75Proposed operational orbit at least 10869 km

1086.42




ConclusionsFirst analysis of the orbit determination requirements and a possible navigation strategy for the European Student Moon OrbiterProposed corridor-targeting approach yields good results at a relatively low Dv cost and with mild orbit determination accuracy

Ideal for a small satellite missions with low ∆v budget

Navigation cost can be further optimised if the size of major manoeuvres is reduced.MBS will fraction the TLI manouvre into several revolutions leading to a reduction of the magnitude of the TCM’s

Future work will address the optimisation of the TCM’s and an orbit determination process tailored to ESMO

This research is partially supported by Surrey Satellite Technology Ltd (SSTL), with thanks to:

Mark Taylor at SSTLDr. Paolo De Pascale at the European Space Operation CentreThe Space.ART MIAS/FD team, which has involved over 20 students since 2006

04/19/2023ESM

O N

AVIGATIO

N AN

ALYSIS & M

ANO

EUVRES D

ESIGN


Recommendations

Do not put the task of writing formal documentation on us (the Universities)It requires a lot of supervision time, the students are unhappy, you are unhappy, the students learn that space/ESA/Industry is only a matter of bureaucracy

It is impossible to achieve the goals of this type of mission only with undergrad students

They are discontinuous, unreliable and require a lot of supervision work beyond the normal supervision time of an academicHowever, the cost of a PhD is ½ of the cost of a YGT and 1/n of a ESA/SSTL staff, therefore consider PhD students as an asset to complete ESMO successfully

Do not trust anyone who says that student time comes for freeEither he/she supports slavery or he/she is lying

When we ask for technical support, please do not charge us at the same rate you would charge ESA.

04/19/2023ESM

O N

AVIGATIO

N AN

ALYSIS & M

ANO

EUVRES D

ESIGN

Documents

ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER