Contents lists available at SciVerse ScienceDirect

Acta Astronautica

Acta Astronautica 82 (2013) 137–145

0094-57

http://d

n Corr

E-m

journal homepage: www.elsevier.com/locate/actaastro

Formation flying and mission design for Proba-3

Markus Landgraf a,n, Agnes Mestreau-Garreau b

a ESA/ESOC, Robert-Bosch-Str. 5, 64293 Darmstadt, Germanyb ESA/ESTEC, Keplerlaan 1, PO Box 299, 2200 AG Noordwijk ZH, The Netherlands

a r t i c l e i n f o

Article history:

Received 22 December 2011

Received in revised form

13 March 2012

Accepted 29 March 2012Available online 15 June 2012

Keywords:

Proba-3

ESA

Mission design

Formation flying

Demonstration

65/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.actaastro.2012.03.028

esponding author.

ail address: Markus.Landgraf@esa.int (M. Lan

a b s t r a c t

The Proba-3 mission is an ambitious European mission to test the design, implementa-

tion and operation of a two-spacecraft formation flying system with a high degree of

autonomy with a launch foreseen in the 2015/2016 time-frame. It comprises two

spacecraft, the coronagraph and the occulter, which are to be inserted into a highly

elliptical orbit. It is intended to perform the formation flying demonstration around the

apogee and use the perigee pass for telemetry, orbit determination, orbit correction, and

formation configuration manoeuvres. The design of the target orbit is driven by the

minimisation of disturbances to the spacecraft formation, and is constrained by the

rather low Dv capability of the spacecraft of less than 100 m s�1 as well as the

characteristics of the selected launch vehicle. The secondary mission objective of

Proba-3 is to operate the formation as a coronagraph with one spacecraft being the

occulter and the other carrying the optics and detectors. The alignment of the formation

with the Sun-direction has as a consequence that the geometry of the formation relative

to the orbit is prescribed for the perigee pass. This geometry also determines the

relative dynamics of the formation. The relationship between formation configuration

and orbital parameters is typical for formation flying missions on elliptical orbits and

requires a careful choice of the launch time such that the constraints on the angle

between the Sun-direction and the orbital plane are fulfilled. Here we present the

design of the operational orbit and transfer phase of Proba-3 together with an analysis

of the separation, formation acquisition, and target formation maintenance. Also the

benefit of available tracking data for contingency situations in the Proba-3 missions is

discussed.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background

The Proba-3 mission is an experimental mission ofthe ESA GSTP programme (general support technologyprogramme) dedicated to the demonstration of newtechnologies and techniques related to high precisionformation flying. Through Proba-3, technologies relevant

ll rights reserved.

dgraf).

for future formation flying missions will be developedto flight level and tested in orbit. This includes GNCalgorithms and formation management methods, metrol-ogy systems, communication links, operational methods,etc. The development and validation of engineeringapproach, ground verification tools and facilities requiredby formation flying will also be developed.

Proba-3 consists of a space segment, a ground segmentand a launch service, with a mission lifetime of two yearsand a launch around 2015–2016. The space segment con-sists of two small satellites launched into high ellipticalorbit to demonstrate formation flying with high precisionand to characterise sensors and other related technologies.

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145138

The ground segment includes the flight operations and theexploitation part.

Proba-3 will demonstrate formation flying in thecontext of a giant (150 m) solar coronagraph scienceexperiment. The main purpose of the Proba-3 coronagraphguest mission [1] is to provide a realistic science missioncase for the formation flying demonstration. In this way ademonstration with the full complexity of a full sciencemission is performed, including aspects such as timing,calibration, alignment, science data handling and delivery.The result of this part of the mission can be appreciated interms of scientific return.

The project is an ESA mission. It has seen a certainamount of evolution with changing mission designs [2].As an ESA project it is currently in phase B and is lead by aconsortium of industrial companies in several ESA mem-ber states.

1.2. Mission objectives

The overall mission objective is to perform the in-orbittechnology demonstrations and proof of concept forma-tion flying demonstrations to build sufficient confidencein the European space industry in order to embark onfuture missions based on formation flying.

Given this overall mission objective the purpose of themission can be divided in the following four categories:

�

Formation flying demonstration: The primary objectiveof Proba-3 is to demonstrate formation flying withhigh precision and to demonstrate it for future forma-tion flying missions. � Equipment qualification: Precision formation flying and

efficient use of propellant calls for technology devel-opment in metrology, e.g. RF metrology systems andhigh accuracy optical metrology systems. The Proba-3mission will demonstrate these technologies.

� Development, design and validation principles for forma-

tion flight: The distributed character of formationflying systems calls for new development, design,implementation and validation principles. Proba-3 willcontribute towards the establishment of these principles,and the development of required tools.

� Guest payload: In addition to the formation flying experi-

ments and demonstrations a scientific guest payload willbe flown—a large (length about 150 m) solar coronagraphinstrument distributed over the formation. Using theProba-3 generic formation flying capabilities, the forma-tion flying of this distributed single virtual instrument willconstitute a convincing demonstration of formation flyingin addition to provide scientific mission return.

2. Mission design

2.1. Orbit selection

For the orbit selection the relevant mission require-ments have to be considered. In general orbits far fromgravity sources are ideal for formation flying mission dueto the low gravity gradient environment. Also a constant

or little varying Sun–Earth geometry would be beneficial.Depending on the scope of the mission such an environ-ment is presented by the libration points of the Sun–Earththree body problem. For a Sun observer the co-linear day-side libration point L1 would be ideal. However, due to thelimited scope of the Proba-3 mission, the orbit selection isfinally driven by the capability of the launcher, so that themaximisation of the mass into final orbit following alaunch by a small to medium sized launch vehicle is thedriving requirement for the orbit selection.

The orbit selection for the operational phase is thus acompromise solution, which is required to minimise thedetrimental effects of a near-Earth environment. Such acompromise solution is a highly elliptical orbit (HEO), whichprovides a benign environment at the apogee and still can bereached by small or medium launchers with a sufficientpayload mass. The inclination of that HEO will be prescribedby the constraints of the selected launch vehicle. Whatremains to be determined are the apogee and perigeealtitudes. The right ascension of ascending node can bechosen freely by selecting the lift-off time. Here we reportthe status of the orbit selection at the start of phase-B. Forthe launch vehicle the European VEGA launcher and theIndian PSLV have been studied as suitable candidate launchvehicles. Here we will focus on the latter option for brevity.The maximum performance departure trajectory of the PSLVdelivers the spacecraft into a HEO with an inclination of17.81. For the PSLV also the argument of perigee is prescribedto be equal to 1801. The initial perigee altitude is 300 km.Another driver for the orbit selection is the ground-stationavailability. It is assumed here that the available ground-station for Proba-3 is the ESA station Redu at the geocentriccoordinates 50.0011N, 5.1451E. In order to achieve visibilityof the apogee (the latitude of which is 01 due to theprescribed argument of perigee), the initial longitude of theapogee must be chosen to be close to the longitude of theRedu station and also the orbital period must be chosen tobe commensurate with the Earths sidereal day of 86,164 s.

In phase-A a number of options for the HEO werediscussed and the current baseline for the HEO calls for ageo-synchronous orbit, i.e. an orbital period of exactly86,163 s. This requires a semi-major axis of 42,164 km.The perigee altitude shall be chosen as small as possible inorder to minimise the size of the perigee raising man-oeuvres in transfer. The minimum value is however by therequirement to avoid reentry into the Earth’s atmosphereunder luni-solar perturbations during the required missionlifetime of two years. For this minimum a value of 800 kmwas found. Given the semi-major axis and perigee altitudethe apogee altitude can be calculated to be 70,786 km. Theright ascension of ascending node is calculated such that thelocal time of the apogee and the Redu station are identical inthe middle of the mission given the drift of the node due tothe oblateness of the Earth. The orbit of Proba-3 during theoperational phase is visualised in Fig. 1. A summary of thebaseline orbit for Proba-3 is given in Table 1.

2.2. Transfer

Two objectives must be met in the transfer: (a) thelongitude of the apogee must drift from its prescribed initial

longitude [°]

latit

ude

[°]

−150 −100 −50 0 50 100 150

−80

−60

−40

−20

0

20

40

60

80 initial orbitafter one yearafter two years

Fig. 1. Ground-track of the operational orbit of Proba-3 at the beginning of the operational phase (red), after one year of operations (black) and after two

years of operations (green). (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)

Table 1Orbital parameters of Proba-3 baseline orbit (PSLV option).

Parameter Value

Semi-major axis 42,164 km

Eccentricity 0.8299

Perigee altitude 800 km

Apogee altitude 70,786 km

Orbital period 86,164 s

Inclination 17.81

Right ascension of ascending node Depends on launch epoch

Argument of perigee 1801

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145 139

value after injection by the launcher to the required value,which is chosen to be such that at the mid-time of themission the local time of the Redu station and the apogeematch, and (b) the perigee must be raised to 800 km altitude.This is achieved by initially selecting a sub-synchronoussemi-major axis and performing an apogee-raising man-oeuvre to achieve the target apogee altitude of 70,786 kmfollowed by a perigee-raising manoeuvre to achieve thetarget perigee altitude of 800 km, thus achieving the geo-synchronous semi-major axis of 42,164 km. The ground-trackof the baseline four-manoeuvre transfer is illustrated in Figs.2–5. It can be seen that the apse line drifts once around theEarth until the geo-synchronous condition is reached atthe end of the transfer such that the apogee is located atthe target longitude as discussed in Section 2.1. The details ofthe transfer design are not discussed here for brevity. Table 2summarises the apogee raising manoeuvres. The apogeeraising phase is followed by a perigee raising manoeuvre ofto increase the perigee from 600 to 800 km. This concludesthe transfer. The total transfer Dv budget amounts to88.3 m s�1, which comprises the apogee raising manoeuvres,the perigee raising manoeuvre, launcher dispersion, and 10%margin.

2.3. Ground-based navigation

Like for Proba-2 (see [3]), the nominal mode of orbitnavigation for Proba-3 is the use of GPS data that arecollected on-board around the perigee passes (where theGPS signal is available). As Proba-3 is a technology demon-stration mission, it is envisaged to validate this approach bydetermining the orbit also by more classical means, i.e. byradiometric measurements. These measurements could alsobe used to substitute the GPS navigation system in case of acontingency. It should be noted that his remark refers to theorbit navigation. Relative navigation was base-lined at thestart of phase-B to be a dedicated formation-flying radiofrequency navigation system.

An analysis was performed to determine the evolutionof knowledge of orbital position and velocity. This analysiswill allow determining whether the formation could bere-established in case of a contingency purely from ground-based data. It was assumed that the spacecraft position wasinitially known to within 100 km (i.e. the knowledge is worsethan the proximity needed for formation flying, which is30 km) and the spacecraft velocity to within 1 m s�1. NoDoppler measurements were considered, but ranging mea-surements every 20 min during visibility (assuming a mini-mum elevation of 101) from either the Redu or the Hawaiiground-station. For this analysis actually another orbit thanthe one discussed in Section 2 was assumed: A commensu-rate 17:14 orbit that provides 17 revolutions in 14 days, andwhich has an inclination of 501. The advantages of this orbitare lower Dv requirement and less radiation exposure. Thenavigation analysis should however also be applicable to thegeo-synchronous orbit described in Section 2.

Of particular interest is the knowledge at a trueanomaly of 1201, at which point the formation shouldbe restored. The following plot shows the measurementstaken by the Redu and Hawaii stations during the 14-dayreference period.

longitude [°]

latu

ityde

[°]

−150 −100 −50 0 50 100 150

−80

−60

−40

−20

0

20

40

60

80

Fig. 2. Transfer trajectory starting at injection just south of Java. The first apogee raising burn is performed at the seventh perigee pass.

longitude [°]

latu

ityde

[°]

−150 −100 −50 0 50 100 150

−80

−60

−40

−20

0

20

40

60

80

Fig. 3. Transfer trajectory stating at the first apogee-raising burn. The second apogee raising burn is performed at the fourth perigee pass after the

first burn.

longitude [°]

latu

ityde

[°]

−150 −100 −50 0 50 100 150

−80

−60

−40

−20

0

20

40

60

80

Fig. 4. Transfer trajectory stating at the second apogee-raising burn. The third apogee raising burn is performed at the fourth perigee pass after the

second burn.

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145140

In Fig. 6 the ranging measurements from the twoground-stations are shown together with the timesof passage through the 71201 points in true anomaly

(green vertical lines). Together the two ground-stationsprovide quite good coverage of the full orbit, at leastaround apogee. The drift of the apogee in longitude is

longitude [°]

latu

ityde

[°]

−150 −100 −50 0 50 100 150

−80

−60

−40

−20

0

20

40

60

80

Fig. 5. Transfer trajectory stating at the third apogee-raising burn. The fourth and final apogee raising burn is performed at the fourth perigee pass after

the third burn.

Table 2Summary of apogee raising manoeuvres.

Man.

#

Perigee

#

Time from inj.

(days)Dva

(m s�1)

Burn duration

(s)

1 7 5.90 24.3 60.4

2 11 9.48 13.5 33.3

3 15 13.20 15.0 36.7

4 19 17.09 9.5 23.1

a Including gravity loss.

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145 141

reflected in the shift of the ranging availability from thestations.

Fig. 7 shows the position knowledge that can beachieved with the ranging-only measurements as a func-tion of the 14-day reference period. The horizontal reddashed line indicates the 30 km requirement for forma-tion acquisition and the vertical green solid lines thepassage through 71201 of true anomaly.

It can be seen that the position knowledge is regainedwithin one orbit to better than 1 km (square-root sum ofall components) on a 3s confidence level. It can beobserved how the knowledge worsens during periods ofnon-availability of data. The knowledge is in first ordernot associated with the orbital phase (i.e. true or meananomaly or time). Like the position knowledge also thevelocity knowledge is recovered quickly, as can be seen inFig. 8.

3. Formation flying design

3.1. Separation

For Proba-3 the separation of the two formation flyingspacecraft will be the first task in formation flying. Variousanalyses on the dynamics of the problem have beenpublished in this respect (e.g. [4]). After separation fromthe stack (to occur in the target orbit described in Section 2)the formation flying payload will need to be commissionedand is therefore not yet available for control of the forma-tion. Therefore, a free drift relative orbit will be required in

the separation phase that avoids collision or evaporation(defined for Proba-3 as separations of more than 10 km atapogee or 100 km at perigee).

The main driver for the separation drift orbit is thedifferential solar radiation pressure acting on the spacecraft;all other forces have lower differential magnitudes due tothe low spatial separation. This drift created by differentialradiation pressure will be superimposed by the relativemotion due to the separation Dv created by the spring-loaded separation mechanism. For an initial orbit with theapse line aligned with the projection of the Sun direction inthe orbital plane the radiation pressure drift will cause arelative motion in the V-bar direction. The separation Dv

can be chosen such that the drift is minimised withoutcreating a collision risk. For the design of the spacecraftapplicable at the time of the system requirements reviewdifferential radiation pressure acceleration in the order of10�8 m s�2 can be expected, which is small compared to thevalue applicable to earlier designs. It can be shown [ref] thatfor such small differential radiation forces a separation Dv

in the order of 1 cm s�1 is sufficient, minimising the Dv

required for formation deployment.It can be seen in Fig. 9 that if the separation Dv is

chosen correctly the drift of the formation at apogee canbe limited to a few kilometres with a minimum closestapproach of about 200 m.

3.2. Acquisition

The strategy of the acquisition phase is to stop the driftof the separation phase by a manoeuvre that is located ata true anomaly of 1201. This location was chosen asa compromise between GPS data availability (aroundperigee), orbit knowledge availability (post perigee),ground-station visibility (around apogee), and Dv minimi-sation (around apogee). This is followed by a manoeuvrethat compensates the relative drift due to the differentialradiation forces until the final tandem formation isachieved, and by a two-point transfer towards the relativeposition, where a take-over by the on-board metrology

0 2 4 6 8 10 12 140

10

20

30

40

50

60

70

time [d]

rang

e [1

03 km

]

ReduHawaii

Fig. 6. Ranging measurements of Proba-3 from the Redu and Hawaii stations. (For interpretation of the references to colour in this figure caption, the

reader is referred to the web version of this article.)

0 2 4 6 8 10 12 1410−2

10−1

100

101

102

103

time [d]

3σ p

ositi

on k

now

ledg

e [k

m]

Fig. 7. Position knowledge of Proba-3 over the 14-day reference period. (For interpretation of the references to colour in this figure caption, the reader is

referred to the web version of this article.)

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145142

0 2 4 6 8 10 12 1410−3

10−2

10−1

100

101

t [d]

3σ v

eloc

ity k

now

ledg

e [m

s−1]

Fig. 8. Velocity knowledge of Proba-3 over the 14-day reference period.

Fig. 9. Drift orbit with separation Dv¼ 1 cm s�1 and an angle of the

projected Sun direction aligned with the apse line shown in the LVLH

frame with the x-axis corresponding to the V-bar and the z-axis to the

R-bar (taken from [5]). The labelled blue markers represent the relative

position of the spacecraft at apogee for 10 orbits. (For interpretation of

the references to colour in this figure caption, the reader is referred to

the web version of this article.)

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145 143

system can occur. The latter is necessary due to the limitedfield of view (751) of the optical metrology devices.

It can be seen from the relative trajectory of thecoronagraph spacecraft during the acquisition phase shownin Fig. 10 that the trajectory following the stop manoeuvrealready exhibits a reduced spacecraft separation at apogee,

as in the simulation it was assumed that the convergingdrift is simultaneously initiated with the stop manoeuvre. Asummary of the formation acquisition manoeuvres is givenin Table 3.

3.3. Target tandem formation

At the end of the acquisition phase the spacecraft are inthe target tandem formation, which is defined by the inter-spacecraft distance to be above 100 m in apogee and below1.2 km at perigee. In this tandem formation the formationflying demonstrations (metrology data acquisition) and guestscience activities will be carried out. As discussed in Section3.1 for the separation phase, the tandem formation wouldslowly drift apart due to the differential radiation pressureforces acting on the two spacecraft. This will have to becontrolled by a formation maintenance algorithm that ispreliminarily defined by the following procedure: On eachorbit (that is, each day) two manoeuvres (M1 and M2) areperformed.

�

M1 is located at true anomalies between 301 and 601.Its purpose is to target the location of M2 such thatwill be close to the origin (that is, the occulter space-craft), but it will avoid a collision, even in the event M2is not performed. � M2 is located at the apogee and is designed to reduce the

relative velocity in the R-bar direction, which is normallyexcited due to the differential radiation pressure forces.

This manoeuvre strategy requires Dv for M1 of1:2 mm s�1 per day and for M2 of 1:0 mm s�1 per day,respectively. This gives a contribution of the formation

Fig. 10. Relative trajectory in the LVLH frame from separation (red line starting at the origin) via acquisition (blue line initiated at a true anomaly of 1201,

represented by the red dots with positive z-values (R-bar)), to the tandem formation orbit (black line, taken from [5]). (For interpretation of the

references to colour in this figure caption, the reader is referred to the web version of this article.)

Table 3

Summary of formation acquisition: list of required Dv, orbit location n,

and time t since initial apogee.

Manoeuvre Dv (cm s�1) n (deg) t (h)

Separation 0a 180 0

Stop and drift back initiation 0.5 120 85

SRP drift correction 0.2 120 109

Two-point transfer man. 1 0.4 120 133

Two-point transfer man. 2 0.6 180 144

a The separation occurs with a Dv of 1 cm s�1. This is however

provided by a spring-loaded mechanism and is non-propulsive.

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145144

maintenance manoeuvres of 1:6 m s�1 to the Dv budget ofthe coronagraph spacecraft.

Regarding the safety of the tandem formation it isfound that very strong requirements have to be formu-lated for the state knowledge at apogee in order toguarantee no collision for an extended drift period in caseof a contingency. In order to avoid collisions for a 7 daydrift period on a 99% confidence level, the relative velocitymust be known better than 0:3 mm s�1.

4. Conclusion

Proba-3 is to be launched in the 2015–2016 time-frameto a HEO. As a baseline for this analysis a geo-synchronous

orbit at low inclination of 17.81 has been considered. Theorbit is chosen to provide good visibility of the apogee overthe ground-station in Redu over the mission lifetime of twoyears. The injection orbit is determined by the choice of thelaunch vehicle, here the Indian PSLV launcher is considered.Alternatively the mission could be launched on a VEGAlauncher to a moderate inclination (501), in which case apropulsion module is required to achieve the transfer to theHEO. For one of the launch option the injection orbit ischosen below the geo-synchronous condition in order to letthe apse-line drift relative to the Earth’s surface such that itcan be positioned in an optimum way for the ground-station. The baseline transfer strategy is a sequence of fourapogee-raising manoeuvres at the perigee number 7, 11, 15,and 19 followed by a perigee raising manoeuvre. The totalDv budget for the mission is below 100 m s�1. A ground-based navigation scenario with two stations (Redu andHawaii) performing permanently ranging-only measure-ments for the full visibility period leads to knowledge ofbetter than 1 km in position and 0:1 m s�1 in velocity (bothon a 3s confidence level) after an initial position knowledgeof 100 km and velocity knowledge of 1 m s�1. The improvedknowledge is clearly the result of the availability of moredata (two stations instead of one station and full visibilityperiod instead of 1 h per day). It was found that after oneorbit the position knowledge is recovered to the same leveleven if the initial knowledge is 1000 km. The amount of

M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145 145

ignorance in the initial state is therefore quickly removed onthe basis of the measurements. It is recommended toassume also the availability of Doppler data for this analysisas Doppler data is collected without extra effort in parallelto ranging data or telemetry. Another alternative navigationscenario could be the use of radar data from the STRATCOMnetwork. This would be available without a cooperatingspacecraft. For the formation flying design it is found thatthe relative dynamics are dominated by the differentialradiation pressure forces, as the occulter spacecraft has amuch lower ballistic coefficient than the coronagraph space-craft. This difference drives the initial separation velocitythat is required in order to avoid collision during theseparation phase. A low separation velocity also allowssmaller manoeuvres for the formation acquisition, whichcomprises a stop manoeuvre that stops the drift of theseparation phase, a drift initiation manoeuvre that starts thedrift of the coronagraph spacecraft back to the occulterspacecraft, and a two-point transfer to achieve the requiredgeometry at the apogee in order to start the tandemformation utilising the on-board metrology systems. Thetotal deterministic Dv required for this phase is below

2 cm s�1. Regarding the stability and safety of the tandemformation it is however found that they depend strongly onthe knowledge of the relative spacecraft state, which placesstrong requirements on the metrology system.

References

[1] P. Lamy, S. Vivs, D. Dam, S. Koutchmy, New perspectives in solarcoronagraphy offered by formation flying: from PROBA-3 to Cosmic

Vision, Proc. SPIE 7010 (2008).[2] B. Borde, F. Teston, S. Santandrea, S. Boulade, Feasibility of the Proba

3 formation flying demonstration mission as a pair of microsats inGTO, in: B. Warmbein (Ed.), Proceedings of the 4S Symposium: SmallSatellites, Systems and Services (ESA SP-571), 20–24 September

2004, La Rochelle, France, 2004.[3] O. Montenbruck, M. Markgraf, S. Santandrea, J. Naudet, GPS Orbit

Determination for Micro-Satellites. The PROBA-2 Flight Experience,AIAA 2010-8261, 2010.

[4] L. Perea, S. Damico, P. Elosegui, Relative formation flying dynamicsand control of a two-element virtual telescope on a HEO using GNSSand optical metrology, J. Guidance Control Dyn., in press.

[5] C. de Negueruela, T.V. Peeters, J. Peyrard, M. Manzano, Proba-3 PhaseB Formation Flying Mission Analysis Report, Issue 2, Revision 1,

October 2009.