- Email: [email protected]
Formation flying and mission design for Proba-3
Acta Astronautica 82 (2013) 137–145
Contents lists available at SciVerse ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Formation flying and mission design for Proba-3 Markus Landgraf a,n, Agnes Mestreau-Garreau b a b
ESA/ESOC, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany ESA/ESTEC, Keplerlaan 1, PO Box 299, 2200 AG Noordwijk ZH, The Netherlands
a r t i c l e i n f o
abstract
Article history: Received 22 December 2011 Received in revised form 13 March 2012 Accepted 29 March 2012 Available online 15 June 2012
The Proba-3 mission is an ambitious European mission to test the design, implementation 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 s1 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.
Keywords: Proba-3 ESA Mission design Formation flying Demonstration
1. Introduction 1.1. Background The Proba-3 mission is an experimental mission of the ESA GSTP programme (general support technology programme) dedicated to the demonstration of new technologies and techniques related to high precision formation flying. Through Proba-3, technologies relevant
n
Corresponding author. E-mail address: [email protected] (M. Landgraf).
0094-5765/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actaastro.2012.03.028
for future formation flying missions will be developed to flight level and tested in orbit. This includes GNC algorithms and formation management methods, metrology systems, communication links, operational methods, etc. The development and validation of engineering approach, ground verification tools and facilities required by formation flying will also be developed. Proba-3 consists of a space segment, a ground segment and a launch service, with a mission lifetime of two years and a launch around 2015–2016. The space segment consists of two small satellites launched into high elliptical orbit to demonstrate formation flying with high precision and to characterise sensors and other related technologies.
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M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145
The ground segment includes the flight operations and the exploitation part. Proba-3 will demonstrate formation flying in the context of a giant (150 m) solar coronagraph science experiment. The main purpose of the Proba-3 coronagraph guest mission [1] is to provide a realistic science mission case for the formation flying demonstration. In this way a demonstration with the full complexity of a full science mission 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 in terms of scientific return. The project is an ESA mission. It has seen a certain amount of evolution with changing mission designs [2]. As an ESA project it is currently in phase B and is lead by a consortium of industrial companies in several ESA member states.
1.2. Mission objectives The overall mission objective is to perform the in-orbit technology demonstrations and proof of concept formation flying demonstrations to build sufficient confidence in the European space industry in order to embark on future missions based on formation flying. Given this overall mission objective the purpose of the mission can be divided in the following four categories:
Formation flying demonstration: The primary objective
of Proba-3 is to demonstrate formation flying with high precision and to demonstrate it for future formation flying missions. Equipment qualification: Precision formation flying and efficient use of propellant calls for technology development in metrology, e.g. RF metrology systems and high accuracy optical metrology systems. The Proba-3 mission will demonstrate these technologies. Development, design and validation principles for formation flight: The distributed character of formation flying systems calls for new development, design, implementation and validation principles. Proba-3 will contribute towards the establishment of these principles, and the development of required tools. Guest payload: In addition to the formation flying experiments and demonstrations a scientific guest payload will be flown—a large (length about 150 m) solar coronagraph instrument distributed over the formation. Using the Proba-3 generic formation flying capabilities, the formation flying of this distributed single virtual instrument will constitute a convincing demonstration of formation flying in addition to provide scientific mission return.
2. Mission design 2.1. Orbit selection For the orbit selection the relevant mission requirements have to be considered. In general orbits far from gravity sources are ideal for formation flying mission due to 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 environment is presented by the libration points of the Sun–Earth three body problem. For a Sun observer the co-linear dayside libration point L1 would be ideal. However, due to the limited scope of the Proba-3 mission, the orbit selection is finally driven by the capability of the launcher, so that the maximisation of the mass into final orbit following a launch by a small to medium sized launch vehicle is the driving requirement for the orbit selection. The orbit selection for the operational phase is thus a compromise solution, which is required to minimise the detrimental effects of a near-Earth environment. Such a compromise solution is a highly elliptical orbit (HEO), which provides a benign environment at the apogee and still can be reached by small or medium launchers with a sufficient payload mass. The inclination of that HEO will be prescribed by the constraints of the selected launch vehicle. What remains to be determined are the apogee and perigee altitudes. The right ascension of ascending node can be chosen freely by selecting the lift-off time. Here we report the status of the orbit selection at the start of phase-B. For the launch vehicle the European VEGA launcher and the Indian PSLV have been studied as suitable candidate launch vehicles. Here we will focus on the latter option for brevity. The maximum performance departure trajectory of the PSLV delivers the spacecraft into a HEO with an inclination of 17.81. For the PSLV also the argument of perigee is prescribed to be equal to 1801. The initial perigee altitude is 300 km. Another driver for the orbit selection is the ground-station availability. It is assumed here that the available groundstation for Proba-3 is the ESA station Redu at the geocentric coordinates 50.0011N, 5.1451E. In order to achieve visibility of the apogee (the latitude of which is 01 due to the prescribed argument of perigee), the initial longitude of the apogee must be chosen to be close to the longitude of the Redu station and also the orbital period must be chosen to be commensurate with the Earths sidereal day of 86,164 s. In phase-A a number of options for the HEO were discussed and the current baseline for the HEO calls for a geo-synchronous orbit, i.e. an orbital period of exactly 86,163 s. This requires a semi-major axis of 42,164 km. The perigee altitude shall be chosen as small as possible in order to minimise the size of the perigee raising manoeuvres in transfer. The minimum value is however by the requirement to avoid reentry into the Earth’s atmosphere under luni-solar perturbations during the required mission lifetime of two years. For this minimum a value of 800 km was found. Given the semi-major axis and perigee altitude the apogee altitude can be calculated to be 70,786 km. The right ascension of ascending node is calculated such that the local time of the apogee and the Redu station are identical in the middle of the mission given the drift of the node due to the oblateness of the Earth. The orbit of Proba-3 during the operational phase is visualised in Fig. 1. A summary of the baseline orbit for Proba-3 is given in Table 1. 2.2. Transfer Two objectives must be met in the transfer: (a) the longitude of the apogee must drift from its prescribed initial
M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145
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initial orbit after one year after two years
80 60
latitude [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0
50
100
150
longitude [°] 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 1 Orbital parameters of Proba-3 baseline orbit (PSLV option). Parameter
Value
Semi-major axis Eccentricity Perigee altitude Apogee altitude Orbital period Inclination Right ascension of ascending node Argument of perigee
42,164 km 0.8299 800 km 70,786 km 86,164 s 17.81 Depends on launch epoch 1801
value after injection by the launcher to the required value, which is chosen to be such that at the mid-time of the mission the local time of the Redu station and the apogee match, and (b) the perigee must be raised to 800 km altitude. This is achieved by initially selecting a sub-synchronous semi-major axis and performing an apogee-raising manoeuvre to achieve the target apogee altitude of 70,786 km followed by a perigee-raising manoeuvre to achieve the target perigee altitude of 800 km, thus achieving the geosynchronous semi-major axis of 42,164 km. The ground-track of the baseline four-manoeuvre transfer is illustrated in Figs. 2–5. It can be seen that the apse line drifts once around the Earth until the geo-synchronous condition is reached at the end of the transfer such that the apogee is located at the target longitude as discussed in Section 2.1. The details of the transfer design are not discussed here for brevity. Table 2 summarises the apogee raising manoeuvres. The apogee raising phase is followed by a perigee raising manoeuvre of to increase the perigee from 600 to 800 km. This concludes the transfer. The total transfer Dv budget amounts to 88.3 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 orbit navigation for Proba-3 is the use of GPS data that are collected on-board around the perigee passes (where the GPS signal is available). As Proba-3 is a technology demonstration mission, it is envisaged to validate this approach by determining the orbit also by more classical means, i.e. by radiometric measurements. These measurements could also be used to substitute the GPS navigation system in case of a contingency. It should be noted that his remark refers to the orbit navigation. Relative navigation was base-lined at the start of phase-B to be a dedicated formation-flying radio frequency navigation system. An analysis was performed to determine the evolution of knowledge of orbital position and velocity. This analysis will allow determining whether the formation could be re-established in case of a contingency purely from groundbased data. It was assumed that the spacecraft position was initially known to within 100 km (i.e. the knowledge is worse than the proximity needed for formation flying, which is 30 km) and the spacecraft velocity to within 1 m s 1. No Doppler measurements were considered, but ranging measurements every 20 min during visibility (assuming a minimum elevation of 101) from either the Redu or the Hawaii ground-station. For this analysis actually another orbit than the one discussed in Section 2 was assumed: A commensurate 17:14 orbit that provides 17 revolutions in 14 days, and which has an inclination of 501. The advantages of this orbit are lower Dv requirement and less radiation exposure. The navigation analysis should however also be applicable to the geo-synchronous orbit described in Section 2. Of particular interest is the knowledge at a true anomaly of 1201, at which point the formation should be restored. The following plot shows the measurements taken by the Redu and Hawaii stations during the 14-day reference period.
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80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
Fig. 2. Transfer trajectory starting at injection just south of Java. The first apogee raising burn is performed at the seventh perigee pass.
80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
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.
80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0
50
100
150
longitude [°] 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.
In Fig. 6 the ranging measurements from the two ground-stations are shown together with the times of passage through the 71201 points in true anomaly
(green vertical lines). Together the two ground-stations provide quite good coverage of the full orbit, at least around apogee. The drift of the apogee in longitude is
M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145
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80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
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 2 Summary of apogee raising manoeuvres. Man. #
Perigee #
Time from inj. (days)
D va (m s 1)
Burn duration (s)
1 2 3 4
7 11 15 19
5.90 9.48 13.20 17.09
24.3 13.5 15.0 9.5
60.4 33.3 36.7 23.1
a
Including gravity loss.
reflected in the shift of the ranging availability from the stations. Fig. 7 shows the position knowledge that can be achieved with the ranging-only measurements as a function of the 14-day reference period. The horizontal red dashed line indicates the 30 km requirement for formation acquisition and the vertical green solid lines the passage through 71201 of true anomaly. It can be seen that the position knowledge is regained within one orbit to better than 1 km (square-root sum of all components) on a 3s confidence level. It can be observed how the knowledge worsens during periods of non-availability of data. The knowledge is in first order not associated with the orbital phase (i.e. true or mean anomaly or time). Like the position knowledge also the velocity knowledge is recovered quickly, as can be seen in Fig. 8.
the separation phase that avoids collision or evaporation (defined for Proba-3 as separations of more than 10 km at apogee or 100 km at perigee). The main driver for the separation drift orbit is the differential solar radiation pressure acting on the spacecraft; all other forces have lower differential magnitudes due to the low spatial separation. This drift created by differential radiation pressure will be superimposed by the relative motion due to the separation Dv created by the springloaded separation mechanism. For an initial orbit with the apse line aligned with the projection of the Sun direction in the orbital plane the radiation pressure drift will cause a relative motion in the V-bar direction. The separation Dv can be chosen such that the drift is minimised without creating a collision risk. For the design of the spacecraft applicable at the time of the system requirements review differential radiation pressure acceleration in the order of 108 m s2 can be expected, which is small compared to the value applicable to earlier designs. It can be shown [ref] that for such small differential radiation forces a separation Dv in the order of 1 cm s1 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 can be limited to a few kilometres with a minimum closest approach of about 200 m.
3.2. Acquisition 3. Formation flying design 3.1. Separation For Proba-3 the separation of the two formation flying spacecraft will be the first task in formation flying. Various analyses on the dynamics of the problem have been published in this respect (e.g. [4]). After separation from the stack (to occur in the target orbit described in Section 2) the formation flying payload will need to be commissioned and is therefore not yet available for control of the formation. Therefore, a free drift relative orbit will be required in
The strategy of the acquisition phase is to stop the drift of the separation phase by a manoeuvre that is located at a true anomaly of 1201. This location was chosen as a compromise between GPS data availability (around perigee), orbit knowledge availability (post perigee), ground-station visibility (around apogee), and Dv minimisation (around apogee). This is followed by a manoeuvre that compensates the relative drift due to the differential radiation forces until the final tandem formation is achieved, and by a two-point transfer towards the relative position, where a take-over by the on-board metrology
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70 Redu Hawaii 60
range [103 km]
50
40
30
20
10
0 0
2
4
6
8
10
12
14
time [d] 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.)
103
3σ position knowledge [km]
102
101
100
10−1
10−2 0
2
4
6
8
10
12
14
time [d] 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) 137–145
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101
3σ velocity knowledge [ms−1]
100
10−1
10−2
10−3 0
2
4
6
8
10
12
14
t [d] Fig. 8. Velocity knowledge of Proba-3 over the 14-day reference period.
as in the simulation it was assumed that the converging drift is simultaneously initiated with the stop manoeuvre. A summary of the formation acquisition manoeuvres is given in Table 3. 3.3. Target tandem formation
Fig. 9. Drift orbit with separation Dv ¼ 1 cm s1 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.)
system can occur. The latter is necessary due to the limited field of view (751) of the optical metrology devices. It can be seen from the relative trajectory of the coronagraph spacecraft during the acquisition phase shown in Fig. 10 that the trajectory following the stop manoeuvre already exhibits a reduced spacecraft separation at apogee,
At the end of the acquisition phase the spacecraft are in the target tandem formation, which is defined by the interspacecraft distance to be above 100 m in apogee and below 1.2 km at perigee. In this tandem formation the formation flying demonstrations (metrology data acquisition) and guest science activities will be carried out. As discussed in Section 3.1 for the separation phase, the tandem formation would slowly drift apart due to the differential radiation pressure forces acting on the two spacecraft. This will have to be controlled by a formation maintenance algorithm that is preliminarily defined by the following procedure: On each orbit (that is, each day) two manoeuvres (M1 and M2) are performed.
M1 is located at true anomalies between 301 and 601.
Its purpose is to target the location of M2 such that will be close to the origin (that is, the occulter spacecraft), but it will avoid a collision, even in the event M2 is not performed. M2 is located at the apogee and is designed to reduce the relative velocity in the R-bar direction, which is normally excited due to the differential radiation pressure forces.
This manoeuvre strategy requires Dv for M1 of 1:2 mm s1 per day and for M2 of 1:0 mm s1 per day, respectively. This gives a contribution of the formation
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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 Separation Stop and drift back initiation SRP drift correction Two-point transfer man. 1 Two-point transfer man. 2
Dv (cm s 1) a
0 0.5 0.2 0.4 0.6
n (deg)
t (h)
180 120 120 120 180
0 85 109 133 144
a The separation occurs with a Dv of 1 cm s1 . This is however provided by a spring-loaded mechanism and is non-propulsive.
maintenance manoeuvres of 1:6 m s1 to the Dv budget of the coronagraph spacecraft. Regarding the safety of the tandem formation it is found that very strong requirements have to be formulated for the state knowledge at apogee in order to guarantee no collision for an extended drift period in case of a contingency. In order to avoid collisions for a 7 day drift period on a 99% confidence level, the relative velocity must be known better than 0:3 mm s1 . 4. Conclusion Proba-3 is to be launched in the 2015–2016 time-frame to a HEO. As a baseline for this analysis a geo-synchronous
orbit at low inclination of 17.81 has been considered. The orbit is chosen to provide good visibility of the apogee over the ground-station in Redu over the mission lifetime of two years. The injection orbit is determined by the choice of the launch vehicle, here the Indian PSLV launcher is considered. Alternatively the mission could be launched on a VEGA launcher to a moderate inclination (501), in which case a propulsion module is required to achieve the transfer to the HEO. For one of the launch option the injection orbit is chosen below the geo-synchronous condition in order to let the apse-line drift relative to the Earth’s surface such that it can be positioned in an optimum way for the groundstation. The baseline transfer strategy is a sequence of four apogee-raising manoeuvres at the perigee number 7, 11, 15, and 19 followed by a perigee raising manoeuvre. The total Dv budget for the mission is below 100 m s1 . A groundbased navigation scenario with two stations (Redu and Hawaii) performing permanently ranging-only measurements for the full visibility period leads to knowledge of better than 1 km in position and 0:1 m s1 in velocity (both on a 3s confidence level) after an initial position knowledge of 100 km and velocity knowledge of 1 m s1 . The improved knowledge is clearly the result of the availability of more data (two stations instead of one station and full visibility period instead of 1 h per day). It was found that after one orbit the position knowledge is recovered to the same level even if the initial knowledge is 1000 km. The amount of
M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145
ignorance in the initial state is therefore quickly removed on the basis of the measurements. It is recommended to assume also the availability of Doppler data for this analysis as Doppler data is collected without extra effort in parallel to ranging data or telemetry. Another alternative navigation scenario could be the use of radar data from the STRATCOM network. This would be available without a cooperating spacecraft. For the formation flying design it is found that the relative dynamics are dominated by the differential radiation pressure forces, as the occulter spacecraft has a much lower ballistic coefficient than the coronagraph spacecraft. This difference drives the initial separation velocity that is required in order to avoid collision during the separation phase. A low separation velocity also allows smaller manoeuvres for the formation acquisition, which comprises a stop manoeuvre that stops the drift of the separation phase, a drift initiation manoeuvre that starts the drift of the coronagraph spacecraft back to the occulter spacecraft, and a two-point transfer to achieve the required geometry at the apogee in order to start the tandem formation utilising the on-board metrology systems. The total deterministic Dv required for this phase is below
145
2 cm s1 . Regarding the stability and safety of the tandem formation it is however found that they depend strongly on the knowledge of the relative spacecraft state, which places strong requirements on the metrology system. References [1] P. Lamy, S. Vivs, D. Dam, S. Koutchmy, New perspectives in solar coronagraphy 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 in GTO, in: B. Warmbein (Ed.), Proceedings of the 4S Symposium: Small Satellites, 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 dynamics and control of a two-element virtual telescope on a HEO using GNSS and optical metrology, J. Guidance Control Dyn., in press. [5] C. de Negueruela, T.V. Peeters, J. Peyrard, M. Manzano, Proba-3 Phase B Formation Flying Mission Analysis Report, Issue 2, Revision 1, October 2009.
Contents lists available at SciVerse ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Formation flying and mission design for Proba-3 Markus Landgraf a,n, Agnes Mestreau-Garreau b a b
ESA/ESOC, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany ESA/ESTEC, Keplerlaan 1, PO Box 299, 2200 AG Noordwijk ZH, The Netherlands
a r t i c l e i n f o
abstract
Article history: Received 22 December 2011 Received in revised form 13 March 2012 Accepted 29 March 2012 Available online 15 June 2012
The Proba-3 mission is an ambitious European mission to test the design, implementation 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 s1 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.
Keywords: Proba-3 ESA Mission design Formation flying Demonstration
1. Introduction 1.1. Background The Proba-3 mission is an experimental mission of the ESA GSTP programme (general support technology programme) dedicated to the demonstration of new technologies and techniques related to high precision formation flying. Through Proba-3, technologies relevant
n
Corresponding author. E-mail address: [email protected] (M. Landgraf).
0094-5765/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actaastro.2012.03.028
for future formation flying missions will be developed to flight level and tested in orbit. This includes GNC algorithms and formation management methods, metrology systems, communication links, operational methods, etc. The development and validation of engineering approach, ground verification tools and facilities required by formation flying will also be developed. Proba-3 consists of a space segment, a ground segment and a launch service, with a mission lifetime of two years and a launch around 2015–2016. The space segment consists of two small satellites launched into high elliptical orbit to demonstrate formation flying with high precision and to characterise sensors and other related technologies.
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M. Landgraf, A. Mestreau-Garreau / Acta Astronautica 82 (2013) 137–145
The ground segment includes the flight operations and the exploitation part. Proba-3 will demonstrate formation flying in the context of a giant (150 m) solar coronagraph science experiment. The main purpose of the Proba-3 coronagraph guest mission [1] is to provide a realistic science mission case for the formation flying demonstration. In this way a demonstration with the full complexity of a full science mission 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 in terms of scientific return. The project is an ESA mission. It has seen a certain amount of evolution with changing mission designs [2]. As an ESA project it is currently in phase B and is lead by a consortium of industrial companies in several ESA member states.
1.2. Mission objectives The overall mission objective is to perform the in-orbit technology demonstrations and proof of concept formation flying demonstrations to build sufficient confidence in the European space industry in order to embark on future missions based on formation flying. Given this overall mission objective the purpose of the mission can be divided in the following four categories:
Formation flying demonstration: The primary objective
of Proba-3 is to demonstrate formation flying with high precision and to demonstrate it for future formation flying missions. Equipment qualification: Precision formation flying and efficient use of propellant calls for technology development in metrology, e.g. RF metrology systems and high accuracy optical metrology systems. The Proba-3 mission will demonstrate these technologies. Development, design and validation principles for formation flight: The distributed character of formation flying systems calls for new development, design, implementation and validation principles. Proba-3 will contribute towards the establishment of these principles, and the development of required tools. Guest payload: In addition to the formation flying experiments and demonstrations a scientific guest payload will be flown—a large (length about 150 m) solar coronagraph instrument distributed over the formation. Using the Proba-3 generic formation flying capabilities, the formation flying of this distributed single virtual instrument will constitute a convincing demonstration of formation flying in addition to provide scientific mission return.
2. Mission design 2.1. Orbit selection For the orbit selection the relevant mission requirements have to be considered. In general orbits far from gravity sources are ideal for formation flying mission due to 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 environment is presented by the libration points of the Sun–Earth three body problem. For a Sun observer the co-linear dayside libration point L1 would be ideal. However, due to the limited scope of the Proba-3 mission, the orbit selection is finally driven by the capability of the launcher, so that the maximisation of the mass into final orbit following a launch by a small to medium sized launch vehicle is the driving requirement for the orbit selection. The orbit selection for the operational phase is thus a compromise solution, which is required to minimise the detrimental effects of a near-Earth environment. Such a compromise solution is a highly elliptical orbit (HEO), which provides a benign environment at the apogee and still can be reached by small or medium launchers with a sufficient payload mass. The inclination of that HEO will be prescribed by the constraints of the selected launch vehicle. What remains to be determined are the apogee and perigee altitudes. The right ascension of ascending node can be chosen freely by selecting the lift-off time. Here we report the status of the orbit selection at the start of phase-B. For the launch vehicle the European VEGA launcher and the Indian PSLV have been studied as suitable candidate launch vehicles. Here we will focus on the latter option for brevity. The maximum performance departure trajectory of the PSLV delivers the spacecraft into a HEO with an inclination of 17.81. For the PSLV also the argument of perigee is prescribed to be equal to 1801. The initial perigee altitude is 300 km. Another driver for the orbit selection is the ground-station availability. It is assumed here that the available groundstation for Proba-3 is the ESA station Redu at the geocentric coordinates 50.0011N, 5.1451E. In order to achieve visibility of the apogee (the latitude of which is 01 due to the prescribed argument of perigee), the initial longitude of the apogee must be chosen to be close to the longitude of the Redu station and also the orbital period must be chosen to be commensurate with the Earths sidereal day of 86,164 s. In phase-A a number of options for the HEO were discussed and the current baseline for the HEO calls for a geo-synchronous orbit, i.e. an orbital period of exactly 86,163 s. This requires a semi-major axis of 42,164 km. The perigee altitude shall be chosen as small as possible in order to minimise the size of the perigee raising manoeuvres in transfer. The minimum value is however by the requirement to avoid reentry into the Earth’s atmosphere under luni-solar perturbations during the required mission lifetime of two years. For this minimum a value of 800 km was found. Given the semi-major axis and perigee altitude the apogee altitude can be calculated to be 70,786 km. The right ascension of ascending node is calculated such that the local time of the apogee and the Redu station are identical in the middle of the mission given the drift of the node due to the oblateness of the Earth. The orbit of Proba-3 during the operational phase is visualised in Fig. 1. A summary of the baseline orbit for Proba-3 is given in Table 1. 2.2. Transfer Two objectives must be met in the transfer: (a) the longitude of the apogee must drift from its prescribed initial
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initial orbit after one year after two years
80 60
latitude [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0
50
100
150
longitude [°] 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 1 Orbital parameters of Proba-3 baseline orbit (PSLV option). Parameter
Value
Semi-major axis Eccentricity Perigee altitude Apogee altitude Orbital period Inclination Right ascension of ascending node Argument of perigee
42,164 km 0.8299 800 km 70,786 km 86,164 s 17.81 Depends on launch epoch 1801
value after injection by the launcher to the required value, which is chosen to be such that at the mid-time of the mission the local time of the Redu station and the apogee match, and (b) the perigee must be raised to 800 km altitude. This is achieved by initially selecting a sub-synchronous semi-major axis and performing an apogee-raising manoeuvre to achieve the target apogee altitude of 70,786 km followed by a perigee-raising manoeuvre to achieve the target perigee altitude of 800 km, thus achieving the geosynchronous semi-major axis of 42,164 km. The ground-track of the baseline four-manoeuvre transfer is illustrated in Figs. 2–5. It can be seen that the apse line drifts once around the Earth until the geo-synchronous condition is reached at the end of the transfer such that the apogee is located at the target longitude as discussed in Section 2.1. The details of the transfer design are not discussed here for brevity. Table 2 summarises the apogee raising manoeuvres. The apogee raising phase is followed by a perigee raising manoeuvre of to increase the perigee from 600 to 800 km. This concludes the transfer. The total transfer Dv budget amounts to 88.3 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 orbit navigation for Proba-3 is the use of GPS data that are collected on-board around the perigee passes (where the GPS signal is available). As Proba-3 is a technology demonstration mission, it is envisaged to validate this approach by determining the orbit also by more classical means, i.e. by radiometric measurements. These measurements could also be used to substitute the GPS navigation system in case of a contingency. It should be noted that his remark refers to the orbit navigation. Relative navigation was base-lined at the start of phase-B to be a dedicated formation-flying radio frequency navigation system. An analysis was performed to determine the evolution of knowledge of orbital position and velocity. This analysis will allow determining whether the formation could be re-established in case of a contingency purely from groundbased data. It was assumed that the spacecraft position was initially known to within 100 km (i.e. the knowledge is worse than the proximity needed for formation flying, which is 30 km) and the spacecraft velocity to within 1 m s 1. No Doppler measurements were considered, but ranging measurements every 20 min during visibility (assuming a minimum elevation of 101) from either the Redu or the Hawaii ground-station. For this analysis actually another orbit than the one discussed in Section 2 was assumed: A commensurate 17:14 orbit that provides 17 revolutions in 14 days, and which has an inclination of 501. The advantages of this orbit are lower Dv requirement and less radiation exposure. The navigation analysis should however also be applicable to the geo-synchronous orbit described in Section 2. Of particular interest is the knowledge at a true anomaly of 1201, at which point the formation should be restored. The following plot shows the measurements taken by the Redu and Hawaii stations during the 14-day reference period.
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80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
Fig. 2. Transfer trajectory starting at injection just south of Java. The first apogee raising burn is performed at the seventh perigee pass.
80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
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.
80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0
50
100
150
longitude [°] 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.
In Fig. 6 the ranging measurements from the two ground-stations are shown together with the times of passage through the 71201 points in true anomaly
(green vertical lines). Together the two ground-stations provide quite good coverage of the full orbit, at least around apogee. The drift of the apogee in longitude is
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80 60
latuityde [°]
40 20 0 −20 −40 −60 −80 −150
−100
−50
0 longitude [°]
50
100
150
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 2 Summary of apogee raising manoeuvres. Man. #
Perigee #
Time from inj. (days)
D va (m s 1)
Burn duration (s)
1 2 3 4
7 11 15 19
5.90 9.48 13.20 17.09
24.3 13.5 15.0 9.5
60.4 33.3 36.7 23.1
a
Including gravity loss.
reflected in the shift of the ranging availability from the stations. Fig. 7 shows the position knowledge that can be achieved with the ranging-only measurements as a function of the 14-day reference period. The horizontal red dashed line indicates the 30 km requirement for formation acquisition and the vertical green solid lines the passage through 71201 of true anomaly. It can be seen that the position knowledge is regained within one orbit to better than 1 km (square-root sum of all components) on a 3s confidence level. It can be observed how the knowledge worsens during periods of non-availability of data. The knowledge is in first order not associated with the orbital phase (i.e. true or mean anomaly or time). Like the position knowledge also the velocity knowledge is recovered quickly, as can be seen in Fig. 8.
the separation phase that avoids collision or evaporation (defined for Proba-3 as separations of more than 10 km at apogee or 100 km at perigee). The main driver for the separation drift orbit is the differential solar radiation pressure acting on the spacecraft; all other forces have lower differential magnitudes due to the low spatial separation. This drift created by differential radiation pressure will be superimposed by the relative motion due to the separation Dv created by the springloaded separation mechanism. For an initial orbit with the apse line aligned with the projection of the Sun direction in the orbital plane the radiation pressure drift will cause a relative motion in the V-bar direction. The separation Dv can be chosen such that the drift is minimised without creating a collision risk. For the design of the spacecraft applicable at the time of the system requirements review differential radiation pressure acceleration in the order of 108 m s2 can be expected, which is small compared to the value applicable to earlier designs. It can be shown [ref] that for such small differential radiation forces a separation Dv in the order of 1 cm s1 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 can be limited to a few kilometres with a minimum closest approach of about 200 m.
3.2. Acquisition 3. Formation flying design 3.1. Separation For Proba-3 the separation of the two formation flying spacecraft will be the first task in formation flying. Various analyses on the dynamics of the problem have been published in this respect (e.g. [4]). After separation from the stack (to occur in the target orbit described in Section 2) the formation flying payload will need to be commissioned and is therefore not yet available for control of the formation. Therefore, a free drift relative orbit will be required in
The strategy of the acquisition phase is to stop the drift of the separation phase by a manoeuvre that is located at a true anomaly of 1201. This location was chosen as a compromise between GPS data availability (around perigee), orbit knowledge availability (post perigee), ground-station visibility (around apogee), and Dv minimisation (around apogee). This is followed by a manoeuvre that compensates the relative drift due to the differential radiation forces until the final tandem formation is achieved, and by a two-point transfer towards the relative position, where a take-over by the on-board metrology
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70 Redu Hawaii 60
range [103 km]
50
40
30
20
10
0 0
2
4
6
8
10
12
14
time [d] 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.)
103
3σ position knowledge [km]
102
101
100
10−1
10−2 0
2
4
6
8
10
12
14
time [d] 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.)
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101
3σ velocity knowledge [ms−1]
100
10−1
10−2
10−3 0
2
4
6
8
10
12
14
t [d] Fig. 8. Velocity knowledge of Proba-3 over the 14-day reference period.
as in the simulation it was assumed that the converging drift is simultaneously initiated with the stop manoeuvre. A summary of the formation acquisition manoeuvres is given in Table 3. 3.3. Target tandem formation
Fig. 9. Drift orbit with separation Dv ¼ 1 cm s1 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.)
system can occur. The latter is necessary due to the limited field of view (751) of the optical metrology devices. It can be seen from the relative trajectory of the coronagraph spacecraft during the acquisition phase shown in Fig. 10 that the trajectory following the stop manoeuvre already exhibits a reduced spacecraft separation at apogee,
At the end of the acquisition phase the spacecraft are in the target tandem formation, which is defined by the interspacecraft distance to be above 100 m in apogee and below 1.2 km at perigee. In this tandem formation the formation flying demonstrations (metrology data acquisition) and guest science activities will be carried out. As discussed in Section 3.1 for the separation phase, the tandem formation would slowly drift apart due to the differential radiation pressure forces acting on the two spacecraft. This will have to be controlled by a formation maintenance algorithm that is preliminarily defined by the following procedure: On each orbit (that is, each day) two manoeuvres (M1 and M2) are performed.
M1 is located at true anomalies between 301 and 601.
Its purpose is to target the location of M2 such that will be close to the origin (that is, the occulter spacecraft), but it will avoid a collision, even in the event M2 is not performed. M2 is located at the apogee and is designed to reduce the relative velocity in the R-bar direction, which is normally excited due to the differential radiation pressure forces.
This manoeuvre strategy requires Dv for M1 of 1:2 mm s1 per day and for M2 of 1:0 mm s1 per day, respectively. This gives a contribution of the formation
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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 Separation Stop and drift back initiation SRP drift correction Two-point transfer man. 1 Two-point transfer man. 2
Dv (cm s 1) a
0 0.5 0.2 0.4 0.6
n (deg)
t (h)
180 120 120 120 180
0 85 109 133 144
a The separation occurs with a Dv of 1 cm s1 . This is however provided by a spring-loaded mechanism and is non-propulsive.
maintenance manoeuvres of 1:6 m s1 to the Dv budget of the coronagraph spacecraft. Regarding the safety of the tandem formation it is found that very strong requirements have to be formulated for the state knowledge at apogee in order to guarantee no collision for an extended drift period in case of a contingency. In order to avoid collisions for a 7 day drift period on a 99% confidence level, the relative velocity must be known better than 0:3 mm s1 . 4. Conclusion Proba-3 is to be launched in the 2015–2016 time-frame to a HEO. As a baseline for this analysis a geo-synchronous
orbit at low inclination of 17.81 has been considered. The orbit is chosen to provide good visibility of the apogee over the ground-station in Redu over the mission lifetime of two years. The injection orbit is determined by the choice of the launch vehicle, here the Indian PSLV launcher is considered. Alternatively the mission could be launched on a VEGA launcher to a moderate inclination (501), in which case a propulsion module is required to achieve the transfer to the HEO. For one of the launch option the injection orbit is chosen below the geo-synchronous condition in order to let the apse-line drift relative to the Earth’s surface such that it can be positioned in an optimum way for the groundstation. The baseline transfer strategy is a sequence of four apogee-raising manoeuvres at the perigee number 7, 11, 15, and 19 followed by a perigee raising manoeuvre. The total Dv budget for the mission is below 100 m s1 . A groundbased navigation scenario with two stations (Redu and Hawaii) performing permanently ranging-only measurements for the full visibility period leads to knowledge of better than 1 km in position and 0:1 m s1 in velocity (both on a 3s confidence level) after an initial position knowledge of 100 km and velocity knowledge of 1 m s1 . The improved knowledge is clearly the result of the availability of more data (two stations instead of one station and full visibility period instead of 1 h per day). It was found that after one orbit the position knowledge is recovered to the same level even if the initial knowledge is 1000 km. The amount of
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ignorance in the initial state is therefore quickly removed on the basis of the measurements. It is recommended to assume also the availability of Doppler data for this analysis as Doppler data is collected without extra effort in parallel to ranging data or telemetry. Another alternative navigation scenario could be the use of radar data from the STRATCOM network. This would be available without a cooperating spacecraft. For the formation flying design it is found that the relative dynamics are dominated by the differential radiation pressure forces, as the occulter spacecraft has a much lower ballistic coefficient than the coronagraph spacecraft. This difference drives the initial separation velocity that is required in order to avoid collision during the separation phase. A low separation velocity also allows smaller manoeuvres for the formation acquisition, which comprises a stop manoeuvre that stops the drift of the separation phase, a drift initiation manoeuvre that starts the drift of the coronagraph spacecraft back to the occulter spacecraft, and a two-point transfer to achieve the required geometry at the apogee in order to start the tandem formation utilising the on-board metrology systems. The total deterministic Dv required for this phase is below
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2 cm s1 . Regarding the stability and safety of the tandem formation it is however found that they depend strongly on the knowledge of the relative spacecraft state, which places strong requirements on the metrology system. References [1] P. Lamy, S. Vivs, D. Dam, S. Koutchmy, New perspectives in solar coronagraphy 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 in GTO, in: B. Warmbein (Ed.), Proceedings of the 4S Symposium: Small Satellites, 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 dynamics and control of a two-element virtual telescope on a HEO using GNSS and optical metrology, J. Guidance Control Dyn., in press. [5] C. de Negueruela, T.V. Peeters, J. Peyrard, M. Manzano, Proba-3 Phase B Formation Flying Mission Analysis Report, Issue 2, Revision 1, October 2009.