TanDEM-X Autonomous Formation Flying System: Flight Results

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1 TanDEM-X Autonomous Formation Flying System: Flight Results J.-S. Ardaens*, D. Fischer** * German Space Operations Center (DLR/GSOC), Wessling, Germany ( jean-sebastien.ardaens@dlr.de) ** EADS Astrium GmbH, 8803 Friedrichshafen, Germany ( denis.fischer@astrium.eads.net) Abstract: The TanDEM-X mission is a scientific and commercial Earth observation mission comprising two satellites flying in close formation. The formation maintenance can be advantageously performed by an onboard autonomous system, which reduces the operational efforts, provides a shorter reaction time in case of contingencies and increases the control performance. The TanDEM-X Autonomous Formation Flying (TAFF) system has been developed for this purpose and is intended to replace the ground-based formation keeping activities during routine operations. TAFF has been activated for the first time in October 2010 for commissioning, during which the autonomous usage of thrusters was prohibited. Afterwards, a closed-loop campaign was successfully conducted in March 2011, demonstrating the capability of TAFF to maintain autonomously the formation. After a brief technical description of the system, the paper presents the key results gained during the commissioning phase and the closed-loop campaign. Keywords: spacecraft autonomy, aerospace control, closed-loop control, navigation systems 1. INTRODUCTION The successful launch of the TanDEM-X (TDX) satellite in June 2010 represents a new milestone in the field of remote sensing. The new spacecraft has joined the existing satellite TerraSAR-X (TSX), which was already flying alone since 2007 as a repeat-pass synthetic aperture radar (SAR), to create a formation of SAR satellites able to reach unprecedented imaging capabilities (Moreira et al. 2004). The mission objective of the formation is the generation of a global Digital Elevation Model of the Earth with a 2 m height resolution by processing the SAR interferometric measurements collected by the satellites over a two years time frame. This formation forms a spaceborne bistatic radar interferometer which requires a flexible baseline between the satellites (from a few hundred meters to several kilometers) in order to obtain different viewing conditions of the same locations on Earth. This characteristic is achieved using two slightly different orbits for the satellites, resulting in a natural relative elliptic motion between them. The hazard of collision is minimized by designing the formation using the concept of separation of the relative inclination and eccentricity vectors, which ensures at any time a minimum distance between the satellites (D Amico et al. 2005). In order to ensure an accurate ground-track repeatability, the formation has to follow closely a reference absolute orbit defined with respect to an Earth-centered Earth-fixed (ECEF) reference frame, thus requiring frequent orbit corrections. All the orbit correction maneuvers done by one spacecraft are replicated by the other one to keep the formation unaltered. These maneuvers are executed using 1 N hydrazine thrusters. The formation itself undergoes some perturbations which need to be compensated for. Among them the effect due to the Earth oblateness or the differential execution errors of the orbit correction maneuvers are predominant. The so-called formation keeping maneuvers are executed only by the TanDEM-X spacecraft which is equipped for this purpose with two 40 mn cold-gas thrusters pointing in flight and antiflight directions. The orbit correction (absolute orbit control) and the formation keeping (relative orbit control) were originally foreseen to be performed by the ground segment. However, the benefit of using an onboard autonomous formation keeping system has rapidly become evident. Onboard autonomy simplifies the operations done on-ground and guarantees superior orbit control performance, short reaction time to contingencies, and an increase of the quality of the data products. The TanDEM-X Autonomous Formation Flying (TAFF) system aims at answering to this need. TAFF is implemented as part as the attitude and orbit control system onboard TanDEM-X and is intended to take over the in-plane formation keeping activities throughout the mission, with a control accuracy of a few meters. After three months of commissioning during which the spacecraft were separated by 20 km, the TanDEM-X Formation Flight Review hold in October 2010 gave the goahead to build the narrow formation. This allowed the establishment of the inter-satellite link, whose operational range cannot exceed 4 km, and subsequently the first activation of TAFF on October 14th. The small distance between the spacecraft requires a rigorous validation of the Copyright by the International Federation of Automatic Control (IFAC) 709

2 autonomous formation keeping system before its routine utilization during the mission, in order to avoid putting the formation at a risk. As a consequence, it was required to inhibit the autonomous usage of thrusters during the commissioning phase. The first months after the activation have been dedicated to analyze the onboard navigation performance, the proper functioning of the logics of the controller and the overall robustness of the system. The data gathered during this phase (more that four months) gave enough confidence in the reliability of the system to allow for a short closed-loop campaign at the end of March 2011, during which all the functionalities of the autonomous software could be successfully tested. 2. TANDEM-X AUTONOMOUS FORMATION FLYING TAFF is implemented as a standalone (relative) Guidance, Navigation and Control (GNC) system which is embedded in the TanDEM-X on-board computer (a ERC-32 microprocessor). The relative navigation part uses the ECEF navigation solutions coming from the MosaicGNSS GPS receivers (Fichter et al. 2001) onboard TerraSAR-X and TanDEM-X as measurements and implements an Extended Kalman Filter (EKF) to estimate the state of the formation. The GPS navigation solution of TerraSAR-X is transmitted in real-time to the TanDEM-X spacecraft via an inter-satellite link. The one-way inter-satellite communication between the spacecraft is realized by using the existing S-Band downlink system on TerraSAR-X and an additional receive and decode equipment on TanDEM-X. The onboard filter provides a continuous real-time onboard relative navigation even in the presence of GPS data gaps. The controller takes as input the state estimated by the onboard filter and executes impulsive formation keeping maneuvers based on an analytical solution of the relative control problem. For simplicity, it has been decided that TAFF performs only in-plane formation keeping in order to avoid any rotation of the spacecraft when using the cold gas thrusters. The design of TAFF has been driven by stringent operational constraints. In particular the formation keeping system is not allowed to use any thruster during the acquisition of SAR images. Furthermore, a deterministic control scheme is mandatory to facilitate the planning of operations and to ease the monitoring of the autonomous system. Finally a parsimonious usage of onboard resources was required. As a consequence, the key design drivers retained during the development of TAFF were robustness, minimization of resource usage, simplicity of utilization and harmonious integration within the ground and space segments. These requirements led to the adoption of a special parameterization of the relative motion using relative orbit elements, on which both navigation and control algorithms are based. The relative motion is parameterized through a set of relative orbit elements obtained by combining the Keplerian elements of the two spacecraft (identified in the following by the subscript k=1,2) (D Amico et al. 2006). Δa a2 a1 a1δ ex a1( e2 cos( ω2) e1 cos( ω1)) a 1Δe y a Δ = = 1( e2 sin( ω2) e1 sin( ω1)) α (1) a1δ ix a1( i2 i1 ) a1δ iy a1( Ω2 Ω1)sin( i1 ) a1δ u a1( u2 u1) represents the state of the EKF and combines the information coming from the semi-major axis a k, the eccentricity e k, the inclination i k, the argument of perigee ω k, the right ascension of the ascending node Ω k and the mean argument of latitude u k. The state defined by (1) describes uniquely and unambiguously the formation geometry and can be used to express in a convenient way the solution of the Hill- Clohessy-Wiltshire equations of motion: ΔrR = Δa / a Δex cosu Δey sinu a ΔrT 3 Δa = Δu + Δiy coti ( u u0) 2Δey cosu + 2Δex sinu a 2 a ΔrN = Δi cosu + Δi sinu y x a Here, Δr R, Δr T and Δr N are the component in radial, alongtrack and cross-track directions of the relative position and u is the mean argument of latitude of TDX. From an operational point of view, the main advantage of this parameterization is to allow a quick insight in the geometry of the formation and to provide at the same time a simple criterion to assess the risk of collision (D Amico et al. 2006). This simple model is able to predict on-board the relative motion of the formation over several orbits with accuracy at the meter level and is used to provide continuously a smooth and accurate relative navigation solution. A streamlined filtering is done onboard in the EKF using a simple dynamical model for the relative motion which considers only the perturbation due to the Earth's equatorial bulge (J 2 ). This perturbation results in a constant secular rotation of the relative eccentricity vector aδe, which needs to be counteracted by the controller. The constant angular drift of aδe is simply called ϕ& in the sequel, ϕ denoting the phase the vector Δe. For a formation composed of two spacecraft with identical inclination like TanDEM-X, this simple dynamical model can be mathematically expressed as (Ardaens et al. 2009) 3 Δ &α = 0 & ϕ aδe y & ϕ aδex 0 0 n Δa, (3) 2 where n denote the spacecraft mean motion. Thanks to this approach, the filter is shown to be very computationally efficient, because the time update does not require any numerical propagation and because the measurement update is done using the simple measurement model defined in Eq. (2) together with the relative position information coming from the GPS receivers. Tests done on a representative onboard computer clocked at 20 MHz have measured an execution time limited to a few milliseconds for each call to T (2) 710

3 the TAFF task (running onboard at 0.1 Hz rate). Finally, the maneuvers executed autonomously are treated as impulsive and included during the time update using the Gauss variational equations adapted to the adopted parameterization. TAFF includes as well the maneuvers commanded directly from the ground, which are simply uploaded shortly before their execution per telecommand. This allows a smooth integration with the ground segment. The controller uses directly the state estimated by the EKF to plan and execute formation keeping maneuvers by the mean of a pair of maneuvers identified by the subscripts k=1,2 and computed as follows (Ardaens 2009): 1 T Δv an δδa 2 an δδa = δδe + ΔvT = + δδe, (4) 4 a 4 a where δδa and δδe are the desired correction of relative orbit elements to be achieved after the pair of maneuvers. The two maneuvers are executed at the following arguments of latitude: Knowing the expected angular drift of aδe between two consecutive pairs of maneuvers (represented by the dashed vertical lines), the controller targets the new value of the phase ϕ to be at one edge of the tolerance window (gray area), so that the natural drift of the vector will make it reach the opposite edge at the end of the control period. The usage of along-track maneuvers modifies temporary the relative semi-major axis, which results in undesired variations of aδu between the two maneuvers of one control cycle. As a consequence, the controller plans a slightly non-vanishing value for Δa after a pair of maneuvers to bring back aδu to its nominal value at the end of the control cycle. In the TanDEM-X mission, this control strategy ensures in addition that the maneuvers are always executed outside the domain of SAR acquisition, which is limited to about half an orbit (represented in gray on Fig. 2). δδe y u M 1 = atan and um 2 = u1 + π. (5) δδex This analytical approach guarantees as well a very low computational load. In order to ease the mission planning activities, the pair of maneuvers is executed on a regular basis, typically every 5-6 orbits. In addition, the controller has been designed to place the first maneuver (of the pair) always close to the ascending node. These efforts to render the autonomous controller as deterministic as possible gives the possibility to predict the behavior of TAFF over several days. The desired correction of relative orbit elements used to compute the maneuvers is requested by the internal guidance function, which ensures that the relative orbit elements describing the formation always stay within a tolerance window centered on the nominal values. Being designed for in-plane relative control, TAFF controls only Δa, aδe and aδu. Figure 1 depicts the adopted control strategy. Fig. 2. Harmonious formation keeping and SAR data takes. The desired correction δδe is in fact theoretically always the same at each maneuver cycle, so that the nominal location u M1 of the first maneuver is as well constant. It can be easily shown that u M1 depends in fact only on the nominal relative eccentricity vector of the formation. u M ΔeX 1 = arctan (6) ΔeY The second maneuver is executed exactly half an orbit after the first maneuver. As a consequence the maneuvers are located on a line perpendicular to the relative eccentricity vector (cf. Fig. 2). By setting properly the nominal relative eccentricity vector of the formation (e.g. ϕ =80 or ϕ =260 ) it can be ensured that the maneuvers are executed outside the SAR acquisition domain. Practically, the locations of maneuvers computed in real-time are affected by relative navigation errors, so that they can deviate slightly from the nominal location. In order to avoid any interference with SAR data takes, a safety mechanism has been implemented which inhibits the execution of maneuvers if the computed location is outside a tolerance angle around the nominal value. 3. OPERATIONAL ROBUSTNESS Fig. 1. Variations during a complete control period of relative semi-major axis (top), phase of relative eccentricity vector (middle) and relative mean argument of latitude (bottom). Enforcing autonomous onboard formation keeping on a highly sensitive scientific and commercial mission requires special care. Being the primary goal of the mission, the routine acquisition of SAR images is an extremely demanding task (subject to a tight mission planning) which 711

4 can not tolerate any interruption of service. As a consequence, it has to be ensured that the onboard formation keeping system is robust against any anomaly, or at least that it is able to detect autonomously any non-nominal situation and to prohibit the execution of maneuvers as soon as the smallest doubt about the validity of the onboard relative navigation exists. In one word, TAFF should in the worse case scenario have no impact on the mission. It has been already described in the previous section how the controller manages to inhibit the execution of maneuvers which could conflict with the primary mission goal. This section focuses on the assessment of the robustness of the relative navigation. Thanks to its simplicity and to the tight dynamics of the relative motion model, the filter is shown to be intrinsically extremely robust against corrupted inputs or misutilization. The filter has to cope with frequent outliers of the differential GPS navigation solution provided as input, which can be one order of magnitude higher than the noise level usually observed. Figure 3 depicts for instance the differential GPS navigation errors observed in February Large error peaks up to 100m needs to be filtered by the relative navigation software. Fig. 3. Differential GPS-navigation solution provided as input to TAFF (rms values). Data gathered during the four months after the activation of TAFF have demonstrated that these outliers do not endanger the onboard relative navigation. Figure 4 depicts for example the impact of a 70 m high error peak on the estimates of the relative orbit elements. The black curves depict the onboard estimates of the relative orbit elements while the red dashed lines represent the reference orbit elements coming from precise orbit products generated routinely at the German Space Operation Center (GSOC) (Montenbruck et al. 2010). Figure 4 demonstrates that the onboard navigation is robust, despite a local degradation of performance, which would result in a degradation of control performance, but without putting the formation at a risk. Another important aspect is the robustness against operational failures. It is for instance foreseen that the ground segment uploads the list of planned maneuvers to the spacecraft, so that the onboard filter can incorporate them during the time update of the state. In case of a mismatch between a-priori maneuver information and really executed maneuvers, TAFF should detect this anomaly and the controller should be deactivated, in order to prevent it from trying to compensate with cold gas propellant a usually larger hydrazine maneuver which would not have been executed. Such a scenario happened on December 11th, when a pair of hydrazine maneuvers (2.3 cm/s) was used to reconfigure the formation but without informing TAFF about it. Fig. 4. Behavior of the onboard navigation (top) during a large differential GPS-navigation peak on Dec. 20 th (bottom). Figure 5 depicts how such an error is detected onboard. The filter computes the modeled observations based on its internal estimated state according to Eq. (2). In case of large errors, the residuals between the modeled observations and the actual measurements exceed a predefined threshold, which increments a navigation error counter. If the navigation error counter reaches a value defined by telecommand, a navigation error flag is raised, triggering the re-initialization of TAFF and the disabling of the controller by the onboard Fault Detection, Isolation and Recovery system. This mechanism, based on the robustness of the inherent strong dynamics of the relative motion, is also used is case of very large outliers of the GPS sensors which could not be filtered. Fig. 5. On-board detection of navigation errors on Dec. 11 th 2010: residuals (top) and navigation error counter (bottom) 4. IN-FLIGHT NAVIGATION AND CONTROL PERFORMANCE The filtering performance of TAFF could be intensively investigated during the long commissioning phase. Figure 6 depicts the daily errors (rms values) of the onboard estimated relative orbit elements compared with precise orbit products over three months. Special attention needs to be paid to the onboard estimates of the relative semi-major axis Δa and of the dimensioned relative eccentricity vector aδe. These two relative orbit elements are of special relevance in the relative control 712

5 scheme. The first quantity drives directly the drift between the satellites (cf. Eq. 3). As a consequence its accurate estimation is necessary to ensure a precise control of the along-track separation. The second quantity is used to compute the location of the maneuver (cf. Eq. 5). Considering the fact that TAFF is allowed to execute maneuvers only on a restricted part of the orbit, the accurate estimation of aδe is of great importance to ensure that no maneuver will be executed during the acquisition of SAR images. Overall the estimate of Δa is accurate to 20 cm and the other relative orbit elements are accurate at the sub-meter level, except the along-track component aδu whose error can reach few meters. been set in closed-loop on March 29 th 2011 at 02:58 UTC and has executed its first autonomous formation keeping maneuver shortly after the activation of the controller. Figure 7 depicts the controlled relative orbit elements during the closed-loop campaign. The blue vertical dashed lines represent the cold gas maneuvers autonomously executed by TAFF. Functionally, the controller was shown to behave as expected. The relative eccentricity vector and relative mean argument of latitude could be successfully controlled within a tolerance window centered on their nominal values (ϕ = 80 and aδu = -54m). Fig. 7. Autonomous formation keeping, March Fig. 6. Long-term analysis of the relative orbit element errors. Despite its simplicity, the filter is able to improve the differential GPS navigation solution provided as input by one order of magnitude and to provide accurate and smooth relative navigation solution during the data gaps. Table 1 summarizes for example the navigation performance observed in February In order to ease the comparison with the simple difference of GPS receiver navigation solutions provided as input to the filter (1 st line of Table 1), the table shows the error of the estimated relative state (2 nd and 3 rd lines), which is a simple linear combination of the relative orbit elements estimated onboard (cf. Eq. 2). Table 1. Onboard navigation performance (Feb. 2011) radial along-track cross-track GPS navigation +0.71± ± ±1.40 solution [m] TAFF relative +0.04± ± ±0.28 position [m] TAFF relative velocity [m/s] 0.00± ± ±0.000 The short closed-loop campaign conducted in March 2011 gave the opportunity to verify the proper integration and functioning of the autonomous control system and to provide a quick look on the potential in term of simplicity and control performance offered by TAFF. During this campaign, the formation was configured as follows: Δα = [ ] T in meters. TAFF has Figure 7 shows however a clear degradation of navigation and control performances after March 30 th at around 06:00 UTC. This sudden drop of performance is due to an unexpected increase of navigation errors affecting the MosaicGNSS receivers (cf. Fig. 8), resulting in a degraded relative navigation. Fig. 8. Differential navigation errors of the MosaicGNSS receiver during the closed-loop campaign. Even if the relative navigation was shown to be robust, as expected from the results of the commissioning phase, the error affecting the estimates of the relative orbit elements increased up to the level of the correction necessary to maintain the formation. In addition to the degradation of control performance, this led to erroneous computations of the locations of maneuvers, simply because the location depends only on the necessary correction of aδe (cf. Eq. 5), which can be affected in this case by errors of the same order of magnitude. As expected, the maneuver inhibition mechanism described previously could successfully prevent the execution of maneuvers outside the tolerance window, set to +/- 10 during the closed-loop campaign. Figure 9 depicts the locations of the 1 st (in red) and 2 nd maneuvers (in green) of the pairs of maneuvers planed during the closed-loop campaign, represented by crosses if the maneuvers have been 713

6 executed and otherwise by circles. The nominal relative eccentricity vector is also represented by a red dashed line. The blue arc depicts the onboard estimate of aδe during the three-day long campaign. It can be recognized that a total of 10 maneuvers have been executed autonomously, while 4 pairs of maneuvers have been rejected by TAFF (March 30 th 10:00, March 31 st 02:00, 08:00 and 15:00 UTC) because they were planed outside the tolerance window, represented by a gray area. by the GPS sensors and to refine the concept of tolerance window for the execution of maneuvers. 5. CONCLUSION AND WAY FORWARD The TanDEM-X Autonomous Formation Flying System demonstrates the successful implementation of a simple and resource-sparing onboard control system for the autonomous formation keeping of a scientific mission. Stringent functional and operational constraints have driven the design of the software, leading to the adoption of streamlined GNC algorithms and dedicated functionalities to guarantee the smooth integration within the ground and space segments. The analyses performed during several months of commissioning have shown that the relative navigation is accurate at the meter level and is robust against the sporadic anomalies of the GPS sensors and operational misutilizations. Fig. 9. Locations of the maneuvers executed by TAFF. In order to ease the mission planning activities, TAFF does not re-plan one orbit later the maneuvers which have not be executed, but skips simply the pair of maneuvers and waits for the next planned maneuver cycle. This strategy results in a high degradation of control performance when maneuvers are not executed. This is the case for example on March 31 st where all the pairs of maneuvers were skipped. As a matter of fact, the formation was not controlled anymore during the last day of the three day long campaign. As a consequence, a meaningful assessment of relative control performance can only be done during the two first days of the closed-loop campaign, when the maneuvers could be successfully executed. Table 2 compares the relative control performance obtained by ground-in-the-loop and onboard control systems for the same formation. Table 2. Ground-based vs. onboard control performance abs(mean/max) radial [m] along-track [m] on-ground control 0.3/ /58.3 March 13-19, 2011 on-board control March 29-30, / /36.3 This table shows the potential in term of control performance brought by onboard autonomy. Compared to ground-in-theloop control, on-board autonomous control presents the advantage of beneficing from reduced control periods because it is freed from the need of ground contacts and does not require any maneuver planning efforts. The formation is typically controlled once per day (15 orbits), while autonomy allows much smaller control periods (4-5 orbits during the closed-loop campaign). As a consequence the relative control performance could be ultimately three times better that what is obtained in a ground in a loop scheme. The next activities will be dedicated to try to improve the navigation provided The commissioning phase has been followed by a short closed-loop campaign, during which TAFF has successfully taken over the in-plane relative control of the formation and demonstrated its operational simplicity and robustness, paving the way for a future operational utilization. Future activities will be dedicated to the improvement of control performance and the planning of additional extended closedloop campaigns. AKNOLEDGEMENTS The TanDEM-X project is partly funded by the German Federal Ministry for Economics and Technology (Förderkennzeichen 50 EE 0601). REFERENCES Ardaens J.-S., D'Amico S. (2009). Spaceborne Autonomous Relative Control System for Dual Satellite Formations; Journal of Guidance, Control and Dynamics 32(6): DOI / D'Amico, S., Montenbruck, O., Arbinger, C., Fiedler, H. (2005). Formation Flying Concept for Close Remote Sensing Satellites, AAS , 15th AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, Colorado. D Amico, S., and Montenbruck, O. (2006). Proximity operations of formation-flying spacecraft, using an eccentricity/inclination vector separation, Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3. Fichter W., Bruder M., Gottzein E., Krauss P., Mittnacht M.; Botchkovski A., Mikhailov N., Vasilyev M. (2001). Design of an Embedded GPS Receiver for Space Applications, Space Technology, IFAC Montenbruck O., Wermuth M., Kahle R. (2010); GPS Based Relative Navigation for the TanDEM-X Mission - First Flight Results; ION-GNSS-2010 Conference, Portland, Oregon. Moreira, A., et al. (2004), TanDEM-X: A TerraSAR-X Addon Satellite for Single-Pass SAR Interferometry, IEEE International Geoscience & Remote Sensing Symposium, Achorage, USA. 714