35th ANNUAL AAS GUIDANCE AND CONTROL CONFERENCE, 3-8 Feb 2012, Breckenridge, Colorado (Preprint) AAS 12-072 THE PRISMA FORMATION FLYING DEMONSTRATOR: OVERVIEW AND CONCLUSIONS FROM THE NOMINAL MISSION Per Bodin,* Ron Noteborn, * Robin Larsson,* Thomas Karlsson,* Simone D’Amico, † Jean Sebastien Ardaens, † Michel Delpech,‡ Jean-Claude Berges‡ The PRISMA in-orbit testbed was launched on June 15, 2010 to demonstrate strategies and technologies for formation flying and rendezvous. OHB Sweden (OHB-SE) is the prime contractor for the project which is funded by the Swedish National Space Board with additional support from the German Aerospace Center (DLR), the French National Space Center (CNES), and the Technical University of Denmark (DTU). In August 2011, PRISMA completed its nominal mission and during the fall of 2011, several additional activities have been performed under a mission extension program. The mission qualifies a series of sensor and actuator systems including navigation using GPS, Vision Based and RF technology as well as a propulsion system based on environmentally friendly propellant technology. The mission also includes a series of GNC experiments using this equipment in closed loop. Separate experiments are implemented by OHB-SE, DLR, and CNES and the paper provides an overview and conclusions from the nominal mission flight results from these experiments. INTRODUCTION The PRISMA mission demonstrates technologies related to Formation Flying and Rendezvous in space. OHB Sweden (OHB-SE) is the prime contractor for the mission which is funded by the Swedish National Space Board (SNSB). The mission is further supported by the German Aerospace Center (DLR/GSOC), the French Space Agency (CNES), and the Technical university of Denmark (DTU). PRISMA consists of two spacecraft: Mango and Tango. The orbit altitude is 750 km, sun synchronous with 06:00 ascending node. The satellites were launched clamped together on June 15, 2010. Tango was separated from Mango on August 11 the same year. The nominal mission was completed by the end of August, 2011. An artist’s impression of the PRISMA satellites in orbit can be seen in Figure 1. BACKGROUND Formation flying and rendezvous has been identified as key enabling technologies in several advanced 1,2,3,4 disciplines involving scientific applications or on-orbit servicing and assembly. Applications include distributed satellite systems for enhanced remote sensing performance, for planetary science, astronomy, the assembly of large structures on-orbit as well as re-supply or repair of orbital platforms. For all these applications, there is a need to implement on-board guidance, navigation, and control (GNC) with a high degree of autonomy. This aspect motivated SNSB and OHB-SE to initiate the development of the PRISMA * OHB Sweden AB, AOCS & SW Department, P.O. Box 1064, SE-171 22 Solna, Sweden DLR/GSOC, Oberpfaffenhofen, D-82234 Weßling, Germany ‡ CNES, 18 avenue Edouard Belin, 31401 Toulouse Cedex 1, France † 1 mission in 2004.5 ,6 Potential participants were invited by the prime to contribute to the mission with different key technologies and to also implement self defined experiments sharing mission time and resources. The resulting mission consisted of several hardware and software experiments involving new technologies for propulsion, vision based sensors, GPS and other RF-based navigation, as well as GNC-algorithms. OHB-SE as well as DLR/GSOC and CNES have developed their own GNC software for the execution of a series of closed loop orbit control experiments. This paper summarizes the results from these experiments. Figure 1. Artist’s impression of the PRISMA satellites in orbit. MISSION AND SYSTEM OVERVIEW 7 The mission includes hardware and software experiments from several contributors. Apart from the mission and system primeship, OHB-SE implements three groups of GPS and vision-based GNC experi8 ,9,10 ments involving passive as well as forced motion. DLR/GSOC provides the GPS absolute and relative navigation system with both the GPS hardware and the on-board navigation software. 11 DLR implements also two different types of closed loop orbit control experiments as well as the on-ground verification precise orbit determination layer.12,13,14 CNES provides the Formation Flying RF (FFRF) sensor and performs also dedicated closed-loop GNC experiments under the Formation Flying In-Orbit Ranging Demonstration (FFIORD).15,16,17 DTU contributes the vision-based sensor (VBS) which is implemented within the autono18 mous star tracker with an addition of two dedicated rendezvous cameras. Table 1. Summary of PRISMA experiments. GNC Experiments Description Organization Key Sensor Passive GPS-based formations and reconfigura- OHB-SE GPS tion. Three-dimensional forced motion under the con- OHB-SE GPS or VBS straints of virtual structures. Docking simulation. Autonomous vision based rendezvous. OHB-SE VBS Passive GPS-based formation flying. Formation DLR GPS keeping and reconfiguration. Autonomous orbit keeping of single spacecraft. DLR GPS DLR’s secondary mission objective. On-ground verification layer. DLR GPS Closed loop GNC experiments involving passive CNES FFRF and forced motion within rendezvous, relative orbit keeping, and collision avoidance. Hardware Experiments Unit Description Organization High Performance Green Propellant Flight qualification of new propulsion technology. SSC/ECAPS Micropropulsion Flight qualification of MEMS based cold-gas propulsion. SSC/Nanospace FFRF In-orbit sensor validation. CNES VBS Flight qualification of vision-based sensor technology. DTU Experiment Set Autonomous Formation Flying (AFF) Proximity Operations and Final Approach/Recede (PROX/FARM) Autonomous Rendezvous (ARV) Spaceborne Autonomous Formation Flying Experiment (SAFE) Autonomous Orbit Keeping experiment (AOK) Precise Orbit Determination (POD) GNC part of Formation Flying InOrbit Ranging Demonstration (FFIORD) SSC/ECAPS provides the High Performance Green Propellant (HPGP) propulsion system. Two thrusters are included which can be used to replace the nominal hydrazine system in dedicated parts of the mis- 2 sion.19 SSC/Nanospace includes a MEMS-based cold-gas micro-propulsion system for flight qualifica20 tion. A Digital Video System (DVS) from Techno System Developments in Naples, Italy is also included 21 22 as well as a newly developed mass spectrometer from the Institute of Space Physics in Kiruna, Sweden. A summary of the different experiments within PRISMA is given in Table 1 . In addition to these experiments, PRISMA provides a test flight for a newly developed Data Handling System and Power Conditioning and Distribution Unit with battery management electronics, acts as a model project for new on-board software developed with model-based design techniques, demonstrates the newly developed ground support and operations software RAMSES and provides a test flight for the DVS and the particle mass spectrometer. Figure 2. Mango mode architecture. The PRISMA space segment consists of a small satellite Mango (150 kg), and a microsatellite Tango (40 kg). Mango has full 3-dimensional attitude independent orbit control capability and is 3-axis attitude stabilized using star trackers and reaction wheels. Tango does not have any attitude control capability and is equipped with a solar magnetic attitude control system still providing 3-axis stabilization. The propulsion system on Mango is based on six 1-N thrusters directed through the spacecraft center of mass and the deltaV capability is approximately 120 m/s. All ground communication is made with Mango. Communication with Tango is made via an inter-satellite link (ISL). The GPS is distributed between the two satellites and GPS messages are transferred from Tango to Mango via the ISL. The GPS navigation software resides within the on-board software of Mango. In this way, relative GPS navigation between Mango and Tango is achieved. Apart from supporting the experiments, the GPS navigation system acts as the primary navigation system in Safe Mode when a safe orbit constellation is entered. The mode architecture of Mango is illustrated with Figure 2. The figure shows that there is basically one mode for each of the GNC experiment groups. In addition there is a Manual mode to support other dedicated hardware experiments such as HPGP. The AFF mode implements the passive GPS-based formation flying. This mode is highly autonomous and requires limited ground intervention. For this reason, the AFF mode acts as a transition hub between all the other experimental modes. The PRISMA satellites are operated from OHB-SE premises in Solna, Sweden using one of SSC’s ground antennas in Kiruna, Sweden.23 The orbit and the antenna result in late afternoon and night-time passages with up to 10 passages per day. Operations included the initial acquisition, LEOP, Tango separation and the nominal mission phase. The Mission Control Center (MCC) is based on the in-house developed RAMSES ground control software. For approximately five months, between March and July 2011, the mission was operated from DLR/GSOC in order to further support the mission and in this way prolong its operational lifetime. A cloned MCC was set up at DLR/GSOC and personnel were trained at OHB-SE. In addition to the Kiruna antenna, DLR/GSOC also made use of ground stations in Weilheim, Germany and Inuvik, Canada. This allowed for an increased amount of passages and day-time operations. EXPERIMENT RESULTS SUMMARY The PRISMA mission is very active and an extensive mission timeline with many different experiment sets has been executed successfully. This has resulted in a large variety of relative orbits, with distances 3 ranging from 1 m to 45 km in along-track separation, up to 1 km cross-track and to 2 km radial distance. Figure 3 illustrates how the distance has varied over the mission. Figure 3. GPS-based relative distance over time up to December 31, 2011. On a few occasions, the GPS relative navigation has not been active. The longest period was during the AOK experiment which implemented absolute orbit keeping of a single spacecraft. This took place shortly after 400 days into the mission. The closest approaches based on GPS were performed around day 200, going as close as 2 m. Later in the mission, at day 450, an even closer approach down to 1 m was performed. This time, navigation was vision based. A summary of the main PRISMA achievements is given in Table 2. The relative use of all of these experimental modes is illustrated with Figure 4. The following sections provide summaries and conclusions from each of the GNC experiment groups of OHB-SE, DLR, and CNES. SUMMARY AND CONCLUSIONS FROM OHB SWEDEN’S GNC EXPERIMENTS AFF The Autonomous Formation Flying Module (AFF) on-board PRISMA has, as of the deadline for this article, accumulated over 9 months of closed loop cooperative satellite formation flying time. There were about 20 days for dedicated AFF experiments, and the rest has been operational routine formation flying, where AFF has been used to support other GNC experiments, maintain and reconfigure the formation between other experiments as well as act as “parking” mode over weekends and holidays. To achieve this, over 170 different formation reconfigurations have been performed. The distance range has been between 30 km down to 10 m. Figure 4. Relative use of GNC modes after Tango separation, as of December 31, 2011. 4 Table 2. Main achievements of the PRISMA mission. OHB-SE AFF: 9 months of closed loop cooperative satellite formation flying of which 20 days in dedicated AFF experiments. The remaining time has been spent in routine formation flight between 30 km to 10 m relative distances.24 PROX/GPS: First flight demonstration of close proximity GPS based forced motion relative orbit control. Full 3D translational capability demonstrated over the region spanned by [along-track cross-track radial] = [±40 ±25 ±45] m and down to 2 m relative distances. 25 PROX/VBS: First flight demonstration of close proximity single camera visual based forced motion relative orbit control over the range from 30 m down to 1 m. ARV: First flight demonstration of autonomous line-of-sight only based target search, orbit determination, orbit alignment, and approach from 30 km to 50 m relative distance. 26 CNES First flight demonstration of autonomous formation flight using a radio frequency relative sensor. Position accuracy was achieved in the range of 1-100 cm and pointing accuracies of <0.1° over the range of 30 km to 3 m relative distances.27 DLR AFC (SAFE): First comprehensive demonstration of GPS-based autonomous formation flight using relative ,29 orbital elements and impulsive control. Accuracies are below 10 m (3D, rms) for separations below 1 km. 28 AOK: First demonstration of autonomous precise absolute orbit keeping of a single spacecraft. Accuracies are below 10 m (1 sigma) on the longitude of the ascending node.30 POD: Generation of routine precise absolute and relative orbit products through GPS Precision Orbit Determination (POD) on-ground. Post-facto relative POD accuracies are below 1 cm (3D, rms).31 GPS navigation: First GPS differential carrier-phase-based real-time navigation system used on routine basis as primary relative sensor. Demonstrated on-board relative positioning is below 10 cm (3D, rms).29 ECAPS First flight and space qualification of the High Performance Green Propellant (HPGP) 1-N thruster system, including more than 34,000 pulses during 200 test sequences and 2.3 hours of firing.* Nano- First flight of the MEMS cold gas micropropulsion system. Electrical validation of control hardware was space possible although unfortunately, full system demonstration could not be performed due to a propellant leak two days in to the mission. PRIMA First flight demonstration of MEMS shutter based low energy (<100 eV) ion mass analyzer.† AFF has proven to be robust, reliable, precise, delta-V lean and at the same time requiring minimal efforts from the operations team. Given the vast amount of data, only a representative sample can be presented in this article. The AFF Completion experiment campaign took place between April 6 and 12, 2011. The activities performed can be summarized in activities A-E: A. Follower position: minus 50 m on the along-track axis. B. Circum traveler: Centered on Tango, radial and cross-track amplitude of 100 m. C. Circum traveler: Centered on Tango, radial and cross-track amplitude of 40 m. D. Phase shift of circum traveler: The relative orbits phase is changed by 25% of an orbit. E. 10 revolutions in 9 orbits: the in-plane relative orbit is changed such that Mango returns on-top of Tango after 90% of an orbit for 10 consecutive times. AFF commands to Mango were only sent before the start of the campaign. During the following 6 days no more AFF commands were sent and all activities were executed triggered on the time tagged commands that were schedule before the start of activity “A”. The duration of each activity is given in Table 3 together with performance statistics. “A” is a stable point on the along-track axis. “B” & “C” are basically the same formation but with different radii. Radial and cross-track motions have a phase difference of about one quarter of an orbit such that radial motion is maximized when cross-track is zero. “D” is the same relative trajectory as “C”, but the * Anflo, K., “ECAPS In-Space Demonstration of the HPGP System Successfully Completed,” Prisma Satellites Mission Events [online blog], URL: http://www.prismasatellites.se/hpgp-4.aspx [cited 27 May 2011]. † Wieser, M., “PRIMA Status Report,” Prisma Satellites Mission Events [online blog], URL: http://www.prismasatellites.se/prima-1.aspx [cited 13 December 2010]. 5 motion has been phase shifted a quarter of an orbit earlier. “E” describes a motion which is typical for trajectories performed when part of an orbit (in this case 10%) is used for forced motion activities. One example is when forming a rigid formation. The motion in the cross-track direction has however in “E” been left unchanged. The result is that each time Mango returns on-top of Tango the cross-track position has changed. This is very visible in Figure 5 which shows images taken with exactly 90% of an orbit between them. The control errors directly depend on the set control box for each phase. For “A”, the hard limits of the control box were set in R/T/N to 3/7/3 m, for “B” through “D”, 10/30/4 m and for “E”, 7/20/4 m. As can be seen from Table 3, the hard limits of the control box were never violated for the complete campaign. Control errors are based on post-processed data (POD). Table 3. Formation reconfiguration and maintenance results from the AFF Completion slot. A B C D E Duration [Orbits] Reconfiguration/Total 0/10.3 4.5/19.1 2.5/18 2.5/16.7 10/16.8 Control errors abs(mean/max) [m] R T N 0/1.6 0.6/3.6 0/1 0.1/3.9 3.5/13 0.1/3.8 0.1/2.6 3.6/12.1 0.1/4 0/1.7 1.7/12.8 0.1/3.6 0/3.5 0.7/11.6 0/3.6 Ideal* 0 133.0 78.0 66.2 171.1 delta-V [mm/s] Total Maintenance/Orbit 3.9 0.37 152.8 1.04 93.8 0.88 71.6 0.32 180.2 0.54 Figure 5 . Tango observed with the DVS on-board Mango. Each image taken with 90% of an orbit after the previous image. Even so, Mango is at the maximum radial position and on-top of Tango. PROX/GPS The PROX GPS experiments have shown the feasibility and practical application of a GPS navigation system in closed loop with an autonomous forced motion control system in extreme proximity of another spacecraft. Full 3D translational capability has been demonstrated with experiments spanning a region of [along-track cross-track radial] = [±40 ±25 ±45] m. Even though the GPS navigation filter originally was not designed for frequent thrust scenarios, it is capable of handling the rapidly changing activities of Mango. The experiments have shown that the PRISMA PROX GPS concept is viable when two spacecraft cooperate. However, if a relative precision below a few decimeters is required, the GPS navigation needs to handover to a navigation system which is more precise in the presence of frequent orbit maneuvers at that stage. The proximity operations and final approach/recede maneuver experiments mimic navigation about a space structure. Typically, this occurs in on-orbit servicing, on-orbit inspection, and on-orbit assembly in near-Earth scenarios. For PRISMA, two different sub modes have been implemented. The first mode is implemented for in orbit inspection of a smaller satellite. In this mode, the targeted satellite is considered to be small enough such that the avoidance region can be considered a sphere around the target satellite. The guidance function is then used to generate a general motion around this avoidance * Ideal refers to the minimum required delta-V to perform the reconfiguration given relative dynamics and no distu rbances. 6 sphere. The second mode is implemented for larger target satellites where the avoidance region can take on any shape. This mode uses an uplinked roadmap containing all the allowed waypoints and paths between waypoints around the virtual structure. The roadmap is intended to represent allowed flight regions around a large space structure. A navigation plan is then commanded containing the different goal points in the map that should be visited by Mango and the desired times for when to reach these points. To date, 86 successful PROX experiments have been executed. Out of these, 14 were performed maneuvering around a large virtual structure. As representative examples, statistics from two very different PROX/GPS experiments are presented below. One V-bar approach that starts 20 m ahead of Tango and takes Mango down to a closest distance of 2 m and then back out again; see the left part of Figure 6. The experiment is an example of a frequent thrust scenario but where the thrusts are rather small, since the relative motion follows V-bar. The second experiment is a much more thrust-heavy scenario where the objectives require a relative motion which is far from the natural orbital dynamics. In this experiment, Mango is assumed to be a service satellite released from a large space station; see the right part of Figure 6. Thrusts are more frequent in the space station experiment in which 0.965 m/s is spent in 98 thrusts during 2.4 orbits. In the 2 m approach 0.123 m/s is spent in 31 thrusts over 0.9 orbits. Figure 6. PROX/GPS experiment. Table 4. On-board GPS navigation errors during PROX. mean±std Scenario Sparse thrust 2 m approach Space station Relative position [cm] R T N 0.03±5.2 0.38±5.0 0.01±3.3 -0.2±6.2 -2.4±6.7 14.3±3.0 -5.4±12.9 -2.1±16.6 -5.6±5.5 Relative velocity [mm/s] R T N 0.02±0.18 -0.03±0.1 0.00±0.09 -0.14±0.58 -0.03±0.48 -0.03±0.23 -0.54±1.98 0±0.67 0.02±0.67 Table 4 summarizes navigation performance for the two different PROX experiments and also compares this with the normal navigation performance in a sparse thrust scenario like AFF where the natural orbit dynamics shapes the relative orbit. It shall be noted that the minimum delta-V for the thruster system was about 0.4 mm/s at the time of these experiments, which is smaller than for the space station experiment. Table 5 summarizes the control performance for the two different PROX experiments both using onboard navigation (input to the controller), and on-ground post processed navigation data. Table 5. Control statistics during the two PROX experiments presented in the article. mean±std Scenario 2m approach Space station Relative position on-board [cm] R T N -7±15 -2±13 -6±9 -29±38 5±25 3±16 7 Relative position POD [cm] R T N -7±13 -4±14 8±9 -34±43 3±35 -3±16 PROX/VBS The use of an optical navigation system in proximity operations was demonstrated in the PROX/VBS experiment. This showed centimeter level positioning performance during station-keeping on V-bar. For this purpose, the Mango spacecraft was equipped with a navigation filter that processes relative position and orientation measurements from a camera. The sensor is the close range camera which is a part of the VBS system provided by DTU. The camera observes active optical markers (flashing Light Emitting Diodes, see Figure 7) and matches the observed pattern with an onboard database of marker positions. The result is a position and orientation of the Tango reference frame, expressed in the camera reference frame. The PRISMA GNC software processes the measurements in order to arrive at a filtered position of the Mango spacecraft, relative to Tango. It also estimates the relative orientation of Tango, with respect to Mango. To this end, only the star tracker attitude measurements for Mango and the VBS position and orientation measurements are used. The other spacecraft instruments, such as the GPS, play no role in this navigation, and hence the experiment is purely optically based. Figure 7. Image (in negative) taken by the VBS Close Range Camera. The LED markers are shown as black dots. The experiment showed a transition from GPS based control to VBS based control on a reference point of 10 m distance on V-bar. The spacecraft was commanded to ensure a transition to optical navigation based control within 10 minutes, reducing the control tolerance from 1 m along track and 0.5 m cross track/radial to 10 and 5 cm respectively. The control frequency changes from 150 s to 50 s and the spacecraft reduces the minimum impulse bit from 0.04 Ns with a factor 100 by using opposed thruster pairs simultaneously with different on times. The station keeping is maintained during one complete orbit. The whole experiment is autonomous, without ground intervention, and concludes with a handover to GPS based control on 20 m, followed by an automatic entry into an AFF controlled safe orbit at some 150 m distance. Table 6 summarizes the positioning performance of the station keeping by means of the VBS navigation filter data, as well as the POD post processed GPS data from DLR. As the GPS is not in the loop of the control system, during this experiment, and the VBS data is not used for post processing, the POD data is a completely independent approach to characterize the relative orbit. The two performance characterizations cannot be compared in terms of bias: the reference frames of both navigation systems are not related to each other. Table 6. Control Performance Statistics of PROX/VBS 10 m station keeping. mean±std Scenario H-SLO-PX-4 mean±std Scenario H-SLO-PX-4 Relative position onboard [cm] R T N 0.2±1.3 -0.5±1.5 0.0±0.9 Relative velocity onboard [mm/s] R T N 0.0±0.5 0.0±0.3 0.0±0.4 8 Relative position POD [cm] R T N 2.9±1.7 0.0±1.3 -1.2±1.0 Relative velocity POD [mm/s] R T N 0.0±0.6 0.0±0.3 0.0±0.4 The advantages of an optical navigation system for a proximity station keeping task under frequent thrusting become clear when the GPS on-board navigation is observed to show a difference in the order of decimeters with the POD data, despite the GPS navigation filter not having been designed for these conditions. The positioning performance with the VBS based navigation is concluded to be stable to better than 5 cm. A large part of this performance is driven by the navigation performance, with quality of actuation as the second major contributor. The latter can be seen in that the control alternates sign between many cycles. An alternative explanation is that the quality of the model prediction in the control is not sufficient in the experimental conditions. This suggestion is substantiated by observed navigation propagation during measurement absence. The left plot of Figure 8 shows a portion of the time history of the experiment, indicating the VBS sensor data (converted into the position of Mango with respect to Tango, in the local orbital frame), the filtered navigation data, and the POD post processed GPS data. It can be seen that the onboard navigation filter reduces a substantial amount of noise, which is not all together Gaussian. The sensor noise at this distance is dominated by an oscillating uncertainty of the Tango orientation, which couples into the position measurement, but is not compensated for onboard. The figure also indicates the control requests in terms of delta-V as black vertical lines. Mango Position in Tango Body Frame [m] 1 10.025 0.5 sensor Tango X Tangent ial Mango Relative Position [m] 10.05 10 sensor 9.975 POD 200 300 400 500 600 700 800 -1 900 0.05 -2 0.025 -4 Tango Y Normal 100 0 -0.025 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 Time [s] 2000 2500 3000 500 1000 1500 2000 2500 3000 -6 -8 -0.05 -10 0 100 200 300 400 500 600 700 800 900 1.5 0.05 1 T ango Z 0.025 Radial POD 0 -0.5 filter 9.95 0 filter 0 -0.025 0.5 0 -0.5 -0.05 0 100 200 300 400 500 Time [s] 600 700 800 -1 900 0 Figure 8. PROX/VBS and FARM experiments. Left: PROX/VBS Station Keeping at 10 m distance on V-bar. Right: FARM time history in Tango body frame with an approach along the Y axis. The approach corridor is shown as a dashed line. FARM Since the relative orientation of the Tango satellite is known from the optical measurements, the VBS based PROX has an additional capability when compared with the GPS based PROX: It is able to position the Mango satellite at points expressed in a reference frame fixed to Tango. Any rotation of Tango will in this way cause Mango to follow along. In an application, this would enable the chaser satellite to perform operations (e.g. docking, maintenance using manipulators, refueling etc) on the target satellite. The PRISMA experiment demonstrates only the positioning capabilities in the close vicinity of the target. One specific experiment is a simulated docking: FARM. The chaser satellite is commanded to approach the tar- 9 get satellite, at a given target body axis, with prescribed speeds and beginning/end points, as well as a definition of a control corridor within which the chaser needs to maintain its position. The FARM experiment is prepared from an initial GPS-based delivery at 10 m along track, by using the optical navigation to position the spacecraft on 10 m fixed relative to the minus Y panel of the Tango satellite. From here, the VBS observes a Tango panel with docking target markers which allow a very short inter-distance. Due to the loose attitude control of the Tango spacecraft, the Tango Y-axis is not aligned with the V-bar in the orbit, and therefore Mango needs to autonomously arrive at a position out of plane. Half an orbit is allowed for this, with a control tolerance of 0.5 m in all axes. Subsequently, the FARM experiment starts with a 1500 s approach down to 2 m, and an equally long retreat back to 10 m, all of this in the moving Tango spacecraft fixed frame. The attitude of Mango is aligned with Tango, so both spacecraft behave as one single entity with only the distance as parameter. The spacecraft then moves itself back to the 10 m along track position, still under optical navigation. Finally, the 20 m point is moved back to GPS based control. The FARM approach is performed in a corridor that is specified as 0.5 m tolerance at the entrance gate (10 m), and 15 cm tolerance at the target (2 m). A velocity of just below 6 mm/s is requested from start to finish. The right plot of Figure 8 shows the time history of a FARM experiment with sensor data, the onboard filtered state estimate and the reconstruction based on DLR’s POD data and the Tango onboard attitude estimator based on magnetometer and sun sensor. Figure 9 shows the same information but in projections of the Tango body frame. Mango in Tango Body Frame - In Plane -2 Out of Plane -2 Tango Y [m] filter -3 -3 -4 -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 -9 -10 -10 -11 -1 -0.5 0 0.5 Tango X [m] 1 -11 -1 POD -0.5 0 0.5 Tango Z [m] 1 Figure 9. FARM experiment in Tango body axes. Projections for in plane and out of plane motion, but fixed to Tango rotating body. During this particular experiment, the minus Y-axis of Tango makes an angle of about 10° with V-bar, both in and out of the orbital plane. At 10 m distance, this accounts for as much as 2 m both in radial as in cross track. At closest approach, there is a sudden change in the rotational rate of Tango, and it rotates the minus Y spacecraft axis from -8° to over +20° out of plane in about 15 minutes before being stabilized. In plane the attitude changes from -5° to -20°. The out of plane position of Mango at 10 m is therefore about 4 m from the orbital plane and 2 m below V-bar. This sudden change in Tango attitude is believed to be a thruster plume impingement effect. It was observed that the VBS measurements are in better agreement with the data based on Tango magnetometer and sun sensor, than the navigation filter results. The disturbed dynamics not being assumed by the navigation filter, the navigation filter lags behind, causing an orientation mismatch of 2 to 3 degrees. As most of this deviation occurs at close distance, the linear positioning errors in Tango body frame are limited. The control system uses the widening recede corridor to the maximum, but the reconstruction based on POD and Tango’s own estimates show that in reality, the spacecraft was about 0.5 m outside the corridor by the end of the recede. The target point at 2 m is reached with an accuracy of 5 cm according to the onboard filter, with the POD difference being about 3 cm larger. During the last meter of closing in, the lateral stability of Mango is better than 2 cm. The 50 minute (half orbit) approach and recede maneuver consumed 16 Ns impulse. 10 ARV The Autonomous Rendezvous experiment (ARV) aims for an exclusively optically based rendezvous maneuver with the Tango spacecraft that is part of the PRISMA satellite duo. To this end, the chaser spacecraft (Mango) uses the VBS developed by DTU. From a distance, Mango is to autonomously detect Tango with this sensor and to perform relative navigation. The challenge in this scheme is that this is done with line of sight information only since range information is not available from the sensor at this distance. Two different kinds of ARV experiments were performed, showing that the PRISMA ARV concept is a viable one and that line of sight only navigation is possible and practical. The major challenge in systems like this has shown to be robustness against false or erroneous sensor data. The critical first detection of Tango must be guarded by checks on the trajectory determined by the navigation filter. The extended Kalman filter line of sight navigation filter developed by OHB Sweden, estimates the trajectory of Mango relative to the Tango, using the line of sight measurements from the VBS and the spacecraft attitude and accelerometer measurements. A key element of the navigation filter turned out to be the correct rejection of false measurements from the sensor. The measures against sensor errors implemented in the navigation filters onboard PRISMA proved to be sufficient to perform the experiments. Despite large residual range errors on long distance, the perspective will ensure a reduction of these errors on delivery. The location of in-plane crossings and perigee is a much more important goal during the alignment and approach, and this proved to work very well. The ARV experiments have been exercised during two campaigns where all the various components of the ARV module were commissioned. The campaigns culminated in a complete rendezvous from 30 km distance. The experiment starts with Mango positioned in a different orbit than Tango at a relative distance of about 30 km. Orbit knowledge of Tango is given with representative errors. Without any further knowledge or operator inputs Mango must complete a full ARV consisting of an initial search for Tango, and a subsequent centering of Tango in the field of view of the VBS. The camera angles are used here directly to guide the attitude of the spacecraft. This phase is followed by several orbits of Orbit Determination, to establish a reference orbit of Tango, starting out from the known Mango orbit. After this, Mango aligns the two orbits to the specified tolerance, apart from the difference in mean anomaly. The final phase reduces the range to Tango in a controlled way, until arrival at the delivery point 50 m away from Tango in alongtrack. Delivery was successful and maintained within ±5 m of the delivery point during the last orbit before terminating the experiment. An overview of the 30 km rendezvous is given in Table 7. Table 7. Overview of 30 km rendezvous. Phase Target Search Orbit Determination Orbit Align Orbit Closing End of Experiment (AFF entrance) Time (UTC) 2011 -04 -05 16:53:29 2011 -04 -05 17:47:51 2011 -04 -05 22:47:38 2011 -04 -06 03:14:57 2011 -04 -06 22:37:33 Navigation accuracy [m] Start: ~6000 End: ~2000 Start: ~2000 End: ~1500 Start: ~1500 End: ~2 Delta V [m/s] 0 0.82 0.94 1.41 FLIGHT RESULTS FROM DLR’S CONTRIBUTIONS TO PRISMA GPS Navigation The GPS navigation system developed by DLR and integrated by OHB-SE into PRISMA represents the primary absolute and relative positioning sensor of the formation. On one hand, it is intended to serve the needs of the spacecraft baseline platform in terms of formation safety monitoring and collision avoid ance. On the other hand, it feeds the on-board feedback controllers which constitute the GNC experimental payloads. The resulting operational scenarios are quite challenging since the formation safety requires robust and reliable relative navigation under all circumstances, whereas the formation control experiments require ultimate relative navigation performance. Due to its fundamental role, the GPS-based navigation system was commissioned during the first two months of the mission, before the official start of the formation flying experiment timeline. In the absence of an independent on-board positioning sensor with sufficient tech- 11 nology readiness level and flight heritage, the characterization of the on-board GPS navigation had to rely mainly on comparisons with POD products generated post-facto on the basis of the same GPS data processed on-board. The strategy adopted to commission the GPS navigation system on PRISMA included three fundamental steps. First, the GPS hardware system on Mango and Tango (see Reference 7, Figure 11) was checked out in terms of functionality, signal acquisition and signal strength. Secondly, the capability and performance of the on-ground POD facility was verified when Mango and Tango were still clamped in a combined configuration. Here, the known constant relative position between the spacecraft center of mass served as a reference to assess the performance of the on-ground relative positioning. Finally, the POD products gave the possibility to evaluate the real-time navigation errors and tune the on-board navigation 31,32 filter in dedicated calibration efforts to obtain the best trade-off between robustness and accuracy. Up to the end of the nominal mission timeline, nearly 1.5 years of GPS-based autonomous closed-loop operations have been completed. High navigation performance could be demonstrated both in formation keeping with passive relative orbits as well as proximity operations with forced motion control. Moreover, the crosscomparison of relative GPS with other experimental relative navigation sensors embarked on PRISMA (i.e., FFRF and VBS) has led to a centimeter accurate in-orbit calibration of novel RF and optical metrology systems which are considered as key technologies for future multi-satellite missions. Figure 10. GPS relative navigation errors and SAFE (AFC) control tracking errors. Left: Onboard GPS relative navigation errors in radial (top), along-track (middle), and cross-track (bottom) derived from POD. Orbit control maneuvers are indicated in red. Right: Onboard SAFE (AFC) control tracking errors in radial (top), along-track (middle), and cross-track (bottom) derived from POD. The left plot of Figure 10 provides the typical relative navigation accuracy obtainable through carrierphase differential GPS on the PRISMA mission. As compared with the POD product, the relative position and velocity errors are about 5.14 cm and 0.14 mm/s (3D, rms) respectively and thus well below the formal requirement of 0.2 m and 1 mm/s defined at the beginning of the mission. It is noted that the tuning of the navigation filter plays a key role in the achievable accuracy, and especially the weights of measurement noise and a-priori standard deviation of the empirical accelerations have to be carefully considered. As an example, the filter settings applied during the considered scenarios introduce relative large empirical accelerations in radial direction as compared to the other components. The resulting loose constraint on the relative dynamics causes larger errors in radial direction, but is shown to be beneficial for the absolute orbit determination accuracy which amounts to 1.7 m and 4.0 mm/s (3D, rms) for the same period of time. More results on the demonstrated accuracy of the GPS-based navigation performance are presented in References 29 and 33. Spaceborne Autonomous Formation-flying Experiment (SAFE) SAFE represents one of the primary PRISMA mission objectives and consists of a self-contained endto-end GNC subsystem for formation flying satellites in low Earth orbit (see AFC mode in Table 1). SAFE is intended to demonstrate autonomous acquisition, keeping, and reconfiguration of passive relative orbits for advanced remote sensing and rendezvous applications. Flight results from the SAFE closed-loop ex- 12 periment executed by DLR in September 2010 and March 2011 are discussed in References 29 and 34. SAFE has demonstrated the capability of the DLR’s GNC subsystem to establish, maintain, and reconfigure arbitrary baselines in space in full autonomy. The applied impulsive relative orbit control scheme is based on the parameterization of the relative motion in terms of relative eccentricity and inclination vectors and has been shown to be fuel efficient and passively safe. The in-plane relative motion is controlled using a pair of maneuvers whereas a single maneuver is enough to control the out-of-plane relative motion. A total of 22 different formations have been prescribed via telecommand during the 35-days flight experiment which have all been smoothly acquired and accurately maintained without ground-intervention. The formation geometries span a wide range and are characterized by mean along-track separations between 0 and 5 km, and oscillation amplitudes in radial and cross-track direction between 0 and 400 m. A minimum separation of 20 m between Mango and Tango was acquired and maintained on March 21, 2011. The average duration of fine formation keeping for each configuration was 13.4 orbits (22.3 h) for a total of 294.7 orbits (20.4 days) or approximately 58.3% of the experiment duration. The maneuver cycle for in-plane control or the distance between consecutive pairs of maneuvers was two orbital revolutions in average. The demonstrated formation keeping accuracies spanned a range from 1.1/1.7/0.1 m in Radial/Along-track/Cross-track directions at approximately 100 m separation up to 30.6/38.0/1.4 m at 5 km along-track distance. Representative control tracking errors during formation control are illustrated with the right plot of Figure 10 and are clearly dominated by second order relative dynamics effects which are neglected by the adopted relative motion model. Formation reconfigurations were characterized by average convergence times in cross-track direction of 1.2 orbits, and two cross-track maneuvers were in general sufficient to obtain any desired out-of-plane correction. The average convergence time in radial and alongtrack directions is correlated and amounted to 2.4 orbits. Typically 2-3 pairs of in-plane maneuvers were sufficient to enter the fine formation keeping phase. Mean along-track reconfigurations required longer convergence times of 3.7 orbit revolutions in average. The total commanded delta-V during SAFE amounted to 38.58 cm/s for formation keeping and 2.63 m/s for formation reconfiguration. More results from the post-facto evaluation of the SAFE experiment are presented in Reference 28. Autonomous Orbit Keeping of a single spacecraft (AOK) The AOK experiment represented the DLR’s secondary mission objective (see AOK mode in Table 1). It was executed successfully from July 18 to August 16, 2011 and demonstrated precise autonomous abso13,30 lute orbit control of a single spacecraft. The main performance requirement was a control accuracy of 10 m (1) on the Longitude of the Ascending Node (LAN) with a maneuver budget constraint of 0.5 m/s. AOK adopts a guidance law for the orbits’ LAN that implements an analytical feedback control algorithm using along- and anti-along-track velocity increments. Using GPS-based absolute navigation data, AOK commanded thruster activations in the orbital frame to autonomously control the orbit within the prescribed window. The position and velocity vector of Mango at 01:00 UTC on July 18, 2011, as estimated by the GPS based POD process, have been taken as initial state for the generation of the reference orbit onground. In a first phase of the experiment, AOK demonstrated reference orbit acquisition capability reducing gradually the LAN deviation from 300 m to within the prescribed control window. After the convergence phase, at steady-state, the control accuracy requirement was fulfilled with slight margin. The mean value of the LAN error controlled by AOK was -3.6 m with a standard deviation of 9.5 m during the fine control phase. The mean maneuver cycle was 11 hours with a standard deviation of 8.3 hours. The total delta-V spent during the entire experiment was 0.1347 m/s corresponding to 27% of the allocated maneuver budget. Conclusions and Way Forward The demonstrated GPS-based guidance, navigation, and control functionalities form one of the first GNC subsystems for autonomous formation acquisition, keeping, and reconfiguration in Low Earth Orbit. The onboard GPS navigation system provides relative orbit information in real time with an accuracy better than 10 cm and 1 mm/s (three-dimensional, root mean square) in position and velocity, respectively. The impulsive formation control achieves accuracies better than 10 m (3D, rms) for separations below 2 km with minimum usage of thrusters, ensuring high predictability for simplified mission operations and minimum collision risk for increased safety. 13 The navigation system has proven to fulfill the design requirements, to be accurate and reliable in most of the circumstances. This is considered a remarkable achievement, especially considering the challenges given by the numerous scenarios encountered on the PRISMA mission and by the utilization of GPS as primary sensor of the formation. Although an optimal set of a-priori and measurements standard deviations of the navigation filter could be tuned in orbit, a weakness of the filter design was found to be the purely absolute handling of empirical accelerations. This does not allow an arbitrary constraining of the relative dynamics without degrading the absolute navigation accuracy. A more balanced and probably more accurate approach is instead to incorporate the a-priori standard deviations for the relative empirical accelerations between the spacecraft in the covariance matrix. A second suggested improvement of the filter design is related to the handling of orbit control maneuvers. Indeed the reduction in accuracy during forced motion control could be mitigated through an estimation of the maneuver delta-Vs over longer periods of time using consecutive GPS measurements instead of only a one-epoch set. SAFE and AOK have shown to fulfill the typical requirements of future distributed satellite systems for Earth observations and outperform the control performances achievable from ground. Nevertheless, the applied control strategies do not exploit the full potential of the navigation state available on-board. In fact, the orbit keeping accuracy as well as the orbit reconfiguration convergence time are constrained by the analytical feedback control law itself which relies on pairs of maneuvers every few orbital revolutions. A weakness of the current formation control interface and logic design is the unavailability of a dedicated independent state machine for mean along-track control. The maneuver cycle for the control of the relative mean argument of latitude is implicitly determined by the violations of the control windows for relative eccentricity/inclination vectors and is not otherwise under user control. This implementation does not facilitate an efficient planning of along-track reconfigurations over a desired time interval in terms of propellant consumption. The identified limitations can be considered as lessons learned from the successful execution of these experiments during the nominal PRISMA mission. The extended mission phase offers the possibility to further study these aspects and demonstrate possible improvements in-orbit. In particular, a new version of the GPS navigation software has already proven improved performance and robustness through playbacks of the gathered telemetry. Moreover, DLR plans a new experiment for execution during the extended mission phase. The experiment is an Advanced Rendezvous demonstration using GPS and Optical Navigation (ARGON). The ultimate goal of ARGON is to demonstrate ground-in-the-loop far-range rendezvous to a non-cooperative client using vision-based navigation. To this end, flight data and user experience acquired during DLR’s PRISMA experiments are being used to accurately design the navigation approach and to predict the related performances. FLIGHT RESULTS FROM THE CNES FFIORD EXPERIMENT CNES participated to the PRISMA mission through the Formation Flying In Orbit Ranging Demonstration experiment (FFIORD). The experiment cornerstone was the Formation Flying Radio Frequency (FFRF) metrology sub-system designed for future outer space FF missions and for which in-flight characterization constituted the first objective. The second objective of FFIORD was to test several Guidance Navigation and Control (GNC) algorithms relying on FFRF sensor data developed to achieve autonomous rendezvous and control of two satellites in close formation. The FFRF Sensor35 has been developed by Thales Alenia Space with a partnership from the Spanish Center for Development of Industrial Technology (CDTI). It is a distributed instrument designed to provide range and Line Of Sight (LOS) measurements at 1 Hz with a typical accuracy of 1 cm and 1°. Its functional principle is inherited from the Topstar GPS using dual frequency S-band signals. Requirements included also the lost in space capability assuming some indirect assistance from the GNC system for signal ambiguity resolution (IAR). Besides, its generic initial design was adapted to fit the accommodation constraints on PRISMA (10 kg and 30 W) and to take into account the formation asymmetric structure composed of a smart chaser satellite (Mango) and a passive target (Tango). In addition, the instrument offers an intersatellite link (ISL). This capability, not part of the nominal PRISMA communication system, was exercised only for validation. 14 The other major FFIORD contribution consists of a complex software (designed to take over Mango or36 bit control) fully developed within the Matlab / Simulink environment. The FFIORD Simulink library was integrated within the GNC core (1 Hz activation) of the whole PRISMA Onboard Software (OBSW) before automatic code generation. The FFIORD GNC software implements its own mode handler and FDIR module together with a set of Navigation, Guidance and Control functions. RF navigation is active whenever the FFRF sensor is active and provides the estimated companion relative state (position, velocity) permanently. Conversely, guidance and control depends on the activity being performed (rendezvous, relative orbit keeping, transfer between two relative states, proximity operations, collision avoidance) and specific algorithms are being triggered in each case. The FFIORD experiment timeline (52 allocated days and 6 m/s budget) has been designed to progressively validate the whole set of functionalities implied in the experiments. The timeline started with passenger experiments (in parallel with other primary experiments), then it went through primary experiments performed in Open Loop (relying on the GPS based PRISMA Formation Flying services), and finished with long duration Formation Flying operations for a total of 12 days. To get the best benefit of the delta-V budget, a very complex and dense mission timeline was built (Table 8). Table 8. Number of FFIORD Formation Flying experiments. GNC Activity Number of occurrences RF Navigation Continuously Standby Proximity operations Rendezvous N*2 maneuvers transfer Collision avoidance Duration 12 days closed loop, 40 days open loop 5 nominal SBY 2 with autonomous transfer in case of anomaly 7 sessions 6 nominal RDV with distances up to 9 km 1 reverse RDV 11 simple 2MT 2 multi-orbits 2MT 2 double boosts (“Soft” CA) 4 single boost (”Drift” CA) 3 days 2 days 4 days 1 day 2 days FFRF Sensor validation FFRF sensor data collection included 52 days altogether and the behavior has been satisfactory in the different functional tests performed during the characterization phases. Detailed results are available in Reference 37 and the main characteristics are summarized below:  once the signal was acquired, FFRF functioned properly from 3 m to 30 km and signal acquisition was 100% successful up to high bearing angles (90°) and distances up to 9 km (no test performed beyond)   LOS initialization was 100% valid up to 35° elevation (IAR process) performances were consistent with expectations: a few cm on distance and < 1° on LOS angles at low elevations and fine performance on distance was available after 20 minutes LOS and distance multi-path calibration were successfully achieved using GPS POD as reference  The FFRF instrument was expected to show measurement errors due to multipath effects for large bearing angles and this limitation was observed in flight with error variations in the 1.5° range for bearing angles up to 80°. Concern was raised when error variations were observed also in presence of tiny excursions about the line of sight since multipath bias was assumed constant in a cone of several degrees around that line (this was attributed to the antenna having a far from optimal accommodation). Another not anticipated weakness, since analysis had shown it negligible, was the sensor temperature sensitivity. After instrument warm-up, small temperature evolutions in the 1° range could produce a 0.1° variation on the most sensitive axis (azimuth). Even though RF navigation included a bearing angles bias estimator, these bias variations negatively impacted navigation performances. The performance level of this S-band instrument strongly depends on the ability to cancel or mitigate different bias sources due to internal signal path delays and particularly the external uncertainties such as antenna characteristics (phase centre position origin) as well multi-path effects. On the ground, calibration 15 tests with representative PRISMA mock-ups have been performed in an anechoic chamber to build a code and phase cartographies function of the bearing angles. Additional calibrations (using GPS POD as reference) were subsequently performed in flight to possibly consolidate this data. Unfortunately, results have shown some overall consistency but differences between maps reached locally the same magnitude as the error itself. Discrepancies have demonstrated the difficulty to reach an acceptable fidelity level for the radio electric mock-ups in the PRISMA context and cancel all perturbations in the whole ground calibration process. It is therefore wiser to concentrate on the calibration of internal error sources (particularly to reduce distance absolute error) and live with the external sources that can be mitigated for instance with a better antenna accommodation on the satellites. Navigation performances (in closed loop activities) The navigation function implements an Extended Kalman Filter with 8 states (3 for relative position, 3 for relative velocity, and 2 states associated with the bearing angles bias). Relative dynamics are indirectly modeled using the difference between the two spacecraft absolute states (obtained from integration of a simplified orbital model including J2 gravity term). RF navigation was validated in open-loop during the extensive sensor characterization phase and was finally qualified for closed loop rendezvous and FF activities. The performances were assessed using GPS POD delivered by DLR and got close to expectations in the different regimes (Table 9). Table 9. FFRF Navigation performances. Errors represent the conversion of the position errors into the two bearing angles (in-plane, cross-track). Mode Distance range Rendezvous 4000 – 200 m Free drift (after CAM*) Relative orbit keeping Proximity operations 60 – 4200 m 60 - 140 m 20 m Position error in SLO (cm) Bias [5.7 24 0.9] Std [1.7 350 7.4] Bias [8 -1.3 2.1] Std [3.5 27 10] Bias [-31 2.3 1.0] Std [3.0 13.0 5.5] Bias [-2.7 6.2 5.4] Std [0.6 2.2 1.8] Angular error (deg) Bias [0.0016 0.0039] Std [0.009 0.091] Bias [0.002 -0.0003] Std [0.037 0.037] Bias [-0.0022 0.0023] Std [0.038 0.093] Bias [0.16 0.028] Std [0.050 0.039] The best performance was obtained during the proximity operations activity at 20 m, with a few cm accuracy on all axes. Conversely, errors during rendezvous reached a few meters on the cross-track component from medium to long ranges. This behavioral difference is actually not significant since angular errors happen to be equivalent and it only shows that the residual angular errors get logically amplified by the range. Even though short range accuracy could not be reduced below the initial target of 1 cm, navigation errors converted in bearing angles which remained below 0.1° for all medium and long range activities and fulfilled therefore the guidance requirements. GNC performances All the 12 days of FFIORD closed loop experiments ran smoothly and the objectives (number of tests, functional behavior , performance) were achieved. Rendezvous guidance38 is based on model predictive like control methods with maneuver dates fixed on ground and L2-norm criteria for the minimization of the consumption. Relative dynamic modeling relies on Yamanaka-Ankersen equations.39 Rendezvous activities included six approaches from distances of 4-7 km to a few hundreds meters and one deployment from 600 m to 5 km. One of these maneuvers is illustrated with the left plot of Figure 11. Rendezvous durations went from 7 to 14 orbits and the delta-V usage covered a 7-29 cm/s domain quite in line with expectations. Final rendezvous accuracy went below 20 cm (dX=-0.16 m, dY=0.08 m, dZ=0.18 m) for the closest delivery point at 160 m whereas it was metric for end points in the kilometer range. The position error major contributors were the maneuver computation (J2 * Collision Avoidance Maneuver 16 term effect is not modeled and this affects accuracy at long range) and maneuver execution whereas the RF navigation effect was actually secondary. 40 Relative orbit-keeping guidance consists of applying periodical delta-Vs computed from the Yamanaka-Ankersen inverse state transition matrix. The typical delta-V period is once per orbit for a typical relative distance of 300 m with 20 m radial and cross-track amplitude. This function was activated during 40 orbits for an overall cost of approximately 7 cm/s translating into a mean budget of 1.7 mm/s/orbit. The demonstrated formation keeping accuracy reaches an average of 30 cm in cross-track direction and a few meters in radial and along-track directions. The collision avoidance function computes one instantaneous open loop maneuver (and a second one if this option is selected) that transfers the spacecraft onto a relative orbit staying outside the safety sphere. The first option (“drift” CA), which is very simple and robust, consists of achieving a relative drift between the two satellites. The second option is inspired by geostationary spacecraft collocation and phases radial and normal separations so that when one is null, the other one is maximal. A total of 5 successful collision avoidance maneuvers were performed with the Mango relative trajectory exiting the prescribed keep-outzone a few seconds after the maneuver. Figure 11. FFIORD experiment. Left: Rendezvous performed from 6.5 km to 500 m on February 2, 2011 with 8 maneuvers (represented by red squares). Bottom plot shows the accuracy achieved at endpoint [0.07 m, 1.0 m, -1.4 m]. Right: Proximity operations control tracking errors based on POD (blue) and on-board FFRF navigation (dotted red) at 20 m distance on March 11, 2011 with and without sub-pulse mode activated. Table 10. Navigation and control accuracy during proximity operations (along SLO axis). Activity 80 m SK no sub-pulse 80 m SK with sub-pulse 20 m SK no sub-pulse 20 m SK with sub-pulse Navigation error (cm) POD as Ref Bias = [-3.7 -11 5] Std = [0.5 4.7 5.4 Bias = [-3.5 -15 14] Std = [0.5 3.4 3.3] Bias = [-2.7 6.2 5.4] Std = [0.6 2.2 1.8] Bias = [-2.8 1 5.7] Std = [0.6 1.4 1.7] Control accuracy (cm) RF nav as Ref Bias = [0.1 0.6 1.6] Std = [1.8 2.5 3.2] Bias = [-0.1 -0.1 0.9] Std = [0.9 1.8 1.6] Bias = [0.2 1.3 1.1] Std = [1.1 2.3 2] Bias = [[-0.4 -0.1 1.4] Std = [1.1 0.7 0.8] Control accuracy (cm) POD as Ref Bias = [3.8 12 -3.4] Std = [1.8 5.7 6.7] Bias = [3.4 14 -13] Std = [0.9 4.1 3.5] Bias = [2.9 -4.7 -4.3] Std = [1.1 3.6 2.7] Bias = [2.4 -1.1 -4.3] Std = [1.3 1.5 1.9] The best control accuracy in the FFIORD experiment was demonstrated during the proximity operations activities which included station-keeping and forced translations. To improve the propulsion system resolu- 17 tion (thruster MIB = 100 ms), the sub-pulse mode was used with thrusters functioning in a differential way to realize the requested inputs. Station keeping at 80 m and 20 m separations was exercised with quasicontinuous activations of the thrusters (200 s control cycle). As illustrated with the right plot of Figure 11, navigation and control errors based on the reference POD show accuracy at centimeter level in both bias and standard deviation. Table 10 summarizes the performance obtained in the different regimes. Conclusion from the FFIORD experiments The FFIORD experiment onboard PRISMA has demonstrated in flight the feasibility of autonomous formation flying operations based on the FFRF sensor and associated navigation functions. Autonomous rendezvous ranging from 10 km down to 100 m have been successfully executed with a typical accuracy of 1 m. This paves the way to the acquisition of future spacecraft formations. Even though the FFRF sensor was presumably a first metrology stage with coarse localization accuracy, proximity operations have been run over long periods of time with a performance close to 1 cm (1σ), hence demonstrating the capability to control a distributed instrument like a telescope, to retarget it and to adjust its focal length. Other formation flying fundamental building blocks have also been validated with the collision avoidance activities ensuring the formation safety, and the standby activities allowing for a coarse and low delta-V consumption control over a relative periodic orbit. CNES has taken advantage of the testing environment flexibility and the extended mission opportunity to perform a complementary experiment in October 2011. CNES delivered a new GNC software including this time vision based navigation using the two platform VBS developed by DTU. The Far Range camera that provides at any range the “target” bearing angles was used to perform vision based rendezvous. The Close Range camera that can determine the relative 3D position of the cooperative target carrying LEDs was further used as a second metrology stage for proximity operations under 30 meters range. Four rendezvous were performed with success from ranges up to 10 km and destinations down to 50 m. Four series of transitions between RF based and VBS based navigation were exercised satisfactorily during tight proximity control to demonstrate the multi-stage metrology system needed for future formation flying missions. Detailed flight results will be presented in future publications. CONCLUSIONS PRISMA has demonstrated a large variety of aspects of formation flying and rendezvous. The GNC experiments include several sets of experiments involving closed loop orbit control using the GPS, VBS, and FFRF on-board sensor systems. 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