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Operational Flight Dynamics System for PROBA-3 Formation Flying Mission

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Operational Flight Dynamics System for PROBA-3 Formation Flying Mission Operational Flight Dynamics System for PROBA-3 Formation Flying Mission 1) 1) 1) By Pablo GARCÍA, Catherine PRAILE, and Jesús ROBLES 1)GMV, Madrid, Spain This paper describes the Flight Dynamics System for PROBA-3. Previous PROBA missions were demonstrating the on-board autonomy capabilities of the spacecraft and hence did not include any FDS on ground. However, PROBA-3 aims to validate the automatic formation flying of two satellites. The high level of activity performed on board imposes some heavy requirements to the ground segment in general, and to the Flight Dynamics System in particular, that forces them to deviate from the standard design of this system. Besides, the FDS is also in charge of evaluating the performances of the on-board formation flying system. Key Words: Proba-3, Flight Dynamics, Formation Flying Nomenclature (FF) and collision avoidance manoeuvres (CAM) between both satellites are automatically computed on board, FDS is 푟̅ : position responsible for the manoeuvre computation for initial 푣̅ : velocity formation acquisition, recovery from CAM and formation Ω : angular velocity resizing. Subscripts - Collision risk evaluation between the two satellites is being OSC : Related to Occulter Spacecraft performed as part of the manoeuvre computation and will be CSC : Related to Coronagraph Spacecraft evaluated accounting for both misperformance and failure to execute any manoeuvre in a commanded batch. 1. Introduction - On-ground FFS calibration, based on the telemetry analysis and the results of the orbit determination, FDS shall perform PROBA-3 is the fourth ESA mission of the PRoject for the calibration of the on-board software in particular for the On-Board Autonomy (PROBA), aimed at the demonstration perigee pass and formation acquisition manoeuvres. of European on-board technology. It is intended to validate Additionally, the flight formation performance analysis in in-orbit formation flying techniques and technologies with the terms of relative orbit and attitude will be also carried out scientific aim of observing the Sun’s corona during a mission within this system. lifetime of 2 years. The mission is composed by two spacecrafts (coronagraph and occulter) on a high-elliptic orbit, 3. PROBA-3 Orbit building a virtual telescope during scientific operations near the orbit apogee. This requires very precise formation flying PROBA-3 will be located in a High Eccentricity Orbit of the two objects distant 150 m from each other around the (HEO) in order to perform Sun coronagraphy around the apogee. apogee. Whereas the ideal orbit to perform such a mission would be a halo around L1, the HEO orbit apogee allows 2. Generic Flight Dynamics Functionality representative environments for most of the intended demonstrations, requiring only reduced launch capabilities 1) PROBA-3 mission has very demanding performance with respect to the orbit around the Lagrange point . requirements for the on-board Guidance Navigation and Table 1 shows the reference orbit parameters for the Control (GNC) system, which is in charge of controlling the PROBA-3 orbit. formation flying through a dedicated system, FFS. However, the monitoring of the system on ground also Table 1. Orbital elements imposes some particular requirements on the flight dynamics Parameter Value system (FDS). This system covers the following Perigee height 600 km Apogee height 60530 km functionalities: Inclination 59º - Orbit determination, focused on the relative distance RAAN 84º between the two satellites, being this critical for the mission Argument of Perigee 188º objectives. - Orbit and events prediction, which has to account for the 3.1. Nominal orbit managed from FFS on-board controlled phases for the formation flying. During the six hours around the orbit apogee, between - Manoeuvre optimisation: whereas routine formation flying approximately 170 and 190 degrees in true anomaly, the two 1 satellites are flying in formation. In this phase, both satellites within GPS visibility range. Relative GPS data is used for the are intended to behave as a solid body, pointing towards the navigation, so at the end of the perigee pass (true anomaly Sun and separated by a constant distance of 150 m, with the close to 118 degrees), the relative position is known with an OSC interposing its disk-shaped body between the CSC and error slightly above 2 cm (1σ) and an estimated bias close to 4 the Sun. The CSC is flying without internal perturbation, cm (1σ). This accuracy is needed for the formation while the OSC uses the Cold Gas Propulsion thrusters reacquisition performed with the second DTM, about one hour (providing a thrust of a few mN) to keep the formation shape. before the start of the formation flying phase. FFS on-board is managing different inputs from the GNC 3.2. Orbit prediction and several instruments (in particular the Fine Longitudinal Orbit prediction is highly influenced by the formation and Lateral Sensor, FLLS, and the Coarse Lateral Sensor, flying performed on board. First of all, not every orbit is CLS) to compute the relative position. The fine metrology is intended to be used for coronagraphy, so the Flight Dynamics available in the CSC and the actuation during the formation system needs to ingest the mission plan in order to know in has to be performed by OSC, so the on-board software must advance when the FFS will be active. compensate the delays of the inter-satellite link (ISL) and Considering that the two satellites are autonomously synchronise the on-board time (OBT) of the two satellites. manoeuvring during the nominal orbits in which science is to After the data synchronisation, the final estimation of the be performed, none of them can be propagated independently relative position and velocity is implemented as a Kalman from the other. Furthermore, the perigee pass preparation and Filter, using the Yamakara-Ankersen formulation for the formation acquisition manoeuvres implemented by the CSC dynamic modelling of the relative motion, and computing and introduce a dependency between the orbit propagation and the commanding the required ∆V to keep the formation2). manoeuvre computation modules within the ground system. After a perigee pass (true anomaly equal to zero), the orbit must be propagated until the start of the formation acquisition phase (defined either by the time after the perigee or by the true anomaly of the CSC). The manoeuvre shall be modelled using the same algorithms used by FFS for the two point transfer manoeuvre that would be implemented on-board. Since in this phase the OSC is not being controlled, the final state of the formation acquisition phase is well defined. Any correction that could be performed on-board in closed-loop to the second thrust of the manoeuvre would lead to the same state after the reacquisition, so only minor errors in the predicted CSC estimation are expected during this manoeuvre. Furthermore, after the manoeuvre calibration performed on ground in the first orbits, it is expected that these errors should decrease during the mission. The next orbital phase consists in the formation flying. CSC is free-flying during this segment, so its orbit can be directly propagated. However, it has to be considered that, during the formation flying, the OSC shadow is being projected on the CSC and therefore, the area of this satellite affected by the solar radiation pressure is much lower than the total surface Fig. 1. PROBA- 3 nominal routine orbit. opposed to the Sun direction. The OSC orbit propagation during this phase can be At the end of the formation flying phase, the CSC becomes performed in two different ways: the simpler one, which the controlled spacecraft. The formation is broken by a should be accurate enough for the obit prediction required by manoeuvre performed by the monopropellant thrusters (1N) in the event computation, is based on the assumption that the the Coronagraph satellite during the first half hour after the FFS is controlling the OSC within the required accuracy and, end of the apogee arc. At this time the FLLS still maintains therefore, the nominal formation is being kept. Following this the lock between the two satellites, so precise knowledge of approach, the OSC orbit can be replaced by a kinematic their relative position is available on-board. evolution based on the following equation: 푟푆푢푛̅ −푟퐶푆퐶̅ This manoeuvre is computed as the first Direct Transfer 푟푂푆퐶̅ = 푟퐶푆퐶̅ + 휆 ∙ |푟푆푢푛̅ −푟퐶푆퐶̅ | (1) Manoeuvre (DTM) for the formation reacquisition in the next 푟푆푢푛̅ −푟퐶푆퐶̅ 푣̅푂푆퐶 = 푣̅퐶푆퐶 + Ω̅푆푢푛 × 휆 ∙ orbit, but it also aims to ensure a safe perigee pass for the two |푟푆푢푛̅ −푟퐶푆퐶̅ | satellites. Therefore, any actuation errors in this manoeuvre is where λ represents the distance between the two satellites in compensated by a cold gas manoeuvre performed right after the formation (nominally 150 m). the first DTM. This strategy also ensures the maximum An alternative to the kinematical solution for the OSC orbit inter-satellite distance during the perigee pass3). is based on the reuse of the algorithms implemented on-board. For about two hours around the perigee, the system is Whereas the FFS is working in closed-loop and, therefore, it 2 is not possible to accurately predict its behaviour, the observations are provided by FLLS (Fig. 2) with a standard Yamanaka-Ankersen formulation4) can be used to predict the deviation of 50 μm (1σ), i.e. two orders of magnitude above expected ∆V evolution of the OSC’s cold gas thrusters during the numerical errors. Therefore it has been preferred to keep the formation flying. This approach is not needed for the orbit the standard implementation of the propagation function, prediction, but would provide a nominal manoeuvre profile obtaining the relative states by differentiation of the absolute that can be compared with the one performed on-board to state vectors rather than integrating the inertia forces of the evaluate the FFS performances.
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