ESA GNC Conference Papers Repository

This paper concerns with the “Laser Doppler Interferometry Mission for Determination of the Earth’s Gravity Field” study of the European Space Agency, a mission for monitoring the variations of Earth’s gravity field at high resolution (up to harmonic degree 200) over a long time period (>6 years). The mission named Satellite-to-Satellite Interferometry (SSI), exploits the use of a heterodyne laser interferometer for the high-resolution measurement of the displacement between two satellites flying at low altitude (around 325 km). More in details, employing a formation of two co-orbiting satellites at 10 km relative distance (see Fig. 1), a resolution of about 1 nm rms is needed in the inter-satellite distance measurement, and the non gravitational accelerations must be measured with a resolution of about 10-10 m/s2 rms to achieve geoid height variation rate error equal to 0.1 mm/year at degree 200. Starting from the geophysical phenomena to be investigated, a detailed derivation of the mission requirements on the orbit, satellite formation and control, measurement instruments (laser interferometer and accelerometer) was performed using analytical models and numerical simulations, and the satellites orbit and attitude control were approached through different techniques. Among the most promising control strategies, the application of Embedded Model Control (EMC) to the satellite control is presented, as potentially applicable to the post-GOCE missions. This method was applied to the GOCE DFAC (Drag Free & Attitude Control) and was successively modified by Thales-Alenia (I) because of the difficulties with micro-thrusters. The same methodology has been applied in several prototypes of laser interferometry, as NanoBalance, reference cavity and metrology lines. Differently from other methodologies, the central point of the EMC is the modelling of the environment to be compensated: the Embedded Model receives as input driving noises, which force the disturbance dynamics to be observed and compensated. Within the application of the EMC to the SSI mission, the drag-free and the attitude control of each satellite were designed in order to let measuring the relative acceleration ?ag between the CoMs (Centre-of-Mass) of satellite 1 and 2 caused only by the action of the Earth gravity field, providing the information for the reconstruction of the geopotential. Since the metrology system provides the measurement of the overall relative acceleration between the CoMs caused by the action of the Earth gravity field and the differential non-gravitational accelerations, the relative acceleration can be measured only using a drag-free control, which compensates the non-gravitational forces acting on each satellite. Moreover, each individual attitude control has to compensate for drifts and rotations of each satellite, in order to keep the visual contact among them within strict requirements along the Local Orbit Reference Frame (LORF). Because of the uncertainty on the absolute inertial position provided by the real-time use of GPS, it was necessary to build up an orbit estimator capable of maintaining the errors of the LORF estimation within the established thresholds. To this purpose, an observer is developed for each satellite on the basis of an estimate and prediction of the CoM inertial position and velocity from GPS measurement, and through the proper definition of the discrete-time embedded model of the spacecraft to be controlled. Accuracy requirements for the attitude ask for microradiant real-time errors in the mission Measurement Bandwidth (MBW), to be compared with an overall sub-milliradiant error range. At the beginning of the study, the DFAC relied on four active mini-thrusters in ‘pyramidal’ configuration for what concerns the rejection of the residual non-gravitational acceleration along the three body axes, and on a cluster of reaction wheels (RW) for the satellite attitude control. The parallel tests on the low-frequency micro-vibrations signature of the magnetic bearing momentum wheels suggested discarding them because of their high noise with respect to the scientific mission requirements, especially at low frequency. Consequently, the new baseline for the satellites DFAC is 8 (up to 12 for redundancy) mini-RIT (radio frequency ion thruster) for full 6-axis control of each spacecraft. Firstly, the paper presents the mission architecture, the measurement models and the derivation of the requirements. After a brief excursus on the actuator assessment, a central section is devoted to the architecture of the drag-free and formation control, which are designed according to the embedded model control approach. Finally, a section is dedicated to the description of the Beam Steering Mechanism (BSM), an innovative design for the fine pointing of the laser beam between the two satellites, in order to relax the requirements on the satellite attitude control otherwise very stringent. The relevant simulation plots are introduced in the last sections, relatively to the control and BSM performance.