Orbit and formation control for low-earth-orbit gravimetry drag-free satellites

Abstract

The paper outlines orbit and formation control of a long-distance (>100 km) two-satellite formation for the monitoring of the Earth gravity. Orbit control applies to a single satellite and performs altitude control. Here, formation control is formulated as a control capable of altitude and distance control at the same time. The satellites being placed in a low Earth orbit, orbit, and formation control employ the measurements of a global navigation system. Formation control is imposed by long-distance laser interferometry, which is the key instrument for gravity measurement. Orbit and formation control are low-frequency control systems in charge of canceling bias and drift of the residual drag-free accelerations. Drag-free control is the core of the orbit/formation control since it allows the formation to fly drag-free only subject to gravity. Drag-free control being required to have a bandwidth close to 1 Hz, is designed as the inner loop of the formation control. In turn, formation control must not destroy drag-free performance, in which objective demands that formation control be effective only below the 0.2 mHz orbital frequency. Control design is based on a new orbit and formation dynamics, which are compared with the classical Hill-Clohessy-Wiltshire equations. The new dynamic equations are the first step in building the embedded model, which is the core of the control unit. Embedded model derivation is explained only for the orbit control, and briefly mentioned for the formation control. Simulated results are provided. Drag-free results are compared with GOCE experimental data.

System and AOCS Challenges for the Design Consolidation of the Next Generation Gravity Mission

“…As a matter of fact, such modelling idea leads to new Clohessy-Wiltshire (CW)-type equations (see Ref. 9).…”

“…After that, the formation triangle kinematic equations in terms of the FLOF angular rate and of the angular acceleration have been obtained, as per Ref. 9.…”

Embedded model control GNC for the Next Generation Gravity Mission

“…Integrated orbit and formation control The orbit and formation control design is driven by an innovative approach to multi-satellite formation and orbit control based on the integration of orbit and formation dynamics and control through the formation triangle concept. As a matter of fact, such modelling idea leads to new CW-type equations (see [6] and Section 4).…”

“…As a consequence, according to the Embedded Model Control methodology, a ninth-order stochastic disturbance dynamics (third order for each axis) driven by a 12th-dimensional bounded noise vector d w allows to account reliably for the high frequency spectral density of drag, thruster noise and accelerometer bias/drift [6]. The final DT model, from sensor to actuator dynamics, which is embedded in the control unit, reads:…”

“…One of the most relevant contribution of this paper is the definition of all the NGGM AOCS architecture control functions within the unified framework of the EMC design methodology. Specifically, for the orbit and formation control, this is enhanced via the definition of an innovative integrated orbit and formation control (IFC) architecture [6]. Such formulation is based on the definition of a peculiar formation reference frame (the formation local orbital frame, FLOF) and the formation triangle virtual structure.…”