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Abstract

Groups of satellites flying in formation require maintaining the specific relative geometry of the formation with high precision. This requirement implies to consider the problem of relative station keeping in a renewed framework. In this framework, issues related to the derivation of reliable relative models as well as to the peculiarity of the synthesis problems must be jointly considered. This paper presents some preliminary results of a robust multi- objective control approach applied to the station keeping of a low Earth observation system, i.e. the interferometric cartwheel, patented by CNES. This wheel is made up of three receiving spacecrafts, which follow an emitting Earth observation radar satellite. The particular geometry of this formation of satellites leads to the derivation of a simplified uncertain state-space model. Atmospheric drag perturbations are included in the linearized equations of the relative motion and the atmospheric density part of the definition of the atmospheric drag force is considered to be uncertain due to its dependence upon the solar activity. In the first part of the paper, an uncertain polytopic state-space model is derived. The second part describes the station keeping strategy of the formation. The station keeping strategy is performed using pure passive actuators. Due to the high stability of the relative eccentricity of the formation, only the relative semi major axis has to be controlled. Differential drag due to a differential orientation of the solar panel is used here to control relative altitude. A robust multi-objective control strategy via state-feedback is developed and tested as autonomous orbit controller. These results are analyzed via highly non linear simulations performed on a platform of CNES.

Mots-Clés / Keywords

Abstract

The problem of the stationkeeping for a small spacecraft is studied and a solution based on periodic feedback control laws is considered. Linearized equations of the relative motion of the satellite near an eccentric reference orbit are derived in the presence of the second zonal gravitational harmonic J2 and atmospheric drag perturbations. The obtained linear continuous-time model of the relative motion is Tperiodic where T is the orbital period. After a discretization of the model, a state-feedback control law with performance requirement defined by the generalized H2 operator norm may be computed by a linear matrix inequality-based algorithm. Illustrative nonlinear simulations show the efficiency of the approach based on the use of linearized spacecraft relative motion dynamics associated to systematic H2 synthesis of stabilizing memoryless N-periodic state-feedback control laws.

Abstract

Station-keeping of a small spacecraft is studied and a solution based on resilient periodic state-feedback control laws is proposed. Linearized equations of the relative motion of the satellite near an eccentric reference orbit are derived in the presence of the second zonal gravitational harmonic J2 and atmospheric drag perturbations. After a discretization of the model, a resilient H2 state-feedback control law is computed by a linear matrix inequality-based algorithm. Illustrative nonlinear simulations show the efficiency of the approach.