Method of Forming a Regular Triangular Tethered Constellation of Microsatellites with Considering Their Motion Relative to the Centers of Mass

Abstract

The process of formation of a rotating tethered constellation of microsatellites in the form of a regular triangle is considered. A combined control method for deploying the system using tether tension control and thrusters is proposed. Two models are used to substantiate the proposed control method. The first model is obtained by the Lagrange method and is intended for constructing a nominal group formation program. In this model, microsatellites are considered as mass points and tethers are inextensible mechanical bonds. The second model is developed to assess the possibility of implementing a nominal control program, since it takes into account the extensibility of tethers, simulates the operation of cable release mechanisms, and takes into account the motion of microsatellites relative to their centers of mass on which the direction of low thrust forces depends. The equations of the spatial motion of the constellation, corresponding to the second model, are written in a fixed geocentric coordinate system and make it possible to estimate the effect of the static and inertial asymmetry of microsatellites on their motion relative to the center of mass. The results of numerical calculations are presented, confirming the possibility of using the proposed control method for the formation of a tethered constellation in the form of a regular triangle, rotating at the constant given angular velocity in its final state.