Establishment of satellite formation with initial uncertainty by control Lyapunov function approach

Abstract

In recent years, dynamics and control of satellite formation flying have been active areas of research. From the mission planning perspective, three main areas namely formation establishment, maintenance and reconfiguration have been discussed. In this paper, a study of formation establishment under initial uncertainty is presented. In this regard, dynamics of low Earth orbit satellite formation is discussed. Control Lyapunov function approach is adopted to bring a deputy satellite, with perturbed initial conditions into formation with a chief satellite. In order to take account of the initial orbit insertion error, uncertainty in initial conditions of the deputy satellite is considered. For a case study, a relatively small formation is adopted, with air-launched Pegasus as the launch vehicle. For several initial conditions, control function and required time to achieve a given mission accuracy are determined, and results are provided as illustration.