Orbit design and control of technology validation mission for refractive space telescope in formation flying

Many proposed formation flying missions seek to advance the state of the art in spacecraft science imaging by utilizing precision dual spacecraft formation flying to enable a "virtual" telescope (VT). Using precision alignment of two spacecraft very long focal lengths can be achieved by locating the optics on one spacecraft and the detector on the other. Furthermore, orders of magnitude improvement in science imaging over conventional single spacecraft instruments is possible with advances in precision formation flying. Precise astrometric alignment control is required for accurate inertial pointing of the VT. This work presents orbit design and control approaches for VT formation flying, with specific application to the recently proposed Virtual Telescope Demonstration Mission (VTDM) using cubesats. The characteristics of the mission orbit are derived from solutions to Hill's equations for the relevant mission orbit. A relative orbit control technique pertaining to the astrometric alignment problem is developed by utilizing the Constrained Model Predictive Control (CMPC) approach. This method enables design of formation flying control laws for a thruster assembly with limited magnitude. Precision formation flying is achieved by use of separate control laws for formation maintenance and precision astrometric alignment. The proposed control scheme compensates for inertial astrometric alignment errors as well as differences in orbital perturbations between the VTDM satellites. Numerical simulations are shown to validate the performance of the proposed relative orbit and alignment control laws for the VTDM. The results satisfy mission requirements and indicate the general applicability of the control algorithm to the VT formation flying architecture. Consequently, the proposed methods of orbit design and control can be applied to inertial astrometric alignment and formation keeping for the many proposed dual spacecraft precision formation flying missions.