Explicit Control Force and Torque Determination for Satellite Formation-Keeping with Attitude Requirements

A simple analytical approach for formation-keeping of satellites in the presence of both orbital and attitude requirements is developed. A leader satellite is assumed to be in a J2-perturbed circular reference orbit and each follower satellite is required to stay in its prescribed, desired orbit with respect to the leader satellite, and at the same time, to point to an arbitrarily chosen specific spot in space that may be time-varying. Nonlinear relative dynamics is considered in its entirety without any approximations, and nonlinear controllers are designed to exactly satisfy the desired orbital and attitude mission requirements for the formation. The analytical approach leads to a separation principle that points out when orbital control is completely unaffected by attitude control. In the presence of sensor measurement noise that leads to incorrect initial conditions at the start of the control maneuver the approach asymptotically satisfies both the orbital and attitude control requirements, at any desired rate of convergence depending on mission requirements. The effect of small unmodelled dynamics is also considered. A numerical example demonstrates the simplicity of the approach, its ease of implementation, accuracy of results, and its robustness to both sensor measurement errors and unmodelled dynamics.