Formation flying of spacecraft has gained a lot of interest within the engineering and scientific community in recent years. However, formation flying leads to an increased complexity of the guidance and control system, whose complexity grows rapidly with the number of spacecraft in the formation. Moreover, there is an increasing need for autonomy to decrease the cost of ground support since ground support operations are often a non-negligible part of the cost of a mission. Therefore, a formation flying guidance and control system needs to perform autonomous decisions and trade-offs in real-time to decrease the number of tasks that need to be performed by the ground segment and make formation flying affordable. This work presents the development of analytical formation flying guidance and control laws for autonomous on-board applications. Firstly, an analytical model of relative motion for elliptical and perturbed reference orbits is developed. This model is solely based on the initial orbit elements of the reference trajectory and can predict the relative motion of any spacecraft orbiting close to the reference trajectory, taking into account the secular drift caused by the J2 perturbation. Secondly, a new tool, the Fuel-Equivalent Space, is presented. The Fuel-Equivalent Space theory maps the relative orbit elements into a mathematical space where similar displacements on any axis is similar in terms of maneuvering fuel cost, therefore translating the minimum fuel problem into a simple distance minimization problem. Then, a neighbouring optimum feedback control law is developed. This feedback control law makes use of the optimal control theory to yield a semi-analytical controller that guarantees near-optimal maneuvering for any of the spacecraft orbiting close to the reference trajectory. Finally, it is shown that all these three new developments can be tied in together with simple analytical guidance laws to yield a fully autonomous guidance and control algorithm applicable to formation reconfiguration.
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