Manoeuvre planning algorithm for satellite formations using mean relative orbital elements

Formation flying missions have increased their importance thanks to the better performances that can be achieved with a distributed system of satellites. One of the most demanding challenges linked to formation flying missions is the formulation of a robust control plan. Due to the recent developments in electrical propulsion, controllers that apply a continuous low-thrust to each spacecraft in the formation have been proposed, achieving precise control. This idea is used in this manuscript, where an open-loop manoeuvre planning algorithm is developed, to provide the control accelerations to achieve a formation reconfiguration in a given temporal frame. The proposed algorithm is based on an innovative control technique, which relies on the mean relative orbital elements as state variables of a first-order dynamic system. It includes the effect of the gravitational field of the Earth. Finally, the algorithm is tested with two different test cases of formation flying reconfiguration, presenting and analysing their results. The test case scenarios considered are based on possible future mission concepts in Low Earth Orbit, aiming at improving the control performances for the mission design.