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A collision-free formation reconfiguration trajectory subject to the linearized Hill’s dynamics of relative motion is analytically\uddeveloped by extending an algorithm for gravity-free space. Based on the initial solution without collision avoidance\udconstraints, the final solution to minimize the designated performance index and avoid collision is found, based on a gradient\udmethod. Simple simulations confirm that satellites reconfigure their positions along the safe trajectories, while trying to spend\udminimum energies. The algorithm is applicable to wide range of formation flying under the Hill’s dynamics

Collision Avoidance Algorithm for Satellite Formation Reconfiguration under the Linearized Central Gravitational Fields