Finding optimal relative orbit transfer trajectories with the particle swarm algorithm and primer vector theory

Spacecraft formation flights are a useful tool to improve mission cost-effectiveness and redundancy, but controlling the satellites within the cluster is a difficult task. The particle swarm evolutionary algorithm is used to find ways to minimize the amount of fuel required for impulsive transfers between periodic orbits in the relative motion problem. Relative orbit elements are used in order to create the solution vectors for the particle swarm, and the Clohessy-Wiltshire-Hill equations are used to define the relative motion of the satellites. These trajectories are then analyzed according to primer vector theory, in order to check the optimality of the trajectories developed via the particle swarm algorithm and determine if they may be improved.