Satellite Formation Design with a Multi-Objective Optimization Technique

Real world optimization problems often contain objective functions with conflicting terms. For the satellite formation flight mission examined in this paper, the goal is to minimize fuel while maximizing observation time. Maximizing observation time for an artificially maintained formation usually results in sub-optimal fuel use. Traditional mission design tools place weights on observation time and fuel terms and find the solution with the minimal total aggregate cost. However, cost function weights are typically user-defined rather than being mathematically optimal. In this paper, we investigate the use of a MultiObjective Particle Swarm Optimization (MOPSO) technique to create a set of candidate solutions that allow a mission designer to select the best tradeoff between fuel and observation time for a particular mission. We present a formation optimization case study based on previous model development and a multi-impulse mission design formulation for the Magnetospheric Multi-Scale (MMS) mission. Nomenclature v = velocity of a particle for the particle swarm optimization algorithm x = position of a particle for the particle swarm optimization algorithm g best = vector location and cost of best candidate solution so far investigated by any particle p best,i = vector location and cost of best candidate solution so far investigated by a specific particle ω = inertial weight factor used to determine influence of current state on next state

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