Particle swarm optimization applied to orbital transfers

The particle swarm optimization (PSO) technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. It mimics the unpredictable motion of bird flocks while searching for food, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. At the end of the process, the best particle (i.e. the best solution with reference to the objective function) is expected to contain the globally optimal values of the unknown parameters. The central idea underlying the method is contained in the formula for velocity updating. This formula includes three terms with stochastic weights: the first term is the so-called inertial component and for each particle is proportional to its velocity in the preceding iteration; the second component is termed the cognitive component, directed toward the personal best position, i.e. the best position experienced by the particle; and finally the third term is the social component, directed toward the global best position, i.e. the best position yet located by any particle in the swarm. This research applies the particle swarm optimization algorithm to the problem of optimizing impulsive and finite-thrust orbital transfers. More specifically, the following problems are considered and solved with the PSO algorithm: (i) determination of the optimal transfer between two coplanar, elliptic orbits with arbitrary orientation; (ii) determination of the optimal two-impulse transfer between two circular, non-coplanar orbits; (iii) optimization of low-thrust orbital transfers between two coplanar, circular orbits. Despite its intuitiveness and simplicity, the particle swarm optimization method proves to be capable of effectively solving all of the orbital transfer problems with great numerical accuracy.