Optimal Finite-Thrust Rendezvous Trajectories Found via Particle Swarm Algorithm

The particle swarm optimization technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. The particle swarm optimization methodology aims at taking advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. This research applies the technique to determining optimal continuous-thrust rendezvous trajectories in a rotating Euler-Hill frame. Five distinct applications, both in two dimensions and in three dimensions, are considered. Hamiltonian methods are employed to translate the related optimal control problems into parameter optimization problems. The transversality condition, which is an analytical condition that arises from the calculus of variations, is proven to be ignorable for these problems, and this property greatly simplifies the solution process. For each of the five applications considered in the paper, despite its simplicity, the swarming algorithm successfully finds the optimal control law corresponding to the minimum-time trajectory with great accuracy.