Minimum-fuel low-thrust rendezvous trajectories via swarming algorithm

The particle swarm optimization technique is a population-based heuristic method developed in recent years and successfully applied in several fields of research. It attempts to take 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, minimum- fuel rendezvous trajectories in a rotating Euler-Hill frame. Hamiltonian methods are employed to translate the related optimal control problem into a parameter optimization problem, in which the parameter set is composed of the initial values of the adjoint variables. A switching function is also defined, and determines the optimal sequence and durations of thrust and coast arcs. The algorithm at hand is extremely easy to program. Nevertheless, it proves to be effective, reliable, and numerically accurate in solving several qualitatively different test cases.