Gravity-assist fuel-optimal low-thrust trajectory design using hybrid optimization techniques

Low-thrust propulsion technology and planetary gravity-assist maneuvers make a promising combination for deep space explorations. Hybrid optimal control methods have proven to be an excellent solution framework which exploits the advantages of both direct and indirect optimization methods, while alleviating their drawbacks. We employ a recently introduced hyperbolic tangent smoothing method to design low-thrust interplanetary trajectories with gravity-assist opportunities. Gravity-assist maneuvers lead to multiple-point boundary-value problems, and to solve them, we use a two-level hybrid optimization method. At the first level, a particle swarm optimization algorithm is used to perform a global search over the unknown parameters of an easy-to-solve problem, namely, a problem with smoother control input. The second level improves upon the solution of the first level to obtain the fuel-optimal solution. In order to gain further insights into the thrusting structure, a numerical continuation is performed over the maximum value of the thrust for a problem from the Earth to Mars via a fly-by with Venus, wherein the notion of thrust envelopes is introduced.