Interplanetary gravity-assist fuel-optimal trajectory optimization with planetary and Solar radiation pressure perturbations

Abstract

Designing optimal spacecraft trajectories is a critical task for any mission design. In particular, mission designers seek to exploit from the combined effects of planetary gravity-assist maneuvers and electric propulsions systems to reduce both the flight time and propellant consumption. In order to obtain more realistic results, disturbances such as (1) gravitational force of secondary bodies, (2) Solar radiation pressure, and (3) non-spherical gravity models have to be considered. Mission designers are, thus, faced with the task of solving a constrained optimal control problem where the complexities are compounded due to the nonlinearity of the dynamical models as well as the existence of intermediate constraints (e.g., gravity-assist constraints). This investigation presents a methodology to incorporate all of the enumerated factors in planetary trajectory design using the indirect optimization method. In order to demonstrate the utility of the method, an interplanetary trajectory from the Earth to Jupiter is considered, while the spacecraft performs a gravity-assist maneuver with the Earth en route to Jupiter. An appealing feature of the developed tool is the flexibility in adding or removing any of the disturbances, which allows us to assess the impact of each item on the final solution. The results are compared against two existing solutions in the literature and demonstrate the utility of the method.