Orbit Transfer Optimization for Asteroid Missions Using Weighted Cost Function

Abstract

This paper presents a method of trajectory optimization based on the well-known primer vector theory, which is modified to accommodate weights in the cost function. This change arises from the need of a fast and accurate analysis obtained with an indirect method that takes into account the velocity increment used for departure from the planet and, particularly for flyby missions, the disregard of the last rendezvous impulse. A detailed derivation of the weighted cost function and its gradient is presented, followed by a discussion on the values of the weights specifically for flyby and rendezvous missions. To test the optimization method, realistic test cases are selected and their results compared against a trajectory using the solution of the Lambert problem and optimization by a nonlinear programming solver. The proposed method showed a fast design of a trajectory with a midcourse impulse, which costs less than the trajectories calculated by the other two methods.