Optimization of low-thrust transfers to libration point orbits

Abstract

Purpose – The purpose of this paper is to develop a superconvergent trajectory optimization method for the design of low-thrust transfer trajectories from parking orbit to libration point orbits near the collinear libration points. Design/methodology/approach – The optimization method is developed by merging the concept of Lyapunov feedback control law with the manifold dynamics. First, the whole transfer trajectory is divided into two segments, raising segment and coast segment. Then, the trajectories of each segment are described in different coordinate frames, and designed with Lyapunov feedback control law and the manifold dynamics, respectively. The Poincaré section is used as an effective tool to search the compatible patching point between these two segments on the manifold. Finally, the transfer trajectory is optimized using sequential quadratic programming. Findings – In the numerical simulation, the proposed optimization method does not have any convergence problem. It is a fast and effective method for the very sensitive trajectory optimization problem. Originality/value – The nonlinear constraints in the original trajectory optimization problem are satisfied by using the Lyapunov feedback control law; hence, the problem is transformed into a nonconstrained parameter optimization problem. The convergence problem of the sensitive optimization problem is solved thoroughly.