Simplified optimization model for low-thrust perturbed rendezvous between low-eccentricity orbits

Abstract

Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has many revolutions. This paper investigated the time-fixed perturbed orbit rendezvous between low-eccentricity orbits and proposed a priori quasi-optimal thrust strategy to simplify the problem into a parametric optimization problem, which significantly reduces the complexity. The optimal trajectory is divided into three stages including transfer to a certain intermediate orbit, thrust-off drifting and transfer from intermediate orbit to the target orbit. In the two transfer stages, the spacecraft is assumed to use a parametric law of thrust. Then, the optimization model can be then obtained using very few unknowns. Finally, a differential evolution algorithm is adopted to solve the simplified optimization model and an analytical correction process is proposed to eliminate the numerical errors. Simulation results and comparisons with previous methods proved this new method’s efficiency and high precision for low-eccentricity orbits. The method can be well applied to premilitary analysis and high-precision trajectory optimization of missions such as in-orbit service and active debris removal in low Earth orbits.