Low-thrust planar transfer for co-planar low Earth orbit satellites considering self-induced collision avoidance

This paper deals with the planar transfer problems (orbit raising and de-orbiting) for co-planar satellites with low-thrust propulsion, taking the self-induced collision avoidance into consideration at the mission design stage. A Blended Error-Correction steering law, with which the thrust direction changes in a self-adaptive way, is developed by blending two types of efficient steering laws and offsetting the errors of the instantaneous orbit with respect to the target orbit. The semi-analytical solutions for orbital elements, which reduce the computational load of propagating long-duration trajectories, are derived by computing the analytical incremental changes in orbital elements after every revolution with an orbital averaging technique. Based on the analytical Blended Error-Correction steering law and semi-analytical solutions, transfers can be computed quickly for any starting times. Finally, the self-induced collision, which is modeled by miss distance, is avoided by scheduling properly the timing to start transfer for every satellite.