Optimal Low-Thrust Orbital Transfers for Rendezvous Between Active Spacecraft with Return Position Constraints

Abstract

In this paper, we consider the problem of determining optimal low-thrust transfers required for rendezvous between two spacecraft in coplanar circular orbits. We specifically allow both spacecraft to perform an orbital transfer to complete the rendezvous. We also consider the that restrict the maneuvering satellites may need to return to their original orbital positions after the rendezvous. Using a direct optimization scheme to solve the formulated optimal control problem, we show via numerical examples that the optimal cooperative solution exhibits a bang-bang solution with intermittent coasting intervals when total transfer time is minimized, in contrast to optimal non-cooperative rendezvous when the thrust remains constant at the maximum level throughout the transfer. Through numerical examples, we compare the characteristics of solutions for non-cooperative rendezvous and cooperative rendezvous with/without return position constraints.