Optimal planning for a multiple space debris removal mission using high-accuracy low-thrust transfers

Abstract

In this paper, we solve the problem of minimizing the fuel and time cost of accurate rendezvous and de-orbiting of multiple pieces of space debris in a single mission. Continuous low thrust maneuvers are used to achieve each orbital transfer. The mission scenario considered requires the chaser to capture and de-orbit the debris into a disposal orbit, after which it releases the first piece of debris and performs a rendezvous with the next piece of debris, continuing until the end of the mission in a recursive fashion. Within each rendezvous phase, the orbital drift of both the chaser and the target are considered. This is done in order to ensure the orbital elements of the chaser are matched to actual location of the debris at the end of the maneuver. Each maneuver is defined as a minimum-time orbital transfer, using low-thrust propulsion, and the transfer is posed as a constrained non-linear optimal control problem, implemented in GPOPS-II. The initial guess for the transfer time constitutes the period over which the given piece of debris is propagated to find the location of the debris after transfer. The location of the debris is then used as an initial guess for the final boundary constraint of the chaser's high-accuracy transfer. This procedure is iterated until the post-propagation location of the debris matches the location of the chaser following the high-accuracy transfer, within certain error bounds. A set of five pieces of debris with small inclination differences and a set of two pieces of debris with a large inclination difference situated in lower Earth orbit have been selected for demonstrating the proposed methodology. The outcome is the best possible trade-off between time and fuel for the multiple-debris removal mission and the transfer characteristics required to achieve it.