Optimal Finite Thrust Rendezvous Maneuvers of Chaser Spacecraft Towards Capturing Target Object

Abstract

Over a couple of decades, the growth of spacecraft launches has increased drastically at LEO, and the statistics show that an average of more than a hundred satellites were launched yearly. Most spacecraft launches have accomplished their mission objective, but some experienced failures, irregularities, and End of Life(EOL) in their missions. As a result, the On-Orbit Servicing (OOS) of such spacecraft becomes an essential aspect of extending the life span of the existing satellite. One of the OOS methods is Space Robotics, whose primary function is to chase, capture, and service the target satellite in orbit. To chase and capture the target spacecraft, the rendezvous maneuver and their efficient executions become a critical component of missions. This paper mainly deals with the numerical formulation of the optimal finite thrust maneuver to reach proximity to the target spacecraft. A finite thrust model solves the finite thrust rendezvous problem, ensuring the continuity of speed changes and containing the spacecraft's optimal rendezvous models. An Interior Point Optimizer(IPOPT) algorithm is used to resolve the rendezvous problem involving a chaser and target spacecraft, which computes an optimal control distribution as a function of time, allowing finite maneuvers. The IPOPT algorithm seamlessly solves the optimal rendezvous problems by looking at the absolute minimum time, minimum fuel, and all cases between scenarios. This algorithm helps us investigate the generation of optimal rendezvous trajectories by using finite thrust duration to be utilized in a robust guidance formulation interested in autonomously onboarding a spacecraft. The results show that when the fuel and time restrictions are removed, the rendezvous trajectory provides the most optimal fuel and time conditions. It has been found that if the maximum thrust value increases and the transfer angle is decreased, the rendezvous time has shortened, and when the expended speed values $\Delta V$ are reduced, the rendezvous time has increased. This paper also compares the IPOPT Method and SGRA results for the exact scenarios. Moreover, it was found that the IPOPT is more efficient and faster than SGRA in generating optimal rendezvous trajectories at optimal fuel and time scenarios, along with the capability of handling inequality constraints by introducing another set of decision variables called the slack parameters and the barrier parameters.