Autonomous Multi-phase Rendezvous, Proximity Operations, and Docking via Model Predictive Control

This paper proposes a new approach to determine the multi-phase optimal control solution for a spacecraft rendezvous, proximity operations, and docking mission (RPOD). Traditionally, RPOD missions are segmented into several phases corresponding to the relative range between the target and chaser spacecraft, and it is not uncommon to have constraints which differ between respective phases. Model predictive control (MPC) is a control method designed to solve an optimal control problem over a finite time horizon. The finite time horizon decreases the computational complexity, which makes it advantageous for onboard use in spacecraft. Additionally, MPC is capable of solving the optimization problem while taking into consideration constraints. This makes MPC an ideal choice for a control method when executing a RPOD mission. Without tracking a reference trajectory, using a single controller for a multi-phase problem is impractical since constraints are time dependent and not state dependent, and the time at which the phase transition occurs is unknown. A phase-independent optimization approach will almost always be sub-optimal to an optimization over the full mission. The proposed approach attempts to come closer to the optimal solution by implementing a separate controller for each phase. The goal of the first phase controller is to guide the spacecraft into the feasible region of the second phase while still targeting the second phase desired state. The two phase approach demonstrated in this paper is a rendezvous in which the chaser is initially outside of a line-of-sight (LOS) cone. The goal of the first phase is to maneuver the spacecraft into the LOS constraint of the second phase without implementing constraints on the spacecraft states. The goal of the second controller is to approach a desired end state while staying within the LOS constraint. The two methods demonstrated in this paper provide spacecraft with the ability to autonomously determine a fuel-optimal trajectory over multiple phases while adhering to varying constraints. Though this specific scenario only encompasses two phases, the methods can be expanded to more. The efficacy of the approach is shown in a simulation study comparing the results to the true optimal solution and phase-independent solutions.