A flatness-based predictive controller for six-degrees of freedom spacecraft rendezvous

TL;DR

The paper addresses six-DOF spacecraft rendezvous with a passive eccentric-orbit target by developing a flatness-based framework that couples translational and attitude dynamics. It first transforms the time-continuous dynamics into algebraic relations using the attitude flatness property and a state-transition matrix, then solves a discretized direct transcription NLP with a B-spline parameterization of the flat output. An MPC scheme linearizes around the previously computed open-loop solution to reject disturbances, providing a computationally efficient online update via a QP in a sliding horizon. The approach is demonstrated on two thruster configurations (10 and 2 thrusters) with LOS constraints and reaction-wheel limits, showing feasible trajectories, fuel savings over LP solutions, and robust disturbance rejection, albeit without a formal stability proof. The work offers a scalable, integrated method for planning and tracking 6-DOF rendezvous maneuvers across mission profiles, highlighting practical pathways for fuel efficiency and constraint satisfaction in autonomous spacecraft operations.

Abstract

This work presents a closed-loop guidance algorithm for six-degrees of freedom spacecraft rendezvous with a passive target flying in an eccentric orbit. The main assumption is that the chaser vehicle has an attitude control system, based on reaction wheels, providing the necessary torque to change its orientation whereas the number of thrusters is arbitrary. The goal is to design fuel optimal maneuvers while satisfying operational constraints and rejecting disturbances. The proposed method is as follows; first, the coupled translational and angular dynamics are transformed to equivalent algebraic relations using the relative translational states transition matrix and the attitude flatness property. Then, a direct transcription method, based on B-splines parameterization and discretization of time continuous constraints, is developed to obtain a tractable static program. Finally, a Model Predictive Controller, based on linearization around the previously computed solution, is considered to handle disturbances. Numerical results are shown and discussed.

Figures (11)

• Figure 1: LVLH frame
• Figure 2: LOS region
• Figure 3: Chaser 3D path of scenario 1 for the first random realization
• Figure 4: Chaser trajectory on the target orbital plane of scenario 1 for all random realizations
• Figure 5: Chaser attitude of scenario 1 for the first random realization