Time Shift Governor for Constrained Control of Spacecraft Orbit and Attitude Relative Motion in Bicircular Restricted Four-Body Problem

TL;DR

This work develops a constrained rendezvous and docking framework for spacecraft in a Bicircular Restricted Four-Body Problem, incorporating both translational and attitude dynamics. The nominal controller combines an averaged-in-time LQR for translational tracking with geometric tracking for attitude, while the Time Shift Governor (TSG) adaptively selects a time-shifted reference to enforce LoS, thrust, and approach-velocity constraints over a prediction horizon. Simulation in a 9:2 NRHO demonstrates that the TSG reliably enforces constraints, drives the virtual target toward the Chief, and achieves docking-like proximity with a small residual relative velocity. The approach advances autonomous RVD capability in realistic cislunar dynamics and provides a path for integrating additional constraints and attitude-docking considerations in future work.

Abstract

This paper considers constrained spacecraft rendezvous and docking (RVD) in the setting of the Bicircular Restricted Four-Body Problem (BCR4BP), while accounting for attitude dynamics. We consider Line of Sight (LoS) cone constraints, thrust limits, thrust direction limits, and approach velocity constraints during RVD missions in a near rectilinear halo orbit (NRHO) in the Sun-Earth-Moon system. To enforce the constraints, the Time Shift Governor (TSG), which uses a time-shifted Chief spacecraft trajectory as a target reference for the Deputy spacecraft, is employed. The time shift is gradually reduced to zero so that the virtual target gradually evolves towards the Chief spacecraft as time goes by, and the RVD mission objective can be achieved. Numerical simulation results are reported to validate the proposed control method.

Figures (7)

• Figure 1: Barycentric frame $b$ and Body-fixed frame $\mathcal{B}$ in the Sun-Earth-Moon system.
• Figure 2: (a) The reference trajectory of nine orbit periods for the Chief spacecraft. (b) the resulting trajectories during the RVD mission with initial and final states.
• Figure 3: The time shift parameter as a function of time during the RVD scenario. The time unit is dimensionalized by dividing it by the mean motion $n$, i.e., $t_{\tt lead}=\tau_{\tt lead}/n$.
• Figure 4: (a) The relative position and (b) relative velocity of the Deputy spacecraft $X_{d}$ to the Chief spacecraft $X_{c}$. (c) The relative position and (d) relative velocity of $X_{d}$ to the virtual target $X_{v}$.
• Figure 5: The constraint trajectories during the RVD simulation using the TSG starting from 10 different initial Deputy states: (a) The LoS cone constraint $h_{1}$; (b) thrust limit $h_{2}$; (c) thrust direction limit $h_{3}$; (d) relative velocity constraint $h_{4}$. Note that the relative velocity constraint activates when the Deputy spacecraft is within 10 km of the Chief spacecraft.