Periodic orbit tracking in cislunar space: A finite-horizon approach

TL;DR

This paper introduces a nonlinear model predictive control method for maintaining spacecraft within families of periodic orbits near libration points in cislunar space, improving fuel efficiency over traditional tracking approaches.

Contribution

It develops a novel NMPC scheme that tracks orbit families rather than fixed references, utilizing continuation methods and polynomial regression for optimal trajectory design.

Findings

Significant fuel savings demonstrated in simulations.

Effective orbit family tracking near L1 and L2.

Integration of EKF for state estimation enhances control accuracy.

Abstract

This paper presents a Nonlinear Model Predictive Control (NMPC) scheme for maintaining a spacecraft within a specified family of periodic orbits near the libration points in cislunar space. Unlike traditional approaches that track a predefined reference orbit, the proposed method designs an optimal trajectory that keeps the spacecraft within the orbit family, regardless of the initial reference. The Circular Restricted Three-Body Problem (CR3BP) is used to model the system dynamics. First, the Pseudo-Arclength Continuation (PAC) method is employed to compute the members of each orbit family. Then, the state of each member is parameterized by two variables: one defining the orbit and the other specifying the location along it. These computed states are then fit to a Multivariate Polynomial Regression (MPR) model. An NMPC framework is developed to generate the optimal reference trajectory and compute the corresponding velocity impulses for trajectory tracking. The control system is integrated with a Extended Kalman Filter (EKF) observer that estimates the spacecraft's relative state. Numerical simulations are conducted for Lyapunov, halo, and near-rectilinear halo orbits near L1 and L2. The results demonstrate a significant reduction in fuel consumption compared to conventional tracking methods.