Advances in Cislunar Periodic Solutions via Taylor Polynomial Maps

TL;DR

This paper introduces novel polynomial-based methods within the Differential Algebra framework to efficiently analyze and control periodic orbits near libration points in cislunar space, enabling low-energy transfer applications.

Contribution

It develops new polynomial regression models and integrates them with Differential Algebra to improve the analysis and control of cislunar periodic orbits, reducing computational effort.

Findings

Polynomial regression models accurately represent initial states.

DA-based propagation reduces computational complexity.

Control law derived shows lower control effort.

Abstract

In this paper, novel approaches are developed to explore the dynamics of motion in periodic orbits near libration points in cislunar space using the Differential Algebra (DA) framework. The Circular Restricted Three-Body Problem (CR3BP) models the motion, with initial states derived numerically via differential correction. Periodic orbit families are computed using the Pseudo-Arclength Continuation (PAC) method and fitted. Two newly developed polynomial regression models (PRMs) express initial states as functions of predefined parameters and are used in the DA framework to evaluate propagated states. The initial states, expressed via PRM, are propagated in the DA framework using the fourth-order Runge-Kutta (RK4) method. The resultant polynomials of both PRM and DA are employed to develop a control law that shows significantly reduced control effort compared to the traditional tracking control law, demonstrating their potential for cislunar space applications, particularly those requiring computationally inexpensive low-energy transfers.