Convex Trajectory Optimization via Monomial Coordinates Transcription for Cislunar Rendezvous

TL;DR

This paper introduces a nonlinear convex guidance algorithm for fuel-efficient cislunar rendezvous, utilizing monomial coordinates and differential algebra to reduce computational load and improve accuracy over traditional linear methods.

Contribution

It presents a novel convex optimization approach using monomial coordinates and differential algebra, eliminating real-time dynamic integration for cislunar rendezvous guidance.

Findings

Demonstrates stability and efficiency in the circular restricted three-body problem

Achieves minimal terminal guidance errors

Outperforms linear methods in accuracy for impulsive maneuvers

Abstract

This paper proposes a nonlinear guidance algorithm for fuel-optimal impulsive trajectories for rendezvous operations close to a reference orbit. The approach involves overparameterized monomial coordinates and a high-order approximation of the dynamic flow precomputed using differential algebra, which eliminates the need for real-time integration. To address non-convexity in the monomial coordinate formulation of the guidance problem, sequential convex programming is applied. Using the methodology presented in this paper, repeatedly evaluating the nonlinear dynamics is not necessary, as in shooting or collocation methods. Instead, only the monomial equations require updating between iterations, drastically reducing computational burden. The proposed algorithm is tested in the circular restricted three-body problem framework with the target spacecraft on a near-rectilinear halo orbit. The results demonstrate stability, efficiency, and low computational demand while achieving minimal terminal guidance errors. Compared to linear methods, this nonlinear convex approach exhibits superior performance in open-loop propagation of impulsive maneuvers in cislunar space, particularly in terms of accuracy. These advantages make the algorithm an attractive candidate for autonomous onboard guidance for rendezvous operations in the cislunar domain.