Optimal Low-Thrust Orbit Transfers Connecting Gateway with Earth and Moon

TL;DR

This paper develops a unified optimal control framework for two-way low-thrust orbit transfers connecting Earth, Moon, and Gateway, using backward propagation and multi-arc optimization to improve trajectory efficiency in cislunar space.

Contribution

It introduces a novel unified formulation for minimum-time low-thrust transfers involving forward and backward propagation, and applies multi-arc optimal control with implicit costate transformation for complex trajectory problems.

Findings

Effective two-way transfer trajectories between Gateway and lunar orbit identified.

Multi-arc optimization reduces computational complexity for multi-body transfer problems.

Backward propagation simplifies rendezvous trajectory design.

Abstract

Gateway will represent a primary logistic infrastructure in cislunar space. The identification of efficient orbit transfers capable of connecting Earth, Moon, and Gateway paves the way for enabling refurbishment, servicing, and utilization of this orbiting platform. This study is devoted to determining two-way minimum-time low-thrust orbit transfers that connect both Earth and Moon to Gateway. Backward time propagation is proposed as a very convenient option for trajectories that approach and rendezvous with Gateway, and a unified formulation is introduced for minimum-time orbit transfers, using either forward or backward propagation. Two-way transfers between Gateway and a specified low-altitude lunar orbit are first determined, using an indirect heuristic method, which employs the necessary conditions for optimality and a heuristic algorithm. Second, two-way orbit transfers that connect Earth and Gateway are addressed. Because these trajectories exist under the influence of two major attracting bodies, the underlying optimal control problem is formulated as a multi-arc trajectory optimization problem, involving three different representations for the spacecraft state. Multi-arc optimal control problems are associated with several corner conditions to be enforced at the junction time that separates distinct arcs. However, these conditions are shown to be solvable sequentially for the problem at hand, leveraging implicit costate transformation. This implies that the multi-arc problem has a set of unknown quantities with the same size as that of a single-arc optimal control problem, with apparent advantages of computational nature. The indirect heuristic method is also applied in this second mission scenario.