Formulation and Analysis for Integrated Spacecraft Routing and Trajectory Design Problem

TL;DR

This paper presents two novel formulations for integrated spacecraft routing and trajectory optimization, addressing the unique challenges of satellite servicing missions with partial en-route refueling.

Contribution

It introduces arc-based and path-based formulations using iterative MILP and column generation, respectively, to improve solution efficiency and robustness.

Findings

The path-based formulation with column generation accelerates route identification.

The arc-based formulation balances solution quality and computational time.

Numerical experiments highlight trade-offs between the two approaches.

Abstract

This paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions involving partial en-route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a dynamic environment, and we need to optimize the spacecraft routing over a network with nonlinear and time-dependent trajectory costs. In this paper, we tackle this problem using two different formulations. The first formulation, referred to as the arc-based formulation, defines variables based on arcs and employs an iterative decoupling scheme that alternates between mixed-integer linear programming and sequential nonlinear trajectory optimization. The second formulation, referred to as the path-based formulation, defines variables based on paths/routes and leverages column generation and a labeling algorithm to accelerate the identification of promising routes. Through a geosynchronous satellite servicing case study and numerical experiments, we quantify the computational trade-offs between these two formulations in terms of the solution optimality, computational time, and robustness against non-converging or trivial solutions.