Low-Thrust Reconfiguration Strategy and Optimization for Formation Flying Using Jordan Normal Form

• Published in: IEEE transactions on aerospace and electronic systems Vol. 57; no. 5; pp. 3279 - 3295
• Main Authors: Bai, Xue, He, Yanchao, Xu, Ming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Canonical forms; Formation flying; Fuels; Invariants; Jordan normal form; low thrust; Mathematical model; Optimization; Orbital elements; Orbits; Polynomials; Reconfiguration; Satellites; Space vehicles; Spectral methods; Thrust; Trajectory; Trajectory control; Trajectory optimization
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2021.3074204

This article proposes a low-thrust reconfiguration strategy for formation flying based on the Jordan normal form and evaluates its performance based on the required control acceleration and fuel cost. First, the relative dynamics of reconfiguration is disposed by Jordan decomposition to describe the unstable component, i.e., the drift velocity along the track direction, which is not explicit in eigenstructure. Next, the initial states of the Jordan-reduced dynamics are regarded as orbital invariants without control to characterize a formation configuration, similar to the definition of orbital elements that are invariants of the unperturbed Keplerian orbit. Based on the derived differential form of ISJD with control, the reconfiguration trajectory is parameterized by a functional integral, the existence of which is then proved analytically by the proposed polynomial series method. The specified optimal trajectories are yielded by the practical Radau pseudospectral method numerically. Finally, the effects of reconfiguring positions and relative orbital orientation on the required acceleration and fuel cost are investigated using a technique for order preference based on similarity to the ideal solution.