Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters

doi:10.1007/s42967-024-00460-4

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (2): 622-639.doi: 10.1007/s42967-024-00460-4

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Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters

Sheng Chen¹, Haofei Hu^2,4, Shihang Wang^2,4, Chongbin Guo^2,3,4

1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, China;
2. Innovation Academy for Microsatellites of Chinese Academy of Sciences, Shanghai, 201304, China;
3. University of Chinese Academy of Sciences, Beijing, 101408, China;
4. Shanghai Engineering Center for Microsatellites, Shanghai, 201306, China

Received:2024-07-28 Revised:2024-09-09 Online:2026-04-07 Published:2026-04-07
Contact: Haofei Hu,E-mail:huhf@microsate.com;Chongbin Guo,E-mail:guocb@microsate.com E-mail:huhf@microsate.com;guocb@microsate.com
Supported by:
This study was supported by The Hong Kong-Macau-Taiwan Science and Technology Cooperation Project of the Science and Technology Innovation Action Plan in Shanghai (No. 23510760200); Oriental Talent Youth Program of Shanghai (No. Y3DFRCZL01); Outstanding Program of the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. Y2023080), and Strategic Priority Research Program of the Chinese Academy of Sciences (Category A: No. Y3ZKXDZL04).

Abstract

Abstract: Dual quaternions are essential for the precise formation flying of satellite clusters and for the Relative Navigation and Positioning (RNP). In this paper, we investigate dual quaternion matrices within the contexts of the precise formation and the RNP. We begin by reformulating the graph model of the formation flying problem using dual quaternion unit gain graphs. Following this, we study the dual quaternion incidence matrix to characterize the balance of these unit gain graphs. We also show that the Perron-Frobenius theorem holds for balanced dual quaternion unit gain graphs. As an application, we study a pose graph optimal problem in the RNP.

Key words: Unit dual quaternion, Gain graph, Balance, Perron-Frobenius theorem, Satellite cluster

CLC Number:

Sheng Chen, Haofei Hu, Shihang Wang, Chongbin Guo. Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters[J]. Communications on Applied Mathematics and Computation, 2026, 8(2): 622-639.

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Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters

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