ORIGINAL PAPERS

Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters

  • Sheng Chen ,
  • Haofei Hu ,
  • Shihang Wang ,
  • Chongbin Guo
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  • 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 date: 2024-07-28

  Revised date: 2024-09-09

  Online published: 2026-04-07

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

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.

Cite this article

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 . DOI: 10.1007/s42967-024-00460-4

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