Circuit Synthesis of 3-D Rotation Orthonormalization

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 68; no. 4; pp. 1502 - 1506
• Main Authors: Wu, Jin, Jiang, Yi, Li, Chong, Sun, Ran, Zhang, Chengxi, Yu, Yang, Zhu, Yilong, Liu, Ming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 3-D registration; algebraic circuits; Automation; Circuit design; Circuit synthesis; Convergence; Eigenvalues and eigenfunctions; Field programmable gate arrays; Pose estimation; Rotation; Rotation orthonormalization; Singular value decomposition; Synthesis
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2020.3027025

In many pose estimation problems, rotation matrices can not always be estimated subject to all nonlinear rigidity constraints. Therefore, engineers tend to obtain the nearest rotation matrix of an improper one, which is called the rotation orthonormalization problem. In this brief, we show a circuit synthesis of such problem by using only simple algebraic components. We give theoretical convergence analysis of the designed circuit. By using the proposed circuit, rotation orthonormalization can be easily performed without the need of previous sophisticated processes like singular value decomposition (SVD) and eigen-decomposition (EIG). Experiments of the developed method's characteristics are conducted. The circuitized scheme has also been implemented on an FPGA platform.