Abstract
The main non-singular alternative to \(3\times 3\) proper orthogonal matrices, for representing rotations in \({\mathbb R}^3\), is quaternions. Thus, it is important to have reliable methods to pass from one representation to the other. While passing from a quaternion to the corresponding rotation matrix is given by Euler-Rodrigues formula, the other way round can be performed in many different ways. Although all of them are algebraically equivalent, their numerical behavior can be quite different. In 1978, Shepperd proposed a method for computing the quaternion corresponding to a rotation matrix which is considered the most reliable method to date. Shepperd’s method, thanks to a voting scheme between four possible solutions, always works far from formulation singularities. In this paper, we propose a new method which outperforms Shepperd’s method without increasing the computational cost.
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Acknowledgments
This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through projects DPI2014-57220-C2-2-P, DPI2017-88282-P, and MDM-2016-0656.
We also want to express our gratitude to Antonio B. Martínez for the financial support of the first author, and to the anonymous reviewers whose comments have led to a number of valuable improvements in the text.
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Sarabandi, S., Thomas, F. (2019). Accurate Computation of Quaternions from Rotation Matrices. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_5
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DOI: https://doi.org/10.1007/978-3-319-93188-3_5
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