Accurate computation of quaternions from rotation matrices
Document typeConference report
PublisherSpringer International Publishing
Rights accessOpen Access
The main non-singular alternative to 3×3 proper orthogonal matrices, for representing rotations in R3, 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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CitationSarabandi, S., Thomas, F. Accurate computation of quaternions from rotation matrices. A: International Conference on Advances in Robot Kinematics. "Vol 8 of Springer Proceedings in Advanced Robotics". Springer International Publishing, 2018, p. 39-46.