Accurate computation of quaternions from rotation matrices

Conference Article


International Symposium on Advances in Robot Kinematics (ARK)





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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.



Author keywords

Quaternions, Rotation matrices

Scientific reference

S. Sarabandi and F. Thomas. Accurate computation of quaternions from rotation matrices, 16th International Symposium on Advances in Robot Kinematics, 2018, Bologna, Italy, in Advances in Robot Kinematics 2018, Vol 8 of Springer Proceedings in Advanced Robotics, pp. 39-46, 2019.