Integrating Rotations Using Nonunit Quaternions
نویسندگان
چکیده
منابع مشابه
Quaternions and Rotations *
Up until now we have learned that a rotation in R3 about an axis through the origin can be represented by a 3×3 orthogonal matrix with determinant 1. However, the matrix representation seems redundant because only four of its nine elements are independent. Also the geometric interpretation of such a matrix is not clear until we carry out several steps of calculation to extract the rotation axis...
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In this paper we address the problem of using quaternions in unconstrained nonlinear optimization of 3-D rotations. Quaternions representing rotations have four elements but only three degrees of freedom, since they must be of norm one. This constraint has to be taken into account when applying e. g. the Levenberg-Marquardt algorithm, a method for unconstrained nonlinear optimization widely use...
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In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection. The three methods are described in some detail. An analysis is performed where the three methods ar...
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A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion me...
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ژورنال
عنوان ژورنال: IEEE Robotics and Automation Letters
سال: 2018
ISSN: 2377-3766,2377-3774
DOI: 10.1109/lra.2018.2849557