... Euler angles, which were used for the development of the so-called rotational and translational confidence limit (RTCL) method. The set of six dual Rodrigues parameters are used to define a parametric space in which a 6 × 6 covariance matrix and a 6D confidence ellipsoid are obtained. An inverse...

... for translation parameters is millimeter and the unit of rotation angle θ is degree. Let λ i ( i = 1, 2, 3) denote the eigenvalues of the covariance matrix (22) and let [ A ] denote a 3 × 3 matrix whose columns are the eigenvectors. They define the variances in the principal directions...

..., the mean and covariance matrix of the distribution of the pose error are analytically determined. Then, the expectation propagation of the multivariate Gaussian and saddlepoint approximation method are employed to calculate the probabilities of kinematic reliability under the rectangular and spherical safe...