An Algorithm for Generating N-Dimensional Rotation Matrix

2021 ◽  
pp. 15-28
Author(s):  
Ognyan Ivanov Zhelezov
Keyword(s):  
Rotation Matrix

Generating function for rotation matrix elements

2011 ◽  
Vol 112 (2) ◽  
pp. 367-372
Author(s):  
S. Ö. Akdemir ◽  
E. Öztekin
Keyword(s):  
Generating Function ◽  
Rotation Matrix ◽  
Matrix Elements ◽  
Rotation Matrix Elements

scholarly journals A Survey on the Computation of Quaternions From Rotation Matrices

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Soheil Sarabandi ◽  
Federico Thomas
Keyword(s):  
Three Dimensional ◽  
Rotation Matrix ◽  
Three Dimensions ◽  
Attitude Dynamics ◽  
Euler Parameters ◽  
Four Dimensions ◽  
Rotation Matrices ◽  
Spacecraft Attitude Dynamics ◽  
Applied Fields ◽  
Quaternion Representation

The parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, three-dimensional image processing, and computer graphics. Nowadays, the main alternative to the use of rotation matrices, to represent rotations in ℝ3, is the use of Euler parameters arranged in quaternion form. Whereas the passage from a set of Euler parameters to the corresponding rotation matrix is unique and straightforward, the passage from a rotation matrix to its corresponding Euler parameters has been revealed to be somewhat tricky if numerical aspects are considered. Since the map from quaternions to 3 × 3 rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clarified. This paper reviews the most representative methods available in the literature, including a comparative analysis of their computational costs and error performances. The presented analysis leads to the conclusion that Cayley's factorization, a little-known method used to compute the double quaternion representation of rotations in four dimensions from 4 × 4 rotation matrices, is the most robust method when particularized to three dimensions.

scholarly journals ROTATION MATRIX SAMPLING SCHEME FOR MULTIDIMENSIONAL PROBABILITY DISTRIBUTION TRANSFER

2016 ◽  
Vol III-7 ◽  
pp. 103-110
Author(s):  
P. Srestasathiern ◽  
S. Lawawirojwong ◽  
R. Suwantong ◽  
P Phuthong
Keyword(s):  
Probability Distribution ◽  
Orthogonal Matrix ◽  
Rotation Matrix ◽  
Sampling Scheme ◽  
Uniform Rotation ◽  
Householder Transformation ◽  
Orthogonal Matrices ◽  
Matrix Sampling ◽  
Paper Address ◽  
Multidimensional Probability

This paper address the problem of rotation matrix sampling used for multidimensional probability distribution transfer. The distribution transfer has many applications in remote sensing and image processing such as color adjustment for image mosaicing, image classification, and change detection. The sampling begins with generating a set of random orthogonal matrix samples by Householder transformation technique. The advantage of using the Householder transformation for generating the set of orthogonal matrices is the uniform distribution of the orthogonal matrix samples. The obtained orthogonal matrices are then converted to proper rotation matrices. The performance of using the proposed rotation matrix sampling scheme was tested against the uniform rotation angle sampling. The applications of the proposed method were also demonstrated using two applications i.e., image to image probability distribution transfer and data Gaussianization.

Kinematic Synthesis of Spatial R-R Dyads for Path Following Revisited Using the Rotation Matrix Approach

1999 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Path Following ◽  
Rotation Matrix ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Serial Chain ◽  
Systematic Development ◽  
Matrix Vector ◽  
Selection Of

Abstract We revisit the dimensional synthesis of a spatial two-link, two revolute-jointed serial chain for path following applications, focussing on the systematic development of the design equations and their analytic solution for the three precision point synthesis problem. The kinematic design equations are obtained from the equations of loop-closure for end-effector position in rotation-matrix/vector form at the three precision points. These design equations form a rank-deficient linear system in the link-vector components. The nullspace of the rank deficient linear system is then deduced analytically and interpreted geometrically. Tools from linear algebra are applied to systematically create the auxiliary conditions required for synthesis and to verify consistency. An analytic procedure for obtaining the link-vector components is then developed after a suitable selection of free choices. Optimization over the free choices is possible to permit the matching of additional criteria and explored further. Examples of the design of optimal two-link coupled spatial R-R dyads are presented where the end-effector interpolates three positions exactly and closely approximates an entire desired path.

scholarly journals Robust Visual Compass Using Hybrid Features for Indoor Environments

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 220 ◽  
Author(s):  
Ruibin Guo ◽  
Keju Peng ◽  
Dongxiang Zhou ◽  
Yunhui Liu
Keyword(s):  
Autonomous Navigation ◽  
Estimation Method ◽  
Rotation Matrix ◽  
Indoor Environments ◽  
3D Mapping ◽  
Orientation Estimation ◽  
Hybrid Features ◽  
Depth Images ◽  
Improved Accuracy ◽  
Crucial Part

Orientation estimation is a crucial part of robotics tasks such as motion control, autonomous navigation, and 3D mapping. In this paper, we propose a robust visual-based method to estimate robots’ drift-free orientation with RGB-D cameras. First, we detect and track hybrid features (i.e., plane, line, and point) from color and depth images, which provides reliable constraints even in uncharacteristic environments with low texture or no consistent lines. Then, we construct a cost function based on these features and, by minimizing this function, we obtain the accurate rotation matrix of each captured frame with respect to its reference keyframe. Furthermore, we present a vanishing direction-estimation method to extract the Manhattan World (MW) axes; by aligning the current MW axes with the global MW axes, we refine the aforementioned rotation matrix of each keyframe and achieve drift-free orientation. Experiments on public RGB-D datasets demonstrate the robustness and accuracy of the proposed algorithm for orientation estimation. In addition, we have applied our proposed visual compass to pose estimation, and the evaluation on public sequences shows improved accuracy.

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