Recently, Zhuang et al. [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a homogeneous matrix equation of the formAX = ZB. They use quaternions to derive explicit linear solutions for X and Z. In this short paper, we present two new solutions that attem...

Nonlinear tracking control of unmanned underwater vehicles (UUVs) in 6 degrees of freedom (DOF) is discussed. The 4-parameter unit quaternion is used in a singularity-free representation of attitude. Several control laws based on a generalized Lyapunov function for the attitude dynamics are derived, including feedback from the vector quaternion, the Euler rotation vector and the Rodrigues param...

Using the Fokker-Planck equation describing trie evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in m the crossover regime from the orthogonal to the unitary symmetry. The correlation functions of the transmission eigenvalues are expressed in terms of quaternion determinants for arbitrary number N of ...

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence ?-anti-Hermitian solution to system constrained matrix equations over algebra. also obtain expression general when it is solvable. Finally, provide numerical example verify main results paper.

We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N , we ...

In this paper we propose a novel approach to measuring curvature in color or vector-valued images (up to 4-dimensions) based on quaternion singular value decomposition of a Hessian matrix. This approach generalizes the existing scalar-image curvature approach which makes use of the eigenvalues of the Hessian matrix [1]. In the case of vector-valued images, the Hessian is no longer a 2D matrix b...

In this paper the unit quaternion is used as a substitute for describing the attitude of a camera to overcome the shortcomings of Euler angles on the description and interpolation of orientation, corresponding collinearity equation is then derived and linearized. At the same time the Spherical linear Interpolation (Slerp) of unit quaternion is introduced into the bundle adjustment of three-line...