• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.583-602
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• 1995

With the theory of a certain type of orders in a Quaternion algebra, we construct Brandt matrices and theta series. As a application, we calculate the class number of a certain type of orders in a Quanternion algebra with the trace formular of Brandt matrices.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.5
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• pp.555-563
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• 2009

When a mobile mapping system or a robot is equipped with only a GPS (Global Positioning System) and multiple stereo camera system, a transformation from a local camera coordinate system to GPS coordinate system is required to link camera poses and 3D data by V-SLAM (Vision based Simultaneous Localization And Mapping) to GIS data or remove the accumulation error of those camera poses. In order to satisfy the requirements, this paper proposed a novel method that calculates a camera rotation in the GPS coordinate system using the three pairs of camera positions by GPS and V-SLAM, respectively. The propose method is composed of four simple steps; 1) calculate a quaternion for two plane's normal vectors based on each three camera positions to be parallel, 2) transfer the three camera positions by V-SLAM with the calculated quaternion 3) calculate an additional quaternion for mapping the second or third point among the transferred positions to a camera position by GPS, and 4) determine a final quaternion by multiplying the two quaternions. The final quaternion can directly transfer from a local camera coordinate system to the GPS coordinate system. Additionally, an update of the 3D data of captured objects based on view angles from the object to cameras is proposed. This paper demonstrated the proposed method through a simulation and an experiment.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.6
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• pp.1-7
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• 2006

This paper presents the study in the development of optimal working method for an outer-hull preprocessing robot using a quaternion. The out-hull preprocessing robot consists of feathering and cleaning parts. This robot should be controlled correctly for feathering work because it is to be worked on a curved plate that can result in the errors of orientation. In this paper, we propose a control algorithm between given two orientations of the out-hull preprocessing robot by using a quaternion with spherical linear interpolation. The proposed control algorithm is shown to be effective in terms of motor angles and torques when compared to a conventional Euler angle interpolation, by using both $MATLAB^{\circledR}$ and $VisualNastran4D^{\circledR}$.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.559-567
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• 2015

This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.

• East Asian mathematical journal
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• v.31 no.1
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1832-1835
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• 2005

This paper presents the steering control algorithm of an up and down motion robot using a quaternion. The up and down motion robot is to be moved on an irregular floor that can inevitably result in the errors of both position and orientation. Especially the orientation error should be compensated every work in order to adjust the misaligned values of current orientation to those commanded values. In this paper, we propose a new steering control algorithm between the two values by using a quaternion with spherical cubic interpolation. The proposed algorithm is shown to be effective in terms of vibration when compared to a conventional simple compensation without interpolation, by using $MATLAB^{(R)}$ and $VisualNastran4D^{(R)}$

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.183-189
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• 2010

This paper deals with the comparison of analysis methodologies by applying both Euler angle and quaternion to observe the kinematical behavior of the universal joint system used as an automotive drive-shaft. At first, conventional approaches are applied to predict a kinematical behavior by introducing only Euler angles into the universal joint system, but turns out to be lack in consistency and reliability of the analysis. Then to overcome this deficiency in numerical analysis a different methodology is proposed by using quaternion in this system. Its corresponding advantage is discussed in terms of kinetic energy, rotational velocity and rotational displacement. The application of quaternions in the numerical experiment is shown to be a more useful and valid way of establishing the ideal analytical model of the universal joint system.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.5
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• pp.475-482
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• 2008

This paper indicates that the use of Euler angles lacks in its consistency and exactness of analysis when it was applied to incorporate the rotational equation of motion for rotor systems by previous researcher. Kinetic energy and angular velocity are different from case to case depending on the way of choosing Euler angles and thus only the linear system has been investigated even though the rotor system has a very nonlinear behavior. A new methodology is applied by using both spherical coordinate and quaternion in the rotor rotation to overcome weaknesses of Euler angles and shows its superiority It is found through numerical examples that the use of quaternion will be a more useful and valid tool to derive the numerical model of the rotor system.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.864-866
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• 1996

The attitude error is expressed using four kinds of quaternion errors. And the explicit relation equations between them are derived four kinds of nonlinear error models of SDINS using the their explicit relation are also proposed for a nonlinear filter which may be available for a system in the presence of a large attitude error the concept of the proposed nonlinear error model is applied to the velocity aided SDINS using a linear Kalman filter and an extended Kalman filter the simulation results reveal a improvement of performance using the nonlinear error model.

• Bulletin of the Korean Chemical Society
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• v.28 no.10
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• pp.1705-1708
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• 2007

Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.