• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.141-149
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• 2005

This paper deals with formulations of the energy equilibrium equation by an introduction of the algebraic description, quarternion, which meets conservations of system energy for the equation of motion. Then the equation is discretized to analyze the dynamits analysis of flexible multibody systems in such a way that the work done by the constrained force completely is eliminated. Meanwhile, Rodrigues parameters we used to express the finite rotation lot the proposed method. This method lot the initial essential step to a guarantee of developments of the 3D dynamical problem provides unconditionally stable conditions for the nonlinear problems through the numerical examples.

• Journal of computational fluids engineering
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• v.14 no.1
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• pp.24-34
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• 2009

The equilibrium molecular-dynamic simulations have been performed to estimate the properties of the three kinds of fluids confined between two plates that are separated by 1.086 nm; included in the statical properties are the density distribution and the static structure, and the autocorrelation velocity function in the dynamic property. Three kinds of fluids considered in this study are the Lennard-Jones fluid, water and aqueous sodium-chloride solution. The water molecules are modeled by using the SPC/E model and the ions by the charged Lennard-Jones particle model. To treat the water molecules, we combined the quaternion coordinates with Euler angles. We also proposed a plausible algorithm to assign the initial position and direction of molecules. The influence of polarization of water molecules as well as the presence of ions in the solution on the properties will be addressed in this study. In addition, we performed the non-equilibrium molecular-dynamic simulation to compute the flow velocity for the case with the gravitational force acting on molecules.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.10
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• pp.1023-1030
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• 2015

The purpose of this paper is to present the basic mathematical modeling of a hexacopter, which could be used to develop proper methods for stabilization and trajectory control. A hexacopter consists of six rotors with three pairs of counter-rotating fixed-pitch blades. This mechanism is an under-actuated, dynamically unstable, six-degrees-of-freedom system. The whole motion of this object consists of translational and rotational motion in three dimensions, where the translational motion is created by changing the direction and magnitude of the upward propeller thrust. The hexacopter is controlled by adjusting the angular velocities of the rotors, which are spun by electric motors. It is assumed to be a rigid body; thus, the differential equation of the hexacopter dynamics can be derived from the Newton-Euler equation. The Euler-angle parametrization of the three-dimensional rotations contains singular points in the coordinate space that can cause failure of both the dynamical model and control. In order to avoid singularities, the rotations of the hexacopter are parametrized in terms of quaternions. This choice has been made considering the linearity of the quaternion formulation and their stability and efficiency. Further, control simulation of a hexacopter applying cascaded-PID control is also presented in this paper.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.160.2-160.2
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• 2012

Unified State Model(이후 USM)은 Altman(1972)에 의해 처음 제안된 이후 Chodas(1981), Raol & Sinha(1985), Vittaldev et al.(2012) 등을 거치며 연구 발전되어 왔다. 이 모델은 공간상 6개 성분의 위치, 속도 벡터를 이용해 위성의 운동을 기술하는 기존 계산 방법과 달리 4개의 Quaternion 변수를 도입하여 위성의 위치를, 3개의 Hodograph 변수를 도입하여 위성의 속도를 각각 기술한다. USM의 장점은 직교좌표계로 표현된 위성의 위치, 속도 변수에 비해 USM 변수의 변화량이 상대적으로 작기 때문에 수치 계산 시 계산의 안정도가 높다. 또한 원궤도(${\omega}$ : undefined)와 적도면 궤도(i = 0, ${\Omega}$ : undefined) 계산 시에 나타나는 특이성(singularity) 문제가 발생하지 않는다. 본 연구에서는 USM 계산방법과 기존 방법에 의한 위성궤도 계산결과의 차이를 비교 분석하였다. 지구궤도 위성의 정밀계산을 위해 이체항 이외에 지구타원체 섭동항과 대기 항력에 의한 섭동항을 추가 적용하였다. 비구형 지구 중력 포텐셜에 의한 섭동은 J4항까지 고려하였으며, 대기 항력은 간단한 exponential 모델을 적용하였다. 또한 수치계산 시 적분 간격과 정밀도 차수를 조절하여 각 모델의 계산 안정성을 테스트하였다. 본 연구의 궤도계산 결과 USM 모델을 이용한 계산방법은 그 정밀성과 계산효율성이 매우 우수한 것으로 검증되었다.

• Journal of Sensor Science and Technology
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• v.28 no.2
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• pp.81-87
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• 2019

One of the major issues in inertial and magnetic measurement unit (IMMU)-based 3D orientation estimation is compensation for magnetic disturbances in magnetometer signals, as the magnetic disturbance is a major cause of inaccurate yaw estimation. In the proposed approach, a kinematic constraint is used to provide a measurement equation in addition to the accelerometer and magnetometer signals to mitigate the disturbance effect on the orientation estimation. Although a Kalman filter (KF) is the most popular framework for IMMU-based orientation estimation, a complementary filter (CF) has its own advantages over KF in terms of mathematical simplicity and ease of implementation. Accordingly, this paper introduces a quaternion-based CF with a constraint-combined correction equation. Furthermore, the weight of the constraint relative to the magnetometer signal is adjusted to adapt to magnetic environments to optimally deal with the magnetic disturbance. In the results of our validation experiments, the average and maximum of yaw errors were $1.17^{\circ}$ and $1.65^{\circ}$ from the proposed CF, respectively, and $8.88^{\circ}$ and $14.73^{\circ}$ from the conventional CF, respectively, showing the superiority of the proposed approach.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.49 no.2
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• pp.129-138
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• 2021

Due to the active progress in space programs for various types of ground and space missions, the high agile spacecraft maneuverability is also required. To meet the requirement of the given space missions, the Control Moment Gyros (CMG) for the alternatives of the classical reaction wheels can release the attitude maneuverability restrictions. In addition, the angular rates of the spacecraft is constrained due to the limited actuator characteristics. In this paper, a sliding mode control technique for the attitude control of the spacecraft equipped with the pyramid type of CSCMG(Constant Speed CMG) is designed, and the stability of the control system is guaranteed by using the Lyapunov stability theory. Finally, the control law proposed is analyized by numertical simulations.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.8
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• pp.703-710
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• 2001

The nonlinear observers are proposed for a nonlinear system. To improve the characteristics such as stability, convergence, and $H^{\infty}$ filter performance criterion, we utilize an $H^{\infty}$ filter Riccati equation or a modified $H^{\infty}$ filter Riccati equation with a freedom parameter. Using the Lyapunov function method, the characteristics of the observers are analyzed. Then the in-flight alignment for a strapdown inertial navigation system(SDINS) is designed using the proposed observer. And the additive quaternion error model is especially used to reduce the uncertainty of the SDINS error model. Simulation results show that the observer with the modified $H^{\infty}$ filter Riccati equation effectively improves the performance of the in-flight alignment.

• Journal of rehabilitation welfare engineering & assistive technology
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• v.7 no.2
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• pp.47-54
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• 2013

In this paper, we present an inertial sensor-based motion capturing system to measure and analyze whole body movements. This system implements a wireless AHRS(attitude heading reference system) we developed using a combination of rate gyroscope, accelerometer and magnetometer sensor signals. Several AHRS modules mounted on segments of the patient's body provide the quaternions representing the patient segments's orientation in space. We performed 3D motion capture using the quaternion data calculated. And a method is also proposed for calculating three-dimensional inter-segment joint angle which is an important bio-mechanical measure for a variety of applications related to rehabilitation. To evaluate the performance of our AHRS module, the Vicon motion capture system, which offers millimeter resolution of 3D spatial displacements and orientations, is used as a reference. The evaluation resulted in a RMSE of 2.56 degree. The results suggest that our system will provide an in-depth insight into the effectiveness, appropriate level of care, and feedback of the rehabilitation process by performing real-time limbs or gait analysis during the post-stroke recovery process.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.7
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• pp.609-618
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• 2015

This paper discusses the attitude determination of the CNUSAIL-1 cube-satellite. The primary mission of the CNUSAIL-1 is sail deployment and operation in low Earth orbit, and the secondary mission is to look into influence of the sail deployment on satellite attitude and orbit. The attitude determination strategy is proposed depending on three mission phases, and its performance and applicability are verified through numerical simulations. This study considers the following sensors: Sun sensors and a three-axis magnetometer as attitude reference sensors, and a three-axis MEMS gyroscope as an inertial attitude sensor. Because sensors used for cube satellites have relatively low performances and worse noise characteristics, an Extended Kalman filter (EKF) is applied to attitude determination. Additionally, it has the merits to deal with the Gaussian noises and to predict the attitude even with no measurements from reference attitude sensors, especially in the eclipse of the cube satellite. The performance of the EKF is compared to a deterministic attitude determination technique, QUEST(QUaternion ESTimation).

• Journal of Biomedical Engineering Research
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• v.27 no.6
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• pp.392-401
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• 2006

Image Guided Surgery (IGS) system which has variously tried in medical engineering fields is able to give a surgeon objective information of operation process like decision making and surgical planning. This information is displayed through 3D images which are acquired from image modalities like CT and MRI for pre-operation. The technique of image registration is necessary to construct IGS system. Image registration means that 3D model and the object operated by a surgeon are matched on the common frame. Major techniques of registration in IGS system have been used by recognizing fiducial markers placed on the object. However, this method has been criticized due to additional trauma, its invasive protocol inserting fiducial markers in patient's bone and generating noise data when 2D slice images are acquired by image modality because many markers are made of metal. Therefore, this paper developed shape-based registration technique to improve the limitation of fiducial marker based IGS system. Iterative Closest Points (ICP) algorithm was used to match corresponding points and quaternion based rotation and translation transformation using closed form solution applied to find the optimized cost function of transformation. we assumed that this algorithm were used in Total Knee replacement (TKR) operation. Accordingly, we have developed region-based 3D registration technique based on anatomical landmarks and this registration algorithm was evaluated in a femur model. It was found that region-based algorithm can improve the accuracy in 3D registration.