• Honam Mathematical Journal
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• v.46 no.2
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• pp.209-223
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• 2024

In this paper, we investigate the spatial quaternionic expressions of the ruled surfaces whose base curves are formed by the Smarandache curve. Moreover, we formulate the striction curves and dralls of these surfaces. If the quaternionic Smarandache ruled surfaces are closed, the pitches and angle of pitches are interpreted. Finally, we calculate the integral invariants of these surfaces using quaternionic formulas.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.89-96
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• 2015

IT is widely used for biomechanics and AHRS sensor also be highlighted with small sized characteristics and price competitiveness in the field of motion measurement and analysis of sports. In this paper, we attach the AHRS to the figure skate shoes to measure the motion data like spin, forward/backward, jump, in/out edge and toe movement. In order to reduce the measurement error, we have adopted the sensors equipped with Madgwick complementary filtering and also use Euler angle to quaternion conversion to reduce the Gimbal-lock effect. We test and experiment the accuracy and execution time of the pattern recognition algorithms like PCA, ICA, LDA, SVM to show the recognition possibility of it on the basic motions of figure skating from the 9-axis trajectory information which is gathered from AHRS sensor. From the result, PCA, ICA have low accuracy, but LDA, SVM have good accuracy to use for recognition of basic motions of figure skating.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.4
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• pp.469-475
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• 2015

This paper describes about the method for designing an extended Kalman filter to accurately measure the position of the spatial-phase system using a semiconductor sensor. Spatial position is expressed by the correlation of the rotated coordinate system attached to the body from the inertia coordinate system (a fixed coordinate system). To express the attitude, quaternion was adapted as a state variable, Then, the state changes were estimated from the input value which was measured in the gyro sensor. The observed data is the value obtained from the acceleration sensor. By matching between the measured value in the acceleration sensor and the predicted calculation value, the best variable was obtained. To increase the accuracy of estimation, designation of the extended Kalman filter was performed, which showed excellent ability to adjust the estimation period relative to the sensor property. As a result, when a three-axis gyro sensor and a three-axis acceleration sensor were adapted in the estimator, the RMS(Root Mean Square) estimation error in simulation was retained less than 1.7[$^{\circ}$], and the estimator displayed good property on the prediction of the state in 100 ms measurement period.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.2
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• pp.63-71
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• 2003

This paper presents a robust slewing control of a flexible space structure based on sliding surface design. A sliding surface is designed for a single-axis rest-to-rest slewing in view of target angle, target angular velocity, and root monent of the flexible appendage. In comparison with the Lypunov control law, both controllers guarantee the stability and command tracking capabilities for nominal system. It is also shown that the designed control law provides further robustness to internal/external uncertainties. Extending the results of a single-axis maneuver, a sliding mode control law was sought for an arbitrary three-axis maneuver. Quaternion was used to determine the attitude of a space structure and sliding surfaces were designed for each axis, thereby a robust control law was derived considering the coupling effects between each rotational axis during the maneuver. Several numerical examples were demonstrated to show the effectiveness of the designed control law.

• Journal of Advanced Navigation Technology
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• v.15 no.2
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• pp.181-188
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• 2011

A small UAVs(Unmaned Aerial Vehicles) have limited by the payload capacity which requires miniaturization of a navigation system. In this paper, the performance of the lightweight and small sized AHRS(Attitude Heading Reference System), which is self-developed, is evaluated at low acceleration environment. The designed AHRS adopts the commercial low-cost MEMS sensors. A quaternion-based attitude calculation method, which eliminates singularity with relatively simple algebra, is used. In an attitude correction algorithm, the Kalman filter is used with accelerometers and magnetometers combined. The fabricated AHRS is also evaluated with reference to a COTS(Commercial Off-The-Shelf) AHRS which reports a number of successful applications to a small UAVs. The test results show that the measurements from the fabricated AHRS provide proper attitude output data with acceptable amount of differences(horizontal axis 0.5$^{\circ}$, vertical axis 1.5$^{\circ}$) in test environment.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.36 no.2
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• pp.43-50
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• 2018

The camera is a key element in image-based three-dimensional positioning, and camera calibration, which properly determines the internal characteristics of such a camera, is a necessary process that must be preceded in order to determine the three-dimensional coordinates of the object. In this study, a new methodology was proposed to determine interior orientation parameters of a camera semi-automatically without being influenced by size and shape of checkerboard for camera calibration. The proposed method consists of exterior orientation parameters estimation using quaternion, recognition of calibration target, and interior orientation parameter determination through bundle block adjustment. After determining the interior orientation parameters using the chessboard calibration target, the three-dimensional position of the small 3D model was determined. In addition, the horizontal and vertical position errors were about ${\pm}0.006m$ and ${\pm}0.007m$, respectively, through the accuracy evaluation using the checkpoints.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.9
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• pp.807-817
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• 2012

An optical payload needs to be validated its image performance after launched into orbit. The image performance was validated by observing star because ground site contains uncertainties caused by atmosphere, time of the year, and weather. Time Delayed and Integration(TDI) technique, which is mostly used to observe the ground, is going to be used to observe the selected stars. A satellite attitude scenario was also developed to observe the selected stars. The scenario is created to enable TDI to operate. Rotation angles of optical payload are determined in order for the selected stars to properly be passed at a desired angular velocity about rotation axis. The result of this research can be utilized to validate the quality of optical payload of a satellite in orbit. In addition, a quaternion for pointing selected stars is calculated minimizing the path from a given arbitrary attitude of satellite.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.10
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• pp.941-946
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• 2013

In this paper, an enhanced method for attitude determination is proposed for systems using an IMU (Inertial Measurement Unit). In attitude determination with IMU, it is generally assumed that the IMU can be located in the center of gravity on the vehicle. If the IMU is not located in the center of gravity, the accelerometers of the IMU are disturbed from additive accelerations such as centripetal acceleration and tangential acceleration. Additive accelerations are derived from the lever arm which is the distance between the center of gravity and the position of the IMU. The performance of estimation errors can be maintained in system with a non-zero lever arm, if the lever arm is estimated to remove the additive accelerations from the accelerometer's measurements. In this paper, an estimation using Kalman filter is proposed to include the lever arm in the state variables of the state space equation. For the Kalman filter, the process model and the measurement model for attitude determination are made up by using quaternion. In order to evaluate the proposed algorithm, both of the simulations and the experiments are performed for the simplified scenario of motion.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.6
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• pp.890-896
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• 2022

In this paper, gimbal camera control through smart gloves was implemented to increase convenience and accessibility to the control of drones used in various fields. Smart gloves identify human gestures and transmit signals through Bluetooth. The received signal is converted into a signal suitable for the drone through a GCS (Gound Control Station). Signals from smart gloves are expressed in a quaternion method to prevent gimbal locks, but for gimbal cameras, conversion is required to use Roll, Pitch, and Yaw methods. The data conversion mission is performed in the GCS. The GCS transmits an input signal to the control board of the drone through Wi-Fi. The control board generates and outputs the transmitted signal in a PWM manner. The output signal is input to the gimbal camera through the SBUS method and controlled. The input signal of the smart glove averaged 0.093 s and up to 0.099 s to output to the gimbal camera, showing that there was no problem in real-time use.