• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2092-2095
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• 2001

In this paper, the performance of a new alternative form of three-axis attitude estimation algorithm for a rigid body is evaluated via simulation for the situation where the observed vectors are the estimated baselines of a GPS antenna array. This method is derived based on a simple iterative nonlinear least-squares with four elements of quaternion parameter. The representation of quaternion parameters for three-axis attitude of a rigid body is free from singularity problem. The performance of the proposed algorithm is compared with other eight existing methods, such as, Transformation Method (TM), Vector Observation Method (VOM), TRIAD algorithm, two versions of QUaternion ESTimator (QUEST), Singular Value Decomposition (SVD) method, Fast Optimal Attitude Matrix (FOAM), Slower Optimal Matrix Algorithm (SOMA).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.3
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• pp.243-248
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• 2010

This study addresses spacecraft moment of inertial estimation approach using Modified Rodrigues Parameters(MRP). The MRP offer advantage by avoiding singularity in Kalman Filter design for attitude determination caused by the norm constraint of quaternion parameters. Meanwhile, MRP may suffer singularity for large angular displacement, so that we designed appropriate reference attitude motion for accurate estimation. The proposed approach is expected to provide stable error covariance update with accurate spacecraft mass property estimation results.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.169-175
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• 2002

A sliding mode control of spacecraft attitude tracking with actuator, especially reaction wheel, is presented. The sliding mode controller is derived based on quaternion parameterization for the kinematic equations of motion. The reaction wheel dynamic equations represented by wheel input voltage are presented. The input voltage to wheel is calculated from the sliding mode controller and reaction wheel dynamics. The global asymptotic stability is shown using a Lyapunov analysis. In addition the robustness analysis is performed for nonlinear system with parameter variations and disturbances. It is shown that the controller ensures control objectives for the spacecraft with reaction wheels.

• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.203-210
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• 2004

Attitude control law design for spacecraft large angle maneuvers is investigated in this paper. The feedback linearization technique is applied to the design of a nonlinear tracking control law. The output function to be tracked is the quaternion attitude parameter. The designed control law turns out to be a combination of attitude and attitude rate tracking commands. The attitude-only output function, therefore, leads to a stable closed-loop system following the given reference trajectory. The principal advantage of the proposed method is that it is relatively easy to produce reference trajectories and associated controller.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.407-427
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• 2024

The purpose of this article is to bring together the Horadam numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and examine a new type of quite big special numbers system, which is called Horadam 3-parameter generalized quaternions (shortly, Horadam 3PGQs), and special cases of them. Besides, we compute both some new equations and classical well-known equations such as; Binet formulas, generating function, exponential generating function, Poisson generating function, sum formulas, Cassini identity, polar representation, and matrix equation. Furthermore, this article concludes by presenting the determinant, characteristic polynomial, characteristic equation, eigenvalues, and eigenvectors in relation to the matrix representation of Horadam 3PGQ.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.92.1-92
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• 2001

Sliding mode control of spacecraft attitude tracking with actuator, especially reaction wheel, is presented. The sliding mode controller is derived based on quaternion parameterization for the kinematic equations of motion. The reaction wheel dynamic equations represented by wheel input voltage are presented. The input voltage to wheel is calculated from the sliding mode controller and reaction wheel dynamics. The global asymptotic stability is shown using a Lyapunov analysis. In addition the robustness analysis is taken for nonlinear system with parameter variations and disturbances. It is shown that the controller ensures control objectives for the spacecraft with reaction wheels.

• 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.

• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.520-526
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• 2003

In the case of a strapdown inertial navigation system (SDINS) with sizeable attitude errors, the uncertainty caused by linearization of the system degrades the performance of the filter. In this paper, a robust filter and various error models for the uncertainty are presented. The analytical characteristics of the proposed filter are also investigated. The results show that the filter does not require the statistical property of the system disturbance and that the region of the estimation error depends on a freedom parameter in the worst case. Then, the uncertainty of the SDINS is derived. Depending on the choice of the reference frame and the attitude error state, several error models are presented. Finally, various in-flight alignment methods are proposed by combining the robust filter with the error models. Simulation results demonstrate that the proposed filter effectively improves the performance.

• 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 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.