• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.101-108
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• 2008

The transposed Jacobian is proposed to transform the control space from task space to joint space, in this paper. Instead of inverse Jacobian, the transposed Jacobian is preferred to avoid singularity problem, short real time calculations and its generality to apply for rectangular Jacobian. On-line Jacobian identification is proposed to cancel parametric errors produced by D-H parameters of manipulator. To identify Jacobian, the joint angles and the end-effector position are measured when tracking a desired trajectory in task space. Stability of control system is analyzed. The control system is simulated for position control of a two-link manipulator driven by permanent magnet dc motors. Simulation results are shown to compare the roles of inverse Jacobian and transposed Jacobian for transforming the control space.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.59-64
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• 1999

The Equations of Chemical kinetics ate very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the approximate chemical jacobian methods such as Gauss-Seidel, Jacobi partial jacobian and diagonalized jacobian that can be stable without full jacobian, We show that Gauss-Seidel jacobian method is stable and accurate as well as full jacobian and that this is more efficient in supersonic combustion problem about $20\%$ than the full jacobian method with same accuracy,

• East Asian mathematical journal
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• v.37 no.5
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• pp.585-590
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• 2021

This paper consider the Jacobian variety of a hyperelliptic curve over a finite field with the formal structure of the mixed type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives an useful tool for finding the local decomposition of the Jacobian variety into isotypic components.

• The Journal of the Acoustical Society of Korea
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• v.25 no.4
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• pp.159-163
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• 2006

In this paper a data-driven method to improve the performance of the Jacobian adaptation (JA) for the noisy speech recognition is proposed. In stead of constructing the reference HMM by using the model composition method like the parallel model combination (PMC), we propose to train the reference HMM directly with the noisy speech. This was motivated from the idea that the directly trained reference HMM will model the acoustical variations due to the noise better than the composite HMM. For the estimation of the Jacobian matrices, the Baum-Welch algorithm is employed during the training. The recognition experiments have been done to show the improved performance of the proposed method over the Jacobian adaptation as well as other model compensation methods.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.647-652
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• 2000

This paper presents a study on the position tracking control of robot system on the uncertain elastic base. The elastic base is modeled as a virtual robot which has passive joints and the control strategy is using approximate Jacobian operators. Jacobian operators represent the overall robot system including base movement. However, because we don't know the base movement we can't estimate the jacobian operators directly. The control algorithm is proposed which uses only Jacobian operators of a real robot as approximate Jacobian operators. The measured errors from external sensor are compensated by approximate Jacobian operators. The simulation results of a single-axis robot system show that the control strategy can be used for position tracking.

• Journal of the Korea Society of Computer and Information
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• v.14 no.8
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• pp.11-18
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• 2009

This paper proposes the way of improving learning speed in Levenberg-Marquardt algorithm using the principal submatrix of Jacobian matrix. The Levenberg-Marquardt learning uses Jacobian matrix for Hessian matrix to get the second derivative of an error function. To make the Jacobian matrix an invertible matrix. the Levenberg-Marquardt learning must increase or decrease ${\mu}$ and recalculate the inverse matrix of the Jacobian matrix due to these changes of ${\mu}$. Therefore, to have the proper ${\mu}$, we create the principal submatrix of Jacobian matrix and set the ${\mu}$ as the eigenvalues sum of the principal submatrix. which can make learning speed improve without calculating an additional inverse matrix. We also showed that our method was able to improve learning speed in both a generalized XOR problem and a handwritten digit recognition problem.

• East Asian mathematical journal
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• v.38 no.5
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• pp.611-616
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• 2022

This paper considers the Jacobian variety of a hyperelliptic curve over a finite field with mixed symmetric formal type. We present the Newton polygon of the characteristic polynomial of the Frobenius endomorphism of the Jacobian variety. It gives a useful tool for finding the local decomposition of the Jacobian variety into isotypic components.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1820-1823
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• 1997

For the Cartesian space position controlled robot, it is required to have the accurate mapping from the Cartesian space to the joint space in order to command the desired joint trajectories correctly. since the actual mapping from Cartesian space to joint space is obtained at the joint coordinate not at the actuator coordinate, uncertainty in Jacobian can be present. In this paper, two feasible neural network schemes are proposed to compensate for the kinematic Jacobian uncertainties. Uncertainties in Jacobian can be compensated by identifying either actuator Jacobian off-line or the inverse of that in on-line fashion. the case study of the stenciling robot is examined.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.12
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• pp.1086-1092
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• 2000

To realize a visual servo control of slender manipulators, two problems to be solved are analysed. The stability problem on so-called noncolocation control and the infinite order problem of the real Jacobian matrix caused by the elastic deformation are discussed. By considering the dynamic relations between rigid and elastic modes, a Jacobian operator is derived and the physical meaning is also explained. Then, for practical control, a simple control scheme using an approximate Jacobian is proposed and its stable conditions are proven by means of the $L_$2$ stability theory. The scheme is structurally similar to the conventional PD control laws, but external sensors(e. g. visual sensor) are used for positioning and internal sensors for damping. A good performance is obtained via control experiments of a slender two link manipulator.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.304-309
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• 1986

This paper is about the Inverse Jacobian for the TOP-1 robot. The robot Jacobian is used for the movement in accordance with differental changes. A Matrix and Homogeneous Transformation Matrix, Differential Motion Vector D are applied to Jacobian equation for the movement of the robot in accordance with the minut changes. The solution of Jacobian equation is acquired and applied for the subtle movement of each arms of the robot. The interface with APPLE-II Micro-computer is searched out too. The Software and the interface resulted from this paper are considered to be higly useful in the accurate control on the robot when they are linked with dynamics of robot.