• 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.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.1074-1077
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• 1997

Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In this paper a new type of load flow equation is summarized as follows: Since inverse calculation of Jacobian matrix is not needed in the suggested algorithm but using complex bus voltage, the calculation process is simple. With the simple structure, reduction of calculation time is achieved.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.799-802
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• 1997

This paper deals with a new method to derive the Generalized Jacobian Matrix of a space robot. In a conventional method to derive the Generalized Jacobian Matrix, generalized coordinates select Joint angles and a space robot body's position and attitude angle. But, in this paper, we select position and attitude angle of the end-effector or the handled floating object as generalized coordinates. Then, we can derive the Generalized Jacobian Matrix of the system which consists of several space robots and a handled floating object. Moreover control methods operated by only one space robot can be easily extended to the cases of cooperation task by several space robots. Computer simulations show that the Generalized Jacobian Matrix derived here is effective.

• Journal of Mechanical Science and Technology
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• v.18 no.5
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• pp.780-788
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• 2004

To avoid the unit inconsistency problem in the conventional Jacobian matrix, new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points was presented (Kim and Ryu, 2003). This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived unit consistent Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1500-1505
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• 2003

In order to avoid the unit inconsistency problem in the conventional Jacobian matrix, previously we presented new formulation of a dimensionally homogeneous inverse Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points based on the velocity relationship [1]. This paper presents force relationships between joint forces and Cartesian forces at the three End-Effector points. The derived force relationships can then be used for analyses of the input/output force transmission. These analyses, forward and inverse force transmission analyses, depend on the singular values of the derived dimensionally homogeneous Jacobian matrix. Using the proposed force relationship, a numerical example is presented for actuator size design of a 3-RRR planar parallel manipulator.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1081-1087
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• 1999

Load Flow calulation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning. operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to slove load flow equation and to modify above defects. And it preserve P-Q bus part of Jacobian matrix to shorten computing time. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical results and the same numbers of iteration obtained by Newton-Raphson method. The effect of computing time reduction showed about 28% , 30% , at each case of 39 bus, 118 bus system.

• 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.

• The Journal of Korea Robotics Society
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• v.12 no.1
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• pp.42-54
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• 2017

Using an inverse of the geometric Jacobian matrix is one of the most popular ways to control robot manipulators, because the Jacobian matrix contains the relationship between joint space velocities and operational space velocities. However, the control algorithm based on Jacobian matrix has algorithmic singularities: The robot manipulator becomes unstable when the Jacobian matrix loses rank. To solve this problem, various methods such as damped and filtered inverse have been proposed, but comparative studies to evaluate the performance of these algorithms are insufficient. Thus, this paper deals with a comparative analysis of six representative singularity avoidance algorithms: Damped Pseudo Inverse, Error Damped Pseudo Inverse, Scaled Jacobian Transpose, Selectively Damped Inverse, Filtered Inverse, and Task Transition Method. Especially, these algorithms are verified through computer simulations with a virtual model of a humanoid robot, THORMANG, in order to evaluate tracking error, computational time, and multiple task performance. With the experimental results, this paper contains a deep discussion about the effectiveness and limitations of each algorithm.

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.178-187
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• 1995

The method that determines the appropriate damping factor is studied for a lens design. When suitable damping factor is applied to the additive damped least-squares (DLS) method, the convergence and the stability of the optimization process are examined in a triplet-type photographic lens design. We calculate eigenvalues of the product of the Jacobian matrix of error functions by using the singular value decomposition (SVD) method. We adopt the median of eigenvalues as an appropriate damping factor. The convergence and the stability of the optimization process are improved by choosing the adequate damping factor for the optimization of a photographic lens. It is known that the numerical inaccuracy in the calculation of normal equation is overcome by using the orthogonal transformations of the Jacobian matrix. Therefore, a combination of the method for setting a proper damping factor and the orthogonal transformations of the Jacobian matrix is good for application to the design of an aspheric lens with high-order terms. terms.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.219-222
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• 2005

A compressible two-fluid two-phase flow computation model using the stiffened-gas equation of state is formulated. Since the conservation equation system is of mixed type, it gives complex eigenvalues. The sonic speeds obtained from the individual single phase have been simply used in the literature for the fastest wave speeds necessary in the HLL scheme. This method has worked fine but proved to be quite diffusive according to our test. To improve the accuracy, we here propose to utilize the analytic eigenvalues evaluated from an approximate Jacobian matrix lot the fastest wave speeds. The interfacial transfer terms were dropped in constituting the Jacobian matrix for this purpose. The present scheme proved efficient, robust and accurate in comparison with other existing methods. We solved the cavitating flow problem using the present scheme. The result shows more detailed wave structure in the cavitating process caused by the strong expansion waves.