• International Journal of Control, Automation, and Systems
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• 제6권1호
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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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• 한국전산유체공학회 1999년도 추계 학술대회논문집
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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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• 제37권5호
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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.

• 한국음향학회지
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• 제25권4호
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• pp.159-163
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• 2006

본 논문에서는 잡음음성인식을 위한 데이터 기반의 향상된 Jacobian 적응 방식을 제안하였다. Jacobian 적응에서 필요로 하는 기준 HMM을 구성하기 위해서 기존에 주로 사용되던 모델결합 방식을 사용하는 대신에 잡음음성을 이용하여 직접 훈련하는 방식을 제안하였다. 이렇게 함으로서 기존의 방법에 비해서 잡음에 의한 음향모델의 변이를 보다 잘 처리할 수 있을 것으로 생각된다 제안된 방법에서는 Jacobian 행렬의 추정을 위해서 훈련과정에서 Baum-Welch 알고리듬을 사용하였다. 잡음음성에 대한 인식실험을 통해서 제안된 방식이 기존의 Jacobian 적응 방식 뿐 만 아니라 다른 형태의 모델적응 방식들에 비해서도 우수한 성능을 보임을 알 수 있었다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 추계학술대회 논문집
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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.

• 한국컴퓨터정보학회논문지
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• 제14권8호
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• pp.11-18
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• 2009

본 논문은 Levenberg-Marquardt 알고리즘에서 Jacobian 행렬의 주부분 행렬을 이용하여 학습속도를 개선하는 방법을 제안한다. Levenberg-Marquardt 학습은 오차함수에 대한 2차 도함수를 계산하기 위해 Hessian 행렬을 사용하는 대신 Jacobian 행렬을 이용한다. 이런 Jacobian 행렬을 가역행렬로 만들기 위해, Levenberg-Marquardt 학습은 ${\mu}$값을 증가시키거나 감소시키는 과정을 수행하고 ${\mu}$값의 변경에 따른 역행렬의 재계산이 필요하다. 따라서 본 논문에서는 ${\mu}$값의 설정을 위해 Jacobian 행렬의 주부분 행렬을 생성하고 주부분 행렬의 고유값 합을 이용하여 ${\mu}$값을 설정한다. 이와 같은 방법은 추가적인 역행렬 계산을 하지 않으므로 학습속도를 개선할 수 있다. 제안된 방법은 일반화된 XOR 문제와 필기체 숫자인식 문제를 대상으로 실험하여 학습속도의 향상을 검증하였다.

• East Asian mathematical journal
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• 제38권5호
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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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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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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.

• 제어로봇시스템학회논문지
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• 제6권12호
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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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• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
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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.