• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.2
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• pp.208-212
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• 2013

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.

• The Journal of Korea Robotics Society
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• v.17 no.1
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• pp.32-39
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• 2022

Since the mobile platform and the manipulator mounted on it move at the same time in a mobile manipulator, the risk of mutual collision increases. Most of the studies on collision avoidance of mobile manipulators cannot be applied to differential drive type mobile platforms or the end-effector tends to deviate from the desired trajectory for collision avoidance. In this study, a collision avoidance algorithm based on null space projection (CANS) that solves these two problems is proposed. To this end, a modified repulsive force that overcomes the non-holonomic constraints of a mobile platform is generated by adding a virtual repulsive force in the direction of its instantaneous velocity. And by converting this repulsive force into a repulsive velocity and applying it to the null space, the end-effector of the robot avoids a collision while moving along its original trajectory. The proposed CANS algorithm showed excellent performance through self-collision avoidance tests and door opening tests.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3253-3269
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• 1994

In this paper a new concept, named the Extended Operational Space Formulation, has been proposed for the effective analysis and real-time control of the robot manipulators with kinematic redundancy. The extended operational space consists of operational space and optimal null space. The operational space is used to describe robot end-effector motion; whereas the optimal null space, defined as the target space of the self motion manifold, is used to express the self motion for the secondary tasks. Based upon the proposed formulation, the kinematics, statics, and dynamics of redundant robots have been analyzed, and an efficient control algorithm has been proposed. Using this algorithm, one can optimize a performance measure while tracking a desired end-effector trajectory with a better computational efficiency than the conventional methods. The effective ness of the proposed method has been demonstrated with simulations.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.635-645
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• 2012

In this study, we investigate the curvature functions of ruled surface with lightlike ruling for a null curve with Cartan frame in Minkowski 3-space. Also, we give relations between the curvature functions of this ruled surface and curvature functions of central normal surface. Finally, we use the curvature theory of the ruled surface for determine differential properties of a robot end-effector motion.

• Journal of the Optical Society of Korea
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• v.6 no.2
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• pp.21-26
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• 2002

Interferometric metrology with a null CGH(computer-generated hologram) is presented for measuring highly aspheric surfaces used in a large screen projection television system with high accuracy. The cubic spline surface model which works in a single-pass configuration with a refractive index of object space 0 is used for designing a null CGH. A hybrid null corrector with plano-concave lens in front of a CGH is presented to make the CGH easier to fabricate. Experimental results are presented to demonstrate the validity of the proposed technique.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.559-564
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• 1993

Nonlinear equation of motion of the flexible manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equations of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to high order. A manipulator with a flexible 4 bar link mechanism is a constrained system whose equations are sensitive to numerical integration error. This constrained system is solved using the null space matrix of the constraint Jacobian matrix. Singular value decomposition is a stable algorithm to find the null space matrix.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.333-342
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• 2006

We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A is an SN-matrix provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of A is S, for each A ${\in}$ Q(A). We have a characterization of an SN-matrix related with L-matrix and we analyze the structure of an SN-matrix.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.41 no.2
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• pp.41-50
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• 2004

Since the MPEG-4 visual standard enables content-based functionalities, it is necessary to extract video objects from video sequences. Segmentation algorithms can largely be classified into two different categories: automatic segmentation and user-assisted segmentation. In this paper, we propose a new user-assisted image segmentation method based on the active contour. If we define a shape space as a set of all possible variations from the initial curve and we assume that the shape space is linear, it can be decomposed into the column space and the left null space of the shape matrix. In the proposed method, the shape space vector in the column space describes changes from the initial curve to the imaginary feature curve, and a dynamic graph search algorithm describes the detailed shape of the object in the left null space. Since we employ the shape matrix and the SUSAN operator to outline object boundaries, the proposed algorithm can ignore unwanted feature points generated by low-level image processing operations and is, therefore, applicable to images of complex background. We can also compensate for limitations of the shape matrix with a dynamic graph search algorithm.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.73-76
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• 1996

An impedance control approach based on an extended task space formulation is addressed to control the kinematically redundant manipulators. Defining a weighted inner product in joint space, a minimal parametrization of the null space can be achieved and we can visualize the null space motion explicitly. Based on this formulation, we propose a control method called inertially decoupled impedance controller to control the motion of the end-effector as well as the internal motion expanding the conventional impedance control. Some numerical simulations are given to demonstrate the performance of the proposed control method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.237-240
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• 1996

Internal Force based control of dual redundant manipulator is proposed. One is resolved acceleration type control in the decoupled joint space which includes null motion space and the other is in the impedance control fashion in which the desired impedances are decoupled in three subspace, internal motion controlled space, orthogonal to that space, and the null motion controlled space. The internal force is formulated with its basis set meaningful. The object dynamics is also briefly evolved beforehand.