• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.130-134
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• 2012

In this paper, we propose a space partitioning technique for swarm robots by using the Centroidal Voronoi Tessellation. The proposed method consists of two parts such as space partition and collision avoidance. The space partition for searching a given space is carried out by a density function which is generated by some accidents. The collision avoidance is implemented by the potential field method. Finally, the numerical experiments show the effectiveness and feasibility of the proposed method.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1892-1893
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• 2011

본 논문에서는 Centroidal Voronoi Tessellation을 이용하여 군집로봇의 협조탐색을 위한 공간분할기법을 제안한다. 탐색공간은 Centroidal Voronoi Tessellation을 이용하여 분할한다. 전역 경로 계획 및 군집 로봇 간의 충돌 회피는 포텐셜 필드를 이용한다. 탐색공간에 밀도 함수를 사용하여 공간분할의 유동성을 부여한다. 마지막으로, 군집로봇의 협조탐색의 가능성을 시뮬레이션을 통하여 확인한다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.293-305
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• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.141-159
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• 2009

In this article, we consider a weighted CVT-based reduced-order modelling for Burgers equation. Brief review of the CVT (centroidal Voronoi tessellation) approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD (Proper Orthogonal Decomposition)-based setting. So far, the CVT was researched with uniform density ($\rho$(y) = 1) to determine the basis elements for the approximatin subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT (CVT-uniform and CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm are reported.

• Journal of Korea Multimedia Society
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• v.9 no.2
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• pp.139-150
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• 2006

A schematic map is a special purpose map which is generated to recognize it's objects easily and conveniently via simplifying and highlighting logical geometric information of a map. To manufacture the schematic map with road, label and icon, we must generate simplified route map and replace many geometric objects. Performing a give task, however, there are an amount of overlap areas between geometric objects whenever we process the replacement of geometry objects. Therefore we need replacing geometric objects without overlap. But this work requires much computational resources, because of the high complexity of the original geometry map. We propose the schematic map generation system whose map consists of icons and label. The proposed system has following steps: 1) eliminating kinks that are least relevant to the shape of polygonal curve using DCE(Discrete Curve Evolution) method. 2) making an evenly distributed route using CVT(Centroidal Voronoi Tessellation) and Grid snapping method. Therefore we can keep the structural information of the route map from CVT method. 3) replacing an icon and label information with collision avoidance algorithm. As a result, we can replace the vertices with a uniform distance and guarantee the available spaces for the replacement of icons and labels. We can also minimize the overlap between icons and labels and obtain more schematized map.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.419-425
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• 2012

This paper presents an approach to implement the behaviors of multi-robots responding to user's input characters. The robots are appropriately displaced to express any input characters. Using our method, any user can easily and friendly control multirobots. The responses of the robots to the user's input are intuitive. We utilize the centroidal Voronoi algorithm and the continuoustime Lloyd algorithm, which have popularly been used for the optimal sensing coverage problems. Collision protection is considered to be applied for real robots. LED sensors are used to identify positions of multi-robots. Our approach is evaluated through experiments with five mobile robots. When a user draw alphabets, the robots are deployed correspondingly. By checking position errors, the feasibility of our method is validated.

• East Asian mathematical journal
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• v.34 no.5
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• pp.661-681
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• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.261-280
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• 2019

We apply a reduced-order method based on B-spline Galerkin finite elements formulation to Rosenau-RLW equation for the first time and explain their process in detail. The ensemble of snapshots is very large generally, and it is difficult to apply POD to the ensemble of snapshots directly. Hence, we try to pick up important snapshots among the whole data. In this paper, we represent three different reduced-order schemes. First, the classical POD technique is examined. Second, (equally sampled snapshots) are exploited for POD technique. Finally, afterward sampling snapshots by CVT, for those snapshots, POD technique is implemented again.