• 제어로봇시스템학회논문지
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• 제19권6호
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• pp.540-546
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• 2013

This paper presents a trajectory planning algorithm for TMR (Two-wheeled Mobile Robots). The trajectory is developed in joint space and considers the physical limits of a TMR. First, we present a process for generating a smooth curve through a Bezier curve. The trajectory for the center of the TMR following the Bezier curve is developed through a convolution operator taking into consideration its physical limits. The trajectory along the Bezier curve is regenerated using time-dependent parameters which correspond to the distance driven by the velocity of the center of the TMR in a sampling time. The velocity commands in the Cartesian space are converted to actuator commands for two wheels. In case that the actuator commands exceed the maximum velocity, the trajectory is redeveloped with compensated center velocity. We also suggest a smooth trajectory planning algorithm in joint space for the two segmented paths. Finally, the effectiveness of the algorithm is shown through numerical examples and application to a simulator.

• 대한수학회보
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• 제60권5호
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• pp.1265-1280
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• 2023

The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of s parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of s parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan s parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null s parameter curve.

• 호남수학학술지
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• 제40권2호
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• pp.251-264
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• 2018

In the present study, we consider the curves in Galilean 4-space ${\mathbb{G}}_4$. We find out the involute curves of order k (k = 1, 2, 3) of a given curve. We get the relationships between the Frenet apparatus of a given curve and its involute curves of order k.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.896-899
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• 1996

A new algorithm for planning a collision free path is developed based on linear parametric curve. A collision-free path is viewed as a connected space curve in which the path consists of two straight curve connecting start to target point. A single intermediate connection point is considered in this paper and is used to manipulate the shape of path by organizing the control point in polar coordinate (.theta.,.rho.). The algorithm checks interference with obstacles, defined as GM (Geometry Mapping), and maps obstacles in Euclidean Space into images in CPS (Connection Point Space). The GM for all obstacles produces overlapping images of obstacle in CPS. The clear area of CPS that is not occupied by obstacle images represents collision-free paths in Euclidean Space. Any points from the clear area of CPS is a candidate for a collision-free path. A simulation of GM for number of cases are carried out and results are presented including mapped images of GM and performances of algorithm.

• 천문학회보
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• 제44권2호
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• pp.54.1-54.1
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• 2019

We use iterative smoothing reconstruction method along with exploring in the parameter space of the light curves of the JLA supernova compilation (Joint Light-curve Analysis) to simultaneously reconstruct the expansion history of the universe as well as putting constrains on the light curve parameters without assuming any cosmological model. Our constraints on the light curve parameters of the JLA from our model-independent analysis seems to be closely in agreement with results assuming ΛCDM cosmology or using Chevallier-Polarski-Linder (CPL) parametrization for the equation of state of dark energy. This implies that there is no hidden significant feature in the data that could be neglected by cosmology model assumption. The reconstructed expansion history of the universe and properties of dark energy seems to be in good agreement with expectations of the standard ΛCDM model. Our results also indicate that the data allows a considerable flexibility for expansion history of the universe.

• 대한수학회지
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• 제48권4호
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• pp.849-866
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• 2011

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space $E^3_1$. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in $E^3_1$. As an example, the obtained results are applied to the case $\rho$ = const. and $k_2$ = const., and are discussed.

• 대한수학회논문집
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• 제12권3호
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• pp.539-541
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• 1997

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

• 대한수학회지
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• 제45권2호
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• pp.393-404
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• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• 대한수학회보
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• 제52권3호
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• pp.963-975
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• 2015

In this paper, we give a representation formula for an isotropic curve with pseudo arc length parameter and define the structure function of such curves. Using the representation formula and the Frenet formula, the isotropic Bertrand curve and k-type isotropic helices are characterized in the 3-dimensional complex space $\mathbb{C}^3$.

• 충청수학회지
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• 제34권1호
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.