• 제어로봇시스템학회논문지
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• 제17권5호
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• pp.429-435
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• 2011

This paper presents a sensor fusion-based estimation of heading and a Bezier curve-based motion planning for unmanned ground vehicle. For the vehicle to drive itself autonomously and safely, it should estimate its pose with sufficient accuracy in reasonable processing time. The vehicle should also have a path planning algorithm that enables to adapt to various situations on the road, especially at intersections. First, we address a sensor fusion-based estimation of the heading of the vehicle. Based on extended Kalman filter, the algorithm estimates the heading using the GPS, IMU, and wheel encoders considering the reliability of each sensor measurement. Then, we propose a Bezier curve-based path planner that creates several number of path candidates which are described as Bezier curves with adaptive control points, and selects the best path among them that has the maximum probability of passing through waypoints or arriving at target points. Experiments under various outdoor conditions including at intersections, verify the reliability of our algorithm.

• Journal of applied mathematics & informatics
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• 제2권2호
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• pp.75-82
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• 1995

4대의 제어점에 의해 정의되는 3차 Bezier 곡선을 구간적 (piecewise) 2차 Bezier 곡선으로 근사 하는 기하적인 알고리듬을 제시한다. 또한 제시한알고리듬의 오차해석을 통하여 수정된 알 고리듬을 구성한다. 분확방법을 동시에 사용하여 주어진 허용오차 이내의 구간적 2차 근사 곡선을 구할수 있다. 제시한 알고리듬은 오차해석을 이용하여 필요한 분활의 수행회수를 미 리 결정할수있는장점을 가지고있다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2743-2746
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• 2003

In this paper, we propose a new weaving trajectory algorithm for the arc welding of a articulated manipulator. The algorithm uses the theory of Bezier spline. We make a comparison between the conventional algorithms using Catmull-Rom curve and the new algorithms using Bezier spline. The proposed algorithm has been evaluated based on the MATLAB environment in order to illustrate its good performance. The algorithm has been implemented on to the industrial manipulator of DR6 so as to show its real possibility. Through simulations and real implementations, the proposed algorithm can result in high-speed and flexible weaving trajectory planning and can reduce the processing time because it needs one-half calculation compared to the conventional algorithm using Catmull-Rom curve.

• 한국전산유체공학회지
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• 제10권3호
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• pp.27-35
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• 2005

A design optimization of hypersonic flight vehicle has been studied by using upwind Navier-Stokes method and numerical optimization method. CFD method is linked to numerical optimization method by using a Bezier curve and a design optimization of blunt nose hypersonic flight vehicle has been studied. Heat transfer coefficient and drag coefficient are selected as objective functions or design constraints. The Bezier curve-based shape function was applied to blunt body shape.

• 한국CDE학회논문집
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• 제12권5호
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• pp.354-365
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• 2007

We present novel methods to generate a sequence of shapes that represents the pattern of morphological development or transformation of Bezier curves. The presented methods utilize the intrinsic geometric structures of a Bezier curve that are derived from rib and fan decomposition (RFD). Morphological development based on RFD shows a characteristic pattern of structural growth of a Bezier curve, which is the direct consequence of development path defined by fans. Morphological transformation based RFD utilizes development patterns of source and target curves to mimic the theory of evolutionary developmental biology: although the source and target curves are quite different in shapes, we can easily find similarities in their younger shapes, which makes it easier to set up feature correspondences for blending them. We also show that further controls on base transformation for intensity of feature blending, and extrapolation can compensate the immaturity of blended curves. We demonstrate the experimental results where transformation patterns are smoother and have unique geometric style that cannot be generated using conventional methods based on multi-linear blending.

• Communications for Statistical Applications and Methods
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• 제23권3호
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• pp.189-201
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• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• 정보처리학회논문지A
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• 제9A권1호
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• pp.99-104
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• 2002

본 논문에서는 벡터공간 $R_n$에서 정의된 Bezier곡선과 Bezier곡면을 Lie군(Lie group)에서 확장하는 일반적인 새로운 생성방법을 제시한다. 이 방법에 의해서 생성된 Bezier곡선과 Bezier곡면은 Lie군의 성질에 의해서 미분 가능한 구조를 갖는다. 이 방법은 공간상에서 움직이는 물체에 대한 부드러운 움직임을 묘사하거나 궤도생성에 사용할 수 있다.

• 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.

• 대한수학회논문집
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• 제20권4호
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• pp.861-873
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• 2005

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic Bezier curves. Each approximation method is $G^1$ end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.151-165
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• 2002

An a1gorithmic approach to degree elevation of NURBS curves is presented. The new algorithms are based on the weighted blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (1) decompose the NURBS curve into piecewise rational Bezier curves, (b) elevate the degree of each rational Bezier piece, and (c) compose the piecewise rational Bezier curves into NURBS curve.