• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.388-393
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• 1990

A robot manipulator and an obstacle are described mathematically in joint space, with the mathematical representation for the collision between the robot manipulator and the obstacle. Using these descriptions, the robot motion planning problem is formulated which can be used to avoide a time varying obstacle. To solve the problem, the constraints on motion planning are discretized in joint space. An analytical method is proposed for planning the motion in joint space from a given starting point to the goal point. It is found that solving the inverse kinematics problem is not necessary to get the control input to the joint motion controller for collision avoidance.

• Journal of Korea Multimedia Society
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• v.18 no.3
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• pp.287-297
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• 2015

A railway security detection system is very important. There are many safety factors that directly affect the safe operation of trains. Security detection technology can be divided into passive and active approaches. In this paper, we will first survey the railway security systems and compare them. We will also propose a subway security detection system with computer vision technology, which can detect three kinds of problems: the spark problem, the obstacle problem, and the lost screw problem. The spark and obstacle detection methods are unique in our system. In our experiment using about 900 input test images, we obtained about a 99.8% performance in F- measure for the spark detection problem, and about 94.7% for the obstacle detection problem.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.1
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• pp.9-21
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• 1998

This paper a new solution approach to moving obstacle avoidance problem of a mobile robot. A new concept avoidability measure (AVM) is defined to describe the state of a pair of a robot and an obstacle regarding the collision between them. As an AVM, virtual distance function (VDF), is derived as a function of the distance from the obstacle to the robot and outward speed of the obstacle relative to the robot. By keeping the virtual distance above some positive limit value, the robot avoids the obstacle. In terms of the VDF ,an artificial potential field is constructed to repel the robot away from the obstacle and to attract the robot toward a goal location. At every sampling time, the artificial potential field is updated and the force driving the robot is derived from the gradient of the artificial potential field. The suggested algorithm drives the robot to avoid moving obstacles in real time. Since the algorithm considers the mobility of the obstacle as well as the distance, it is effective for moving obstacle avoidance. Some simulation studies show the effectiveness of the proposed approach.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.893-905
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• 2012

Kirsi Majava and Xue-Cheng Tai [12] proposed a modified level set method for solving a free boundary problem associated with unilateral obstacle problems. The proximal bundle method and gradient method were applied to solve the nonsmooth minimization problems and the regularized problem, respectively. In this paper, we extend this approach to solve the bilateral obstacle problems and employ Rung-Kutta method to solve the initial value problem derived from the regularized problem. Numerical experiments are presented to verify the efficiency of the methods.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.7
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• pp.809-822
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• 1992

A mathematical approach to solving the time-varying obstacle avoidance problem is pursued. The mathematical formulation of the problem is given in robot joint space(JS). View-time concept is used to deal with time-varying obstacles. The view-time is the period in which a time-varying obstacles. The view-time is the period in which a time-varying obstacle is viewed and approximated by an equivalent stationary obstacle. The equivalent stationary obstacle is the volume swept by the time-varying obstacle for the view-time. The swept volume is transformed into the JS obstacle that is the set of JS robot configurations causing the collision between the robot and the swept volume. In JS, the path avoiding the JS obstacle is planned, and a trajectory satisfying the constraints on robot motion planning is planned along the path. This method is applied to the collision-free motion planning of two SCARA robots, and the simulation results are given.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.175-181
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• 2000

The purpose of this to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods .

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.491-496
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• 1992

An analytic solution approach to the time-varying obstacle avoidance problem is pursued. We formulate the problem in robot joint space(JS), and introduce the view-time concept to deal with the time-varying obstacles. The view-time is a set of continuous times in which a time-varying obstacle is viewed and approximated by an equivalent stationary obstacle. The equivalent stationary obstacle is transformed into the JS obstacle. In JS, the path and trajectory avoiding the JS obstacle is planned.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.495-505
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• 2023

In this note, we study a comparison principle for elliptic obstacle problems of p-Laplacian type with L¹-data. As a consequence, we improve some known regularity results for obstacle problems with zero Dirichlet boundary conditions.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.9
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• pp.1266-1272
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• 2014

We define the mobile robot navigation problem as an optimization problem to minimize the cost function with the pose error between the goal position and the position of a mobile robot. Using Gauss-Newton method for the optimization, the optimal speeds of the left and right wheels can be found as the solution of the optimization problem. Especially, the rotational speed of wheels of a mobile robot can be directly related to the overall speed of a mobile robot using the Jacobian derived from the kinematic model. When the robot detects the obstacle using sensors, the sub-goal switching method is adopted for the efficient obstacle avoidance during the navigation. The performance was evaluated using the simulation and the simulation results show the validity of the proposed method.