• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.973-978
• /
• 2005

In this paper, we investigate an improved mobile robot localization method using Kalman filter. The highlight of the paper lies in the formulation of combined Kalman filter and its application to mobile robot experiment. The combined Kalman filter is a kind of extended Kalman filter which has an extra degree of freedom in Kalman filtering recursion. It consists of the standard Kalman filter, i.e., the predictor-corrector and the perturbation estimator which reconstructs unknown dynamics in the state transition equation of mobile robot. The combined Kalman filter (CKF) enables to achieve robust localization performance of mobile robot in spite of heavy perturbation such as wheel slip and doorsill crossover which results in large odometric errors. Intrinsically, it has the property of integrating the innovation in Kalman filtering, i.e., the difference between measurement and predicted measurement and thus it is so much advantageous in compensating uncertainties which has not been reflected in the state transition model of mobile robot. After formulation of the CKF recursion equation, we show how the design parameters can be determined and how much beneficial it is through simulation and experiment for a two-wheeled mobile robot under indoor GPS measurement system composed of four ultrasonic satellites. In addition, we discuss what should be considered and what prerequisites are needed to successfully apply the proposed CKF in mobile robot localization.

• Structural Engineering and Mechanics
• /
• v.61 no.2
• /
• pp.193-207
• /
• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.749-762
• /
• 2018

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 2003.11a
• /
• pp.210-214
• /
• 2003

The static and dynamic characteristics of HDD slider with ulta-low flying height are analyzed using Direct Numerical method with Boundary Fitted Coordinate System. The slip flow effect is considered using the Boltzmann equation solution in a form of the flow rate database. The air film stiffness and damping are evaluated by the small perturbation method.

• Coupled systems mechanics
• /
• v.2 no.3
• /
• pp.255-269
• /
• 2013

This paper targets to investigate the solution of fuzzy quadratic Riccati differential equations with various types of fuzzy environment using Homotopy Perturbation Method (HPM). Fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are depicted in term of plots to show the efficiency of the proposed method.

• Steel and Composite Structures
• /
• v.24 no.2
• /
• pp.141-149
• /
• 2017

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.411-423
• /
• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.11 no.2
• /
• pp.12-21
• /
• 1974

Perturbation thorpe for quantum mechanics is extended to the derivation of a power equation for microwave propagation in a rectangular waveguiad filled with N-type silicon which is transversely magnetized. This approximation evolves in a unified manner from the eigenvalue formulation of maxwell's equation wherein the wave numbers are tthe eigenvalues of a linear operator. TE10 wave at 9.61GHz is employed for the experimental investigation of the microwave propagation through a transversely magnetized semiconductor. Results from first order perturbation agree well with the experiment where the bridge method using two Magic Tees is employed.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.391-399
• /
• 2006

In order to solve the optimization problem of designing the trajectory of three-dimensional horizontal well, we establish a multi-phase, nonlinear, stochastic dynamic system of the trajectory of horizontal well. We take the precision of hitting target and the total length of the trajectory as the performance index. By the integration of the state equation, this model can be transformed into a nonlinear stochastic programming. We discuss here the necessary conditions under which a local solution exists and depends in a continuous way on the parameter (perturbation). According to the properties we propose a revised Hooke-Jeeves algorithm and work out corresponding software to calculate the local solution of the nonlinear stochastic programming and the expectancy of the performance index. The numerical results illustrate the validity of the proposed model and algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.2
• /
• pp.125-136
• /
• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.