• Journal of Institute of Control, Robotics and Systems
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• v.19 no.6
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• pp.555-562
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• 2013

This paper presents the optimal array of optical mice for the accurate velocity estimation of a mobile robot. It is assumed that there can be some restriction on the installation of two or more optical mice at the bottom of a mobile robot. First, the velocity kinematics of a mobile robot with an array of optical mice is derived, which maps the velocity of a mobile robot to the velocities of optical mice. Second, taking into account the consistency in physical units, the uncertainty ellipsoid is obtained to represent the error characteristics of the mobile robot velocity estimation owing to noisy optical mouse measurements. Third, a simple but effective performance index is defined as the inverse of the volume of the uncertainty ellipsoid, which can be used for the optimization of the optimal optical mouse placement. Fourth, simulation results for the optimal placement of three optical mice within a given elliptical region are given.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.103-121
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• 2008

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

• Management Science and Financial Engineering
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• v.14 no.2
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• pp.13-23
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• 2008

The pricing/lot-sizing problem of determining the robust optimal order quantity and selling price is discussed. The uncertainty of parameters characterized by an ellipsoid is explicitly incorporated into the problem. An approximation scheme is proposed to transform the problem into a geometric program, which can be efficiently and reliably solved using interior-point methods.

• Proceedings of the Korean Geotechical Society Conference
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• 2010.09a
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• pp.1024-1029
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• 2010

The conventional factor of safety as used in geotechnical engineering does not reflect the degree of uncertainty of the relevant parameters. Then in the geotechnical engineering, there have been efforts to reflect the uncertainties of the geotechnical properties through probabilistic analysis. In this study, a practical method for calculation the second moment reliability index using the optimization tool of a spreadsheet software is introduced. And this methodology was proposed by Low, B. K.(1996). The method is based on the perspective of an ellipsoid that just touches the failure surface in the original space of the variables. The method is applied to vertical drains(PVD) and compared with th result of Monte Carlo Simulation method.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.99-107
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• 2007

We consider (worst-case) robust optimization versions of the Economic Order Quantity (EOQ) model with decreasing cost functions. Two variants of the EOQ model are discussed, in which the purchasing costs are decreasing power functions in either the order quantity or demand rate. We develop the corresponding worst-case robust optimization models of the two variants, where the parameters in the purchasing cost function of each model are uncertain but known to lie in an ellipsoid. For the robust EOQ model with the purchasing cost being a decreasing function of the demand rate, we derive the analytical optimal solution. For the robust EOQ model with the purchasing cost being a decreasing function of the order quantity, we prove that it is a convex optimization problem, and thus lends itself to efficient numerical algorithms.

• Journal of The Korean Society of Agricultural Engineers
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• v.53 no.6
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• pp.1-6
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• 2011

The conventional factor of safety as used in geotechnical engineering does not reflect the degree of uncertainty of the relevant parameters. Then in the geotechnical engineering, there have been efforts to reflect the uncertainties of the geotechnical properties through probabilistic analysis. In this study, a practical method for probabilistic analysis using the Hasofer-Lind reliability index is introduced. The method is based on the perspective of an ellipsoid that just touches the failure surface in the original space of the variables. The method is applied to prefabricated vertical drains (PVD) and compared with the result of Monte Carlo Simulation method.