三次元空間上のn個の点列のペア {X_1,...,X_n}, {Y_1,...,Y_n} ∈ R^{3×n} に対し、剛体回転のみを用いた最適な重ね合わせについて考える。最も有名な定式化として、点列ペア間の RMSD (二乗平均平方根偏差) を最小化する回転行列を求める Kabsch-Umeyama algorithm による方法が広く知られている。本発表では、まずこの点列ペア間の RMSD 最小化に関する数理的な背景を整理し、RMSD 最小化問題がモニック

に帰着されるという先行研究を紹介する。その後、解の縮退に対しに数値的に不安定であったという問題を回避する実装を紹介し、この実装が単精度浮動小数点でも安定して計算できることを示す。

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This paper describes a local scan matching method that can estimate displacements of position and orientation between two successive scans fast, accurately and robustly. To estimate displacements of position and orientation, the conventional methods need to utilize nonlinear optimization method such as Levenberg-Marquardt method since there is no closed-form solution available which minimizes an evaluation function. Due to such nonlinear optimization method, the conventional method is so time consuming. In this paper, we formulate estimating displacements of position and orientation as a constrained least square problem and provide a closed-form solution which minimizes the evalution function defined by point-to-plane error metric. In the formulation, we show that a quartic function of Lagrange multiplier can be approximated by a linear function. These formulation enables our local scan matching method to be faster than the conventional method. The experimental results in three kinds of real office environment show the usefulness of our method.

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Among vibrations which are generated by machines, the vibration of belt is one which is not yet fully analyzed. If the characteristics of the vibration of belt is made clear, it may be plausible to find some pertinent measures to remove it. One method is presented here, how to find the frequency of vibration in the moving belt. The frequency is determined directly as zero-points of a series which converges rapidly. In some case calculation can be done with first few terms. As for the fundamental vibration, an accurate value of frequency can be obtained when the speed of the belt does not exceed the critical speed. The results of present experiments can be explained by the above mentioned analysis.

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The formulas for displacement and velocity analyses are derived for a spatial four-link mechanism with two revolute pairs, a spherical pair and a cylindrical pair. Then, a procedure for determining instantaneous screw axes is presented and their behaviors in the neighborhood of limit positions are clarified. The condition for limit positions of the driving-link motion is obtained on the basis of force transmission from the coupler link to the driven link and the determinant composed of the coefficients of simultaneous equation for velocity analysis. The conditional function is investigated geometrically and a quantity is proposed in order to evaluate motion and force transmission characteristics.

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