報(bào)告時(shí)間：2022年6月16日（星期四）21:00-22:30
報(bào)告平臺(tái)：騰訊會(huì)議 ID:723 990 484
報(bào) 告 人：Qiaode Jeffrey Ge 教授
工作單位：美國(guó)紐約州立大學(xué)
舉辦單位：機(jī)械工程學(xué)院
報(bào)告簡(jiǎn)介：
Many applications in biomechanics and medical imaging call for the analysis of the kinematic errors in a group of patients statistically using the average displacement and the standard deviations from the average.This talk studies the problem of computing the average displacement from a set of given spatial displacements using three types of parametric representations: Euler angles and translation vectors, unit quaternions and translation vectors, and dual quaternions.
It has been shown that the use of Euclidean norm in the space of unit quaternions reduces the problem to that of computing the average for each quaternion component separately and independently. While the resulting algorithm is simple, the change of the sign of a unit quaternion could lead to an incorrect result. A novel kinematic measure based on dual quaternions is introduced to capture the separation between two spatial displacement. This kinematic measure is then used to formulate a constrained least squares minimization problem. It has been shown that the problem decomposes into that of finding the optimal translation vector and the optimal unit quaternion. The former is simply the centroid of the set of given translation vectors and the latter can be obtained as the eigenvector corresponding to the least eigenvalue of a $4\times 4$ positive definite symmetric matrix. It is found that the weight factor used in combining rotations and translations in the formulation does not play a role in the final outcome.Examples are provided to show the comparisons of these methods.
報(bào)告人簡(jiǎn)介：
Qiaode Jeffrey Ge教授美國(guó)紐約州立大學(xué)石溪分校機(jī)械工程系主任，是ASME（美國(guó)機(jī)械工程師協(xié)會(huì)）Fellow。主要研究方向包括計(jì)算設(shè)計(jì)方法, 機(jī)構(gòu)學(xué)/機(jī)器人學(xué), CAD/CAM, 計(jì)算機(jī)圖形學(xué)與VR技術(shù)的工程應(yīng)用。一直在ASME設(shè)計(jì)工程部門(mén)執(zhí)行委員會(huì)（DED）任職，并多次擔(dān)任ASME機(jī)構(gòu)學(xué)和機(jī)器人學(xué)委員會(huì)和ASME多個(gè)學(xué)術(shù)會(huì)議的主席和重要獎(jiǎng)項(xiàng)的評(píng)委會(huì)成員。他也多次擔(dān)任IFToMM世界大會(huì)（機(jī)械設(shè)計(jì)領(lǐng)域最頂級(jí)國(guó)際會(huì)議）的組織委員會(huì)的成員、首席美國(guó)代表和IFToMM美國(guó)成員組織主席。
Qiaode Jeffrey Ge教授目前是ASME的機(jī)械設(shè)計(jì)雜志（Journal of Mechanical Design）的機(jī)構(gòu)學(xué)方向主編，并曾擔(dān)任 ASME Journal of Mechanisms and Robotics、International Journal of Mechanics Based Design of Structures and Machines等機(jī)構(gòu)學(xué)與機(jī)器人方向國(guó)際著名期刊的副主編。自2002年起，他成為中國(guó)機(jī)械工程學(xué)會(huì)的機(jī)構(gòu)學(xué)委員會(huì)理事。他也是美國(guó)國(guó)家科學(xué)基金會(huì)的評(píng)審小組成員以及美國(guó)國(guó)家科研委員會(huì)、香港政府科研資助委員會(huì)、新加坡政府科研資助委員會(huì)和奧地利科學(xué)基金的評(píng)審人。
