報告時間：2023年7月3日（星期一）19:00-21:00
報告平臺：騰訊會議 ID:720-650-856
報 告 人：Qiaode Jeffrey Ge 教授
工作單位：紐約州立大學石溪分校
舉辦單位：機械工程學院
報告簡介：
This presentation studies the statistical concept of confidence region for a set of uncertain displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of ???? (2). However, the former relies on the exponential map to parameterize an element of ???? (2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present. Extension from planar displacements to spatial displacements are also discussed.
報告人簡介：
Q.J.Ge教授是紐約州立大學石溪分校機械工程系主任，ASME Fellow（美國機械工程師協會的會士）。在ASME機構學和機器人學執行委員會任職三年，并在2011年擔任委員會主席。Ge教授一直是ASME Machine Design Award評委會, ASME Leonard Da Vinci Award評委會,和ASME Barnett Uzgiris Award評委會的成員。近年來,他擔任ASME多個高水平期刊（JMD、JMR）的主編或副主編，并一直在ASME設計工程部門執行委員會任職。目前,他也是IFToMM世界大會（機械設計領域最頂級國際會議）的首席美國代表和IFToMM美國成員組織主席。在期刊和會議論文集上共發表了160多篇同行評審的論文，開發了計算運動學幾何領域，是最早將運動學和計算幾何領域結合在一起的人之一。
