报告时间：2023年7月3日（星期一）19:00-21:00

报告平台：腾讯会议 ID:720-650-856

报 告 人：Qiaode Jeffrey Ge 教授

工作单位：纽约州立大学石溪分校

举办单位：机械工程学院

报告简介：

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 𝑆𝐸 (2). However, the former relies on the exponential map to parameterize an element of 𝑆𝐸 (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.

报告人简介：

Q.J.Ge教授是纽约州立大学石溪分校机械工程系主任，ASME Fellow（美国机械工程师协会的会士）。在ASME机构学和机器人学执行委员会任职三年，并在2011年担任委员会主席。Ge教授一直是ASME Machine Design Award评委会, ASME Leonard Da Vinci Award评委会,和ASME Barnett Uzgiris Award评委会的成员。近年来,他担任ASME多个高水平期刊（JMD、JMR）的主编或副主编，并一直在ASME设计工程部门执行委员会任职。目前,他也是IFToMM世界大会（机械设计领域最顶级国际会议）的首席美国代表和IFToMM美国成员组织主席。在期刊和会议论文集上共发表了160多篇同行评审的论文，开发了计算运动学几何领域，是最早将运动学和计算几何领域结合在一起的人之一。