»ã±¨±êÌâ (Title)£ºDual Quaternions and Augmented Quaternions £¨¶ÔżËÄÔªÊý¼°Ôö¹âËÄÔªÊý£©

»ã±¨ÈË (Speaker)£ºÆîÁ¦Èº ½ÌÊÚ£¨Ïã¸ÛÀí¹¤´óѧ¡¢º¼Öݵç×ӿƼ¼´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê10ÔÂ16ÈÕ(ÖÜÒ») 9:00-11:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309»áÒéÊÒ

Ô¼ÇëÈË(Inviter)£ºÍõÇäÎÄ ½ÌÊÚ

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»ã±¨ÌáÒª£ºIn this talk, I will first report our work on eigenvalues of Hermitian dual quaternion matrices. This work extends the classical theory of eigenvalues of Hermitian complex matrices and Zhang's 1997 result on eigenvalues of Hermitian quaternion matrices. Then we apply this result to the formation control study, while formation control is very important in the UAV research. Then I will report our work on augmented quaternions, and formulate hand-eye calibration, which is a basic problem in robotic research, and SLAM (Simultaneous Location and Mapping), which is a very hot topic in robotic research, as equality constrained augmented dual quaternion optimization problems. This approach reduces the size of the

problem and keep the smoothness of the model. We explore these two directions from two different points of view to quaternions and dual quaternions. In this talk, I will explain these two different points of view.