Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM  

作　　者：Liqun Qi 

机构地区：[1]Department of Mathematics,School of Science,Hangzhou Dianzi University,Hangzhou,310018,Zhejiang,China [2]Department of Applied Mathematics,The Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong,China

出　　处：《Communications on Applied Mathematics and Computation》2023年第4期1469-1483,共15页应用数学与计算数学学报（英文）

基　　金：Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA).

摘　　要：Several common dual quaternion functions,such as the power function,the magnitude function,the 2-norm function,and the kth largest eigenvalue of a dual quaternion Hermitian matrix,are standard dual quaternion functions,i.e.,the standard parts of their function values depend upon only the standard parts of their dual quaternion variables.Furthermore,the sum,product,minimum,maximum,and composite functions of two standard dual functions,the logarithm and the exponential of standard unit dual quaternion functions,are still standard dual quaternion functions.On the other hand,the dual quaternion optimization problem,where objective and constraint function values are dual numbers but variables are dual quaternions,naturally arises from applications.We show that to solve an equality constrained dual quaternion optimization(EQDQO)problem,we only need to solve two quaternion optimization problems.If the involved dual quaternion functions are all standard,the optimization problem is called a standard dual quaternion optimization problem,and some better results hold.Then,we show that the dual quaternion optimization problems arising from the hand-eye calibration problem and the simultaneous localization and mapping(SLAM)problem are equality constrained standard dual quaternion optimization problems.

关 键 词：Standard dual quaternion functions Dual quaternion optimization Quaternion optimization Hand-eye calibration Simultaneous localization and mapping(SLAM) 

分 类 号：O24[理学—计算数学]