论文标题
标准双季节优化及其在手眼校准中的应用和猛击
Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM
论文作者
论文摘要
几个常见的双重四元素函数，例如功率函数，幅度函数，$ 2 $ - 函数和$ k $ the hermitian hermitian矩阵的最大特征值，是标准的双季节函数，即其功能的标准零件仅取决于其二次Quaternion varia的标准部分。此外，两个标准双函数的总和，产品，最小，最大和复合函数，标准单位双重四基因函数的对数和指数仍然是标准的双季节函数。另一方面，双重四元优化问题，目标和约束函数值是双重数字，但变量是双重四个问题，自然来自应用。我们表明，要解决一个平等约束的双重四基因优化问题，我们只需要解决两个四个季节优化问题。如果所涉及的双季节函数都是标准配置的，则将优化问题称为标准双重四个季节优化问题，并且有一些更好的结果。然后，我们表明是由手眼校准问题以及同时定位和映射（SLAM）问题引起的双重四基因优化问题，是平等约束的标准双重季节优化问题。
Several common dual quaternion functions, such as the power function, the magnitude function, the $2$-norm function and the $k$th 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 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.
