刚体位姿加权配准问题的线性近似求解方法  

Linear approximation method for weighted rigid-body registration

作　　者：吴聊[1] 杨向东[1] 徐静[1] 缪东晶[1] 陈恳[1] 

机构地区：[1]清华大学精密仪器与机械学系,机器人及其自动化实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2013年第10期1424-1428,共5页Journal of Tsinghua University(Science and Technology)

基　　金：国家"八六三"计划重点专项基金资助项目(2009AA043701);清华大学摩擦学国家重点实验室基金资助项目(SKLT09A03);国家自然科学基金资助项目(50975148)

摘　　要：为了提高刚体位姿配准问题的求解精度,利用附加在数据点上的综合噪声的马氏距离来构造优化目标函数,使更加可靠的点和方向被赋予更大的权重,将未加权配准问题转化为加权配准问题。针对该问题提出了一种线性近似求解方法,先将平移向量表达为旋转矩阵的函数,然后用李代数来近似旋转矩阵,消除旋转矩阵的非线性约束,通过迭代求解出最优解。3组仿真实验表明,相对于另外3种方法,该方法可以得到更为精确的配准结果,尤其适用于对配准精度要求较高的应用场合。The Mahalanobis distance of the composite noise in the point data is used to construct an optimization objective function to improve the accuracy of rigid-body registration. The method gives more reliable points and directions larger weights to convert the unweighted registration into a weighted problem. A linear approxi- mation method is used to solve this problem. The translation vector is expressed as a function of the rotation matrix. Constraints on the rotation matrix are eliminated by approximating the rotation matrix with its Lie algebra. The optimal solution is obtained by iteration. Results of three groups of simulations show that this method gives more accurate registration than three other methods and is suitable for applications where high accuracy is required.

关 键 词：刚体配准 线性近似 非均匀 异向 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]