EPnL:一种高效且精确的PnL问题求解算法  

EPnL: An Efficient and Accurate Algorithm to the PnL Problem

作　　者：王平[1] 何卫隆 张爱华[1] 姚鹏鹏 徐贵力[3] WANG Ping;HE Wei-Long;ZHANG Ai-Hua;YAO Peng-Peng;XU Gui-Li(College of Electrical and Information Engineering,Lanzhou University of Technology,Lanzhou 730050,China;Institute of Textiles and Clothing,Hong Kong Polytechnic University,Hong Kong 999077,China;College of Automation Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]兰州理工大学电气工程与信息工程学院,兰州730050 [2]香港理工大学纺织与制衣学系,中国香港999077 [3]南京航空航天大学自动化学院,南京211106

出　　处：《自动化学报》2022年第10期2600-2610,共11页Acta Automatica Sinica

基　　金：国家自然科学基金(62001198,62073161,61866021);流程工业综合自动化国家重点实验室开放基金(PAL-N201808);甘肃省国际合作科技计划(18YF1WA068);甘肃省青年科技基金(20JR10RA-186)资助。

摘　　要：现有Perspective-n-line (PnL)问题求解算法无法在获得高求解精度的同时保证高求解效率.为解决这个缺点,提出了同时兼具求解效率和求解精度算法EPnL.该方法首先将PnL问题转换为求二次曲面方程组交点的问题,然后利用单位四元数中变量不同时为零的特性,分类参数化PnL问题中的旋转矩阵.最后,为克服常规优化方法可靠性和效率较低的问题,同时兼具求解效率和求解精度算法利用二次曲面方程组自身的结构信息,采用低次项参数化高次项的方式将二次曲面方程组的求解问题转换为单变量多项式的求解问题.实验表明,相比于现有算法,该算法在具有高求解精度的同时也兼具有高求解效率.The existing algorithms for solving the perspective-n-line(PnL) problem cannot achieve high accuracy as well as maintain high computational efficiency. To solve this disadvantage, the EPnL algorithm is proposed. The EPnL firstly transfers the PnL problem into the problem of finding the intersection of quadratic surface equations,and then uses a classification parametrization, which is derived from the fact that variables are not simultaneously zero in the unit-quaternion, to parameterize the rotation matrix in the PnL problem. At last, to overcome the problem of low reliability and low efficiency of conventional optimization methods, the EPnL uses the structure information of the system of quadratic surface equations, and transfers the problem of finding the intersection of quadratic surface equations into the solving problem of univariate polynomials using the strategy that the higher order terms are parameterized by the lower order terms in the system of quadratic surface equations. Experimental results show that the proposed algorithm has high accuracy as well as high efficiency compared with existing algorithms.

关 键 词：计算机视觉 PnL问题 位姿估计 视觉导航 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]