基于LMI优化的对偶四元数手眼标定算法

Dual Quaternion Hand-eye Calibration Algorithm Based on LMI Optimization

针对相机标定误差和机器人正运动学求解的误差对手眼标定精度的影响以及传统对偶四元数法用奇异值分解求解手眼标定时易受到外界干扰产生较大误差的问题,提出一种基于LMI优化的对偶四元数手眼标定算法。该方法以对偶四元数的形式将手眼标定方程分解成两部分,简化问题模型,分别估计旋转矩阵和平移向量。该方法先用线性矩阵不等式优化的方法替代传统奇异值分解法求得精确度更高的旋转矩阵,再通过改写平移向量的标定方程,建立新的目标函数,然后用线性矩阵不等式优化的方法求得平移向量。最后,通过开源数据集实验和手眼标定平台上的实测实验结果分析,证明了该算法在求解精度和稳定性上都优于传统对偶四元数(CDQ)算法、经典算法Tsai法和Navy法,并验证了该算法在实际应用中的可行性。

Aiming at the influence of camera calibration error and robot positive kinematics solution error on the hand⁃eye calibra⁃tion accuracy,and the hand⁃eye calibration is susceptible to external interference and a large error is produced when singular value de⁃composition is used in traditional dual quaternion method,an optimized dual quaternion hand⁃eye calibration algorithm was proposed.In this algorithm,the hand⁃eye calibration equation was decomposed into two parts in the form of dual quaternion,to simplify the prob⁃lem model,and to estimate the rotation matrix and translation vector respectively;the linear matrix inequality optimization method was used to replace the traditional singular value decomposition method to obtain a more accurate rotation matrix,then the calibration equa⁃tion of the translation vector was rewrote to establish a new objective function,and then the linear matrix inequality optimization method was used to obtain the translate vector.Finally,through analyzing the test results of the open source data set experiment and the actual measurement experiment on the hand⁃eye calibration platform,it is proved that the algorithm is superior to the traditional dual quaterni⁃on(CDQ)algorithm,the classic Tsai algorithm and the Navy algorithm in terms of accuracy and stability,the feasibility of the algo⁃rithm is verified in practical applications.