凸松弛全局优化机器人手眼标定

摘要

针对机器人运动学正解及相机的外参数标定存在偏差时,基于非线性最优化的手眼标定算法无法确保目标函数收敛到全局极小值的问题,提出基于四元数理论的凸松弛全局最优化手眼标定算法.考虑到机械手末端相对运动旋转轴之间的夹角对标定方程求解精度的影响,首先利用随机抽样一致性(RANSAC)算法对标定数据中旋转轴之间的夹角进行预筛选,再利用四元数参数化旋转矩阵,建立多项式几何误差目标函数和约束,采用基于线性矩阵不等式(LMI)凸松弛全局优化算法求解全局最优手眼变换矩阵.实测结果表明,该算法可以求得全局最优解,手眼变换矩阵几何误差平均值不大于1.4 mm,标准差小于0.16 mm,结果稍优于四元数非线性最优化算法.%Hand-eye calibration based on nonlinear optimization algorithm can not guarantee the convergence of the objective function to the global minimum,when there are errors in both robot forward kinematics and camera external parameters calibration.To solve this tricky problem,a new hand-eye calibration algorithm based on quatemion theory by convex relaxation global optimization was proposed.The critical factor of the angle between different interstation rotation axes by a manipulator was considered,an optimal set of relative movements from calibration data was selected by Random Sample Consensus (RANSAC) approach.Then,rotation matrix was parameterized by a quatemion,polynomial geometric error objective function and constraints were established based on Linear Matrix Inequality (LMI) convex relaxation global optimization algorithm,and the hand-eye transformation matrix could be solved for global optimum.Experimental validation on real data was provided.Compared with the classical quatemion nonlinear optimization algorithm,the proposed algorithm can get global optimal solution,the geometric mean error of hand-eye transformation matrix is no more than 1.4 mm,and the standard deviation is less than 0.16 mm.