Abstract:

To solve the problem that the traditional hand-eye calibration algorithms have large solution errors due to the noise interference in the processes of vision sensor calibration and robot kinematics solution， a robot hand-eye calibration algorithm based on Covariance Matrix Adaptation Evolutionary Strategy （CMAES） was proposed. Firstly， the mathematical tool Dual Quaternion （DQ） was used to establish the objective functions and geometric constraints for both rotation and translation， and the solution model was simplified. Then， the penalty function method was used to transform the constrained problem into an unconstrained optimization problem. Finally， CMAES algorithm was used to approximate the global optimal solution of hand-eye calibration rotation and translation equations. An experimental platform of robot and camera measurement was built， and the proposed algorithm was compared with two-step Tsai algorithm， the nonlinear optimization algorithm INRIA， and the DQ algorithm. Experimental results show that the solution error and variance of the proposed algorithm are smaller than those of traditional algorithms for both rotation and translation. Compared with Tsai algorithm， the proposed algorithm has the rotation accuracy improved by 4.58%， and the translation accuracy improved by 10.54%. It can be seen that the proposed algorithm has better solution accuracy and stability in the actual hand-eye calibration process with noise interference.

Key words: robot, Covariance Matrix Adaptation Evolutionary Strategy (CMAES), Dual Quaternion (DQ), hand-eye calibration, constrained optimization

摘要：

针对视觉传感器标定和机器人运动学求解过程中存在噪声干扰，导致传统的手眼标定算法求解误差较大的问题，提出一种基于协方差矩阵自适应进化策略（CMAES）的机器人手眼标定算法。首先，采用对偶四元数（DQ）对旋转和平移分别建立目标函数和几何约束，简化求解模型；其次，采用惩罚函数法将约束问题转化成无约束优化问题；最后，使用CMAES算法逼近手眼标定旋转和平移方程的全局最优解。搭建机器人、相机实测实验平台，将所提算法与Tsai两步法、非线性优化算法INRIA、DQ算法进行对比。实验结果表明：所提算法在旋转和平移上的求解误差和方差均小于传统算法；与Tsai算法相比，所提算法的旋转精度提升了4.58%，平移精度提升了10.54%。可见在存在噪声干扰的实际手眼标定过程中，所提算法具有更好的求解精度与稳定性。

关键词: 机器人, 协方差矩阵自适应进化策略, 对偶四元数, 手眼标定, 约束优化