基于对偶四元数的机器人手眼标定算法研究

Study on robot hand-eye calibration using dual quaternion

针对机器人手眼视觉系统中的手眼标定问题,对机械手末端执行器与摄像机之间的手眼转换关系进行了研究。对手眼标定问题中求解齐次矩阵的方法进行了归纳,建立了完整的基于运动位姿的视觉模型;利用改进对偶四元数方法分别求解了手眼齐次变换矩阵中的旋转矩阵和平移向量;为保证获得的平移向量是最优解,在求解平移向量过程中引入了无穷范数最小化,通过迭代求取了局部最优解的值;基于所考虑的求解最优,利用Matlab对平移向量算法进行了仿真研究,并将该算法标定结果与线性解耦估计算法和传统对偶四元数算法进行了比较。研究结果表明:该算法在标定精度、对噪声的鲁棒性、对运动位姿个数的敏感性和稳定性方面均优于其他两种算法,能满足手眼标定的精度要求。

Aiming at hand-eye calibration problem in robotic hand-eye vision system, the hand-eye conversion relationship between end-effector and camera of manipulator was studied, the method of solving homogeneous matrix in hand-eye calibration was summarized, and a vision model based on motion posture was set up. The improved dual quaternion approach was used for solving separately the rotation parts and the translation of the hand-eye homogeneous transformation matrix. In order to obtain the optimum solution of the translation vector, the infinite norm minimization was introduced during the solving process of translation vector, the local optimal solution of translation vector was obtained by iteration. Simulations based on the considered optimal translation vector algorithm were performed in Matlab, and the classic sol-ving using dual quaternion and linear decoupling estimation algorithm were also implemented for comparison. The results indicate that the proposed method is better than traditional methods in the precision of calibration, robustness of noise and sensitivity and stability of motion posture numbers. It can meet the accuracy requirement of hand-eye calibration.