机器人手眼校准线性算法及可靠性分析

机器人手眼矩阵计算是机器人视觉、机器人校准以及视觉伺服等研究领域共同的课题。文中利用矩阵直积和参数矩阵特征向量推导了机器人手眼转换矩阵的线性方程 ,通过最小二乘法得到线性闭解 ,采用Rodrigues公式对所求解的旋转部分进行正交化以消除测量噪声的影响 ,由计算试验证明正交化所引入的误差在绝大多数情况是允许的 ,所求线性解严格满足手眼方程。并通过数值仿真计算 ,验证了算法对测量数据的平移、转动扰动具有较高的鲁棒性。

Linear Solution for Robot Hand-Eye Calibration and Algorithm Robustness Analysis

Robot hand-eye calibration is a vivid research subject for machine vision, robot calibration and robot visual servoing. By Kronecker product and the eigenvector of the coefficient matrix, the linear equations set for the hand-eye transformation matrix is derived and the error induced by discarding a block line equation in Nicolas method is overcome. The equations can be solved with least square technique. Computation is simplified and efficiency is improved rapidly. Rodrigues rotation formula is applied to assure the orthogonality of the rotation matrix, and to immunize from the infection of the measurement noise. Simulation results show that the error arising from the orthogonalization can be neglected in most cases. The solution satisfies the hand-eye formulae strictly. Our algorithm is robust to the translational and rotational disturbances introduced by robot end-effector and camera pose observations.