基于奇异值分解的刚体位姿误差检测方法

Detection of pose errors for a rigid body based on singular value decomposition method

为评估机床的运动精度,提出一种采用矩阵奇异值分解法来计算刚体实际位姿的方法。把3RPS并联机构的动平台视为空间刚体,采用奇异值分解法分析激光跟踪仪所测量的动平台上多个（5~10个）测量点的坐标值,得到动平台的实际位姿。与相应的理论位姿比较,检测出动平台在实际工作中的位姿误差。在分析实测数据时以位姿变换后测量点的位置误差平方和为目标函数,通过目标函数值可以剔除实测数据中的坏点,从而排除坏点对计算结果的影响。利用多个测量点计算刚体位姿可以避免只用3个测量点计算时,因坏点导致的错误结果的出现。通过实例计算验证了奇异值分解法的合理性和可行性,该方法适用于空间刚体位姿误差检测方面的研究。

To evaluate the motion accuracy of machine tool,a method for determining the actual pose of rigid body based on Singular Value Decomposition（SVD） method was proposed.The moving platform of 3RPS parallel machine was considered as a rigid body in space,by measuring the coordinate value of multi-points（5~10） in moving platform with laser tracker,the actual pose of the moving platform was obtained by SVD method.The moving platform pose errors were detected in practice by comparing real pose to the corresponding theoretical one.The sum of squares of body points＇ position errors obtained after pose transformation was used as objective function for analyzing the measurements,and bad point was rejected according to the objective function value,so that the effect of bad points on the result was removed.The proposed method avoided bad result which was calculated just from three points because of bad point.Practical examples verified the rationality and feasibility of SVD method,which was applicable to the study of pose errors detection of a rigid body in space.