激光跟踪仪三维坐标转换综合优化方法

Comprehensive optimization for three-dimensional coordinate transformation of laser tracker

为了减少飞机等大型机械产品在安装过程中公共点测量误差的影响,提高坐标转换的精度,提出一种加权点匹配计算方法。该方法以匹配残差加权平方和最小作为解的最优性条件,根据不等精度测量时的加权原则,按照公共点的点位误差确定权重。基于广义逆矩阵理论,建立了近似的测量误差传递模型,分析了测量误差和权重对匹配结果的影响。为了指导跟踪仪位置的优选,借鉴结构力学理论提出一个公共点分布评价指标。重复测量实验表明,在相同测量条件下,与奇异值分解法相比,该匹配算法转换参数的标准差减小了约10%,稳定性较好。对某型飞机附件测量方案的优选实例表明,应用该评价指标有助于选择转换精度较高的跟踪仪站位。

To reduce the influence of large mechanical products such as aircraft on measurement errors of common points,and to improve the accuracy of coordinate transformation,a weighted point matching method and a performance index of laser tracker position were proposed.The minimum weighted sum of matching errors squares was taken as the optimality conditions to setthe weights in fitting model according to the measurement accuracy of common points.Based on generalized inverse matrix theory,a simplified error propagation model was deduced to analyze the influence of weights.The results of repeated measurement experiments showed that the proposed matching method was effective to reduce the influence of random errors,and the standard deviation of matching results was reduced by 10%than SVD method.An application case during aircraft accessories installation of this method was introduced,and the proposed index would be helpful to optimize the measurement scheme.