基于M-估计的线性化稳健配准算法研究

复杂曲面在制造中的广泛应用对曲面配准技术提出了新的要求,特别是不同区域精度存在差异的复杂曲面配准问题日益突出。为了稳健估计思想推广到不同区域精度存在差异的复杂曲面配准,给出了基于M-估计的一种稳健配准算法。该算法利用M-估计子削弱复杂曲面低精度数据对配准结果的影响,但是这一模型目标函数是高度非线性的分段函数,求解效率不高。现有配准方法已能够迅速获得较好初始位置,因此利用Taylor展式线性逼近偏差函数,得到配准问题M-估计的线性化模型,提高了配准模型估计效率。每步迭代利用F-范数最小逼近旋转矩阵。对仿真数据和实测叶片数据进行试验,结果证明,对精度存在差异的复杂曲面所提算法比最近点迭代算法更加合理。

Linearized Robust Registration Algorithm Based on M-estimation

Rapid and wide application of the complex surface in modern manufacturing makes new demands of the registration techniques on complex surface. Although significant progress has been made in complex surface registration, it remains a difficult problem in some situation. For a complex part with multiple freeform surfaces, the precision of measurement points often exists different in different surface regions due to a variety of measurement methods. Meanwhile, the manufacture precision in different regions is also not the same in complex manufacture process. Problems of registration on complex surface, have become increasingly prominent and new methods are bound to be found. Robust principle was generalized to the complex surface registration in which the precision difference existed in different surface regions. A robust registration was presented based on M-estimation. The effect of low precision measured data was weakened for the registration result by M-estimation functions. But the solving efficiency of the model was low due to the highly nonlinear and piecewise of the objective function. A good initial position was easily available with current registration method, and the error functions were linearly approximated by Taylor expansion when the rotation transform was slight. A linear registration model was found and the efficiency was improved. An approximation of the rotation matrix based on the minimization of Fibonacci norm was adopted in each iteration. Both theoretical and experimental results confirmed the stabilization and efficiency.