对称工件定位问题的研究

ON THE LOCALIZATION OF SYMMETRIC WORKPIECES

以微分几何作为工具，阐述了对称工件定位的理论问题。首先分析对称工件的位姿空间，将其位姿空间等同于欧氏群的齐次空间；然后，研究该齐次空间的几何结构，提出适用于各种对称工件定位的统一几何算法；最后通过仿真结果显示该算法几个特征：①易于实现。②鲁棒性好。③计算精度高。④计算效率高，收敛速度快。

Present a geometric theory for efficient and accurate localization of symmetic features. Firsts, show that the configuration spaces of a symmetric feature can be naturally identified with the homogeneous spacse SE(3)/G0 of the Euclidean group SE(3), where G0 is the symmetry group of the feature. Then, explore the geometric structure of the homogeneous space and present a simple and unifying algorithm for symmetric localization. Finally, give simulation results illustrating several unique features of the algorithm: implementational simplicity, robustness with respect to initial conditions, highly accuracy in computed results, and computational efficiency.