基于投影圆度和遗传算法的空间圆柱面拟合方法

Spatial Cylinder Fitting Based on Projection Roundness and Genetic Algorithm

针对空间圆柱面拟合非线性强、鲁棒性差和稳定性弱的问题,提出基于投影圆度和遗传算法的空间圆柱面拟合方法。首先,通过坐标变换计算圆柱面在平面上的投影圆度。然后,借助遗传算法的全局寻优特性快速搜索最优投影圆度所在平面的法向量,进而利用平面投影计算空间圆柱面的半径及轴线方程。最后,利用坐标逆变换得到原始坐标下的空间圆柱面特征参数。由于空间圆柱面投影圆度只与投影平面法向量的方向角有关,因此只须合理设置法向量方向角的取值范围,即可使得解空间覆盖所有位姿的空间圆柱面。另外,遗传算法具有良好的全局寻优性和收敛性,在空间圆柱面拟合这类多变量非线性寻优问题中能够取得良好的效果。仿真实验和实际应用表明,相对于传统拟合方法,基于投影圆度和遗传算法的空间圆柱面拟合方法具有无须预估初值、鲁棒性强、拟合精度高和稳定性好等优点,是实现任意位姿空间圆柱面拟合的有效方法。

In order to solve the problem of strong nonlinearity,poor robustness and weak stability of spatial cylindrical surface,a method of fitting spatial cylindrical surface based on projection roundness and genetic algorithm is proposed.First of all,the projection roundness of a cylindrical surface on a plane is calculated by coordinate transformation.Then,the normal vectors of the plane in which the optimal projection roundness lies are searched quickly by means of the global optimization characteristic of genetic algorithm,and then the radius and axis equation of the cylindrical surface in space are calculated by plane projection.Finally,the inverse coordinate transformation is used to obtain the spatial cylindrical surface feature parameters under the original coordinates.Since the projection roundness of the cylindrical surface is only related to the direction angle of the normal vector of the projection plane,the solution space can cover all the spatial cylindrical surface of the pose only by reasonably setting the range of the direction angle of the normal vector.In addition,the genetic algorithm has good global optimization and convergence,and can achieve good results in spatial cylindrical surfaces and such multivariable nonlinear optimization problems.Simulation experiments and practical applications show that compared with the traditional fitting method,the spatial cylindrical fitting method based on projection roundness and genetic algorithm has the advantages of no need to estimate initial value,strong robustness,high fitting precision and good stability.This algorithm is an effective method to achieve cylinder fitting of arbitrary pose space.