论文标题
关于3-RPR操纵器的基于同质延续的奇异距离计算
On homotopy continuation based singularity distance computations for 3-RPR manipulators
论文作者
论文摘要
众所周知，并行操纵器遭受了奇异的配置。评估给定配置与最接近单数的距离之间的距离是工业应用的感兴趣（例如，无奇异路径计划）。对于Stewart-Gough类型的并行操纵器，已知的几何有意义的距离度量是已知的，它们用于计算奇异距离作为优化问题的全局最小化器。对于六足动物和线性五足动物，由于未知数的程度和数量，由于Grobner Basen方法无法找到相应多项式Lagrange函数的临界点。但是，这种方程式系统可以通过依靠同型延续的数值代数几何形状的软件工具来求解。为了获得对上述空间操纵器的处理经验，本文试图找到最小的多均匀性贝佐特数字，用于基于同型持续持续的奇异性距离计算，相对于平面欧几里德/equiliform/equiform的各种代数运动表示。根据3-RPR操纵器比较并讨论了正在研究的同质和非族裔表示。
It is known that parallel manipulators suffer from singular configurations. Evaluating the distance between a given configuration to the closest singular one is of interest for industrial applications (e.g.\ singularity-free path planning). For parallel manipulators of Stewart-Gough type, geometric meaningful distance measures are known, which are used for the computation of the singularity distance as the global minimizer of an optimization problem. In the case of hexapods and linear pentapods the critical points of the corresponding polynomial Lagrange function cannot be found by the Grobner basis method due to the degree and number of unknowns. But this polynomial system of equations can be solved by software tools of numerical algebraic geometry relying on homotopy continuation. To gain experiences for the treatment of the mentioned spatial manipulators, this paper attempts to find minimal multi-homogeneous Bezout numbers for the homotopy continuation based singularity distance computation with respect to various algebraic motion representations of planar Euclidean/equiform kinematics. The homogenous and non-homogenous representations under study are compared and discussed based on the 3-RPR manipulator.
