基于同伦延拓的3- RPR机器人奇异距离计算
On homotopy continuation based singularity distance computations for 3-RPR manipulators
摘要：
并联机器人具有奇异位形的特点。评估给定配置与最接近的奇异配置之间的距离对于工业应用（例如，无奇异路径规划）。对于Stewart-Gough型并联机器人，几何意义的距离措施是已知的，这是用于计算的奇异性距离作为全局最小的优化问题。在六足动物和线性五足动物的情况下，由于未知数的次数和数量，相应的多项式拉格朗日函数的临界点不能通过Grobner基方法找到。但是这个多项式方程组可以通过数值代数几何的软件工具依赖于同伦延拓来求解。为了获得经验的治疗提到的空间机械臂，本文试图找到最小的多齐次Bezout数同伦连续的奇异距离计算相对于各种代数运动表示的平面欧氏/同构运动学。基于3-RPR操作器，对所研究的齐次和非齐次表示进行了比较和讨论。
英文摘要：
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.
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