2020/04/17 by Aditya Kapilavai, Kapilavai, Aditya, Georg Nawratil +1
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Polynomial and algebraic computation #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.2004.08359
openalex publication_date 2020/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that parallel manipulators suffer from singular configurations.\nEvaluating the distance between a given configuration to the closest singular\none is of interest for industrial applications (e.g. singularity-free path\nplanning). For parallel manipulators of Stewart-Gough type, geometric\nmeaningful distance measures are known, which are used for the computation of\nthe singularity distance as the global minimizer of an optimization problem. In\nthe case of hexapods and linear pentapods the critical points of the\ncorresponding polynomial Lagrange function cannot be found by the Grobner basis\nmethod due to the degree and number of unknowns. But this polynomial system of\nequations can be solved by software tools of numerical algebraic geometry\nrelying on homotopy continuation. To gain experiences for the treatment of the\nmentioned spatial manipulators, this paper attempts to find minimal\nmulti-homogeneous Bezout numbers for the homotopy continuation based\nsingularity distance computation with respect to various algebraic motion\nrepresentations of planar Euclidean/equiform kinematics. The homogenous and\nnon-homogenous representations under study are compared and discussed based on\nthe 3-RPR manipulator.\n