Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On homotopy continuation based singularity distance computations for
  3-RPR manipulators   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.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an