On the forward kinematics of cable-driven parallel robots.
A. Pott, and V. Schmidt. IEEE/RSJ International Conference on Intelligent Robots and Systems, page 3182-3187. IEEE, (2015)
Abstract
Most cable-driven parallel robots are kinematically
over-constrained mechanisms. This results in a non-trivial
computation of the forward kinematic transformation. It is
well known that the forward kinematics of parallel robots
may have multiple solutions and in general the convergence
of numerical methods is unknown. In recent works, it was
proposed to formulate the forward kinematics as optimization
problem that models the cables as linear springs in order
to compute the platform pose which has minimal potential
energy in the cables. In this paper, we analyzed this objective
function. Using the Hessian matrix, we show that under certain
conditions the problem at hand is convex and we can expect a
unique and stable minimum. The computations are exemplified
for point-shaped platforms as well as for the planar case. For
the spatial case, we present an encouraging numerical study. An
ordinary least squares method is then applied to find a position
approximation and an improvement to previous methods is
demonstrated.
%0 Conference Paper
%1 Pott2015b
%A Pott, Andreas
%A Schmidt, Valentin
%B IEEE/RSJ International Conference on Intelligent Robots and Systems
%D 2015
%I IEEE
%K Import180214 imported myown
%P 3182-3187
%T On the forward kinematics of cable-driven parallel robots.
%X Most cable-driven parallel robots are kinematically
over-constrained mechanisms. This results in a non-trivial
computation of the forward kinematic transformation. It is
well known that the forward kinematics of parallel robots
may have multiple solutions and in general the convergence
of numerical methods is unknown. In recent works, it was
proposed to formulate the forward kinematics as optimization
problem that models the cables as linear springs in order
to compute the platform pose which has minimal potential
energy in the cables. In this paper, we analyzed this objective
function. Using the Hessian matrix, we show that under certain
conditions the problem at hand is convex and we can expect a
unique and stable minimum. The computations are exemplified
for point-shaped platforms as well as for the planar case. For
the spatial case, we present an encouraging numerical study. An
ordinary least squares method is then applied to find a position
approximation and an improvement to previous methods is
demonstrated.
@inproceedings{Pott2015b,
abstract = {Most cable-driven parallel robots are kinematically
over-constrained mechanisms. This results in a non-trivial
computation of the forward kinematic transformation. It is
well known that the forward kinematics of parallel robots
may have multiple solutions and in general the convergence
of numerical methods is unknown. In recent works, it was
proposed to formulate the forward kinematics as optimization
problem that models the cables as linear springs in order
to compute the platform pose which has minimal potential
energy in the cables. In this paper, we analyzed this objective
function. Using the Hessian matrix, we show that under certain
conditions the problem at hand is convex and we can expect a
unique and stable minimum. The computations are exemplified
for point-shaped platforms as well as for the planar case. For
the spatial case, we present an encouraging numerical study. An
ordinary least squares method is then applied to find a position
approximation and an improvement to previous methods is
demonstrated.},
added-at = {2018-02-14T08:37:06.000+0100},
author = {Pott, Andreas and Schmidt, Valentin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/208528e66cb805d27dac59602b4c3cc8e/andreaspott},
booktitle = {IEEE/RSJ International Conference on Intelligent Robots and Systems},
interhash = {652a8efcbccaf72974773324504d3d4c},
intrahash = {08528e66cb805d27dac59602b4c3cc8e},
keywords = {Import180214 imported myown},
pages = {3182-3187},
publisher = {IEEE},
timestamp = {2018-02-14T08:03:04.000+0100},
title = {On the forward kinematics of cable-driven parallel robots.},
year = 2015
}