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Simplified Voronoi diagrams for motion planning of quadratically-solvable Gough-Stewart platforms

AuthorsVaca, Rubén; Aranda López, Juan; Thomas, Federico
KeywordsPath planning
Pure condition
Voronoi diagrams
Gough-Stewart platform
Issue Date2012
CitationLatest Advances in Robot Kinematics: 157-164 (2012)
AbstractThe obstacles in Configuration Space of quadratically-solvable Gough-Stewart platforms, due to both kinematic singularities and collisions, can be uniformly represented by a Boolean combination of signs of 4×4 determinants involving the homogeneous coordinates of sets of four points. This Boolean combination induces a measure of distance to obstacles in Configuration Space from which a simplified Voronoi diagram can be derived. Contrary to what happens with standard Voronoi diagrams, this diagram is no longer a strong deformation retract of free space but, as Canny proved in 1987, it is still complete for motion planning. Its main advantage is that it has lower algebraic complexity than standard Voronoi diagrams based on the Euclidean metric.
DescriptionPresentado al 13th International Symposium on Advances in Robot Kinematics (ARK) celebrado en Austria del 24 al 28 de junio de 2012.
Publisher version (URL)http://dx.doi.org/10.1007/978-94-007-4620-6_20
Identifiersdoi: 10.1007/978-94-007-4620-6_20
isbn: 978-94-007-4619-0
Appears in Collections:(IRII) Libros y partes de libros
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