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

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1387-Simplified-Voronoi-Diagrams-for-Motion-Planning-of-Quadratically-Solvable-Gough-Stewart-Platforms.pdf (940,9Kb)
 
10.1007/978-94-007-4620-6_20
 
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hdl:2117/19513

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Vaca Alzate, Rubén Hernando
Aranda López, JuanMés informacióMés informacióMés informació
Thomas, FedericoMés informacióMés informació
Document typeConference report
Defense date2012
PublisherSpringer
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
Abstract
The 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.
CitationVaca, R.; Aranda, J.; Thomas, F. Simplified Voronoi diagrams for motion planning of quadratically-solvable Gough-Stewart platforms. A: International Symposium on Advances in Robot Kinematics. "Latest advances in robot kinematics". Innsbruck: Springer, 2012, p. 157-164. 
URIhttp://hdl.handle.net/2117/19513
DOI10.1007/978-94-007-4620-6_20
ISBN978-94-007-4620-6
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