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Open Access item A branch-and-prune solver for distance constraints

Authors:Porta Pleite, Josep Maria
Ros Giralt, Lluís
Thomas Arroyo, Federico
Torras Genís, Carme
Keywords:Branch-and-prune, Cayley–Menger determinant, Direct and inverse kinematics, Distance constraint, Interval method, Kinematic and geometric constraint solving, Octahedral manipulator, Robots
Issue Date:2005
Publisher:Institute of Electrical and Electronics Engineers
Citation:IEEE Transactions on Robotics 21(2): 176-187 (2005)
Abstract:Given some geometric elements such as points and lines in R3, subject to a set of pairwise distance constraints, the problem tackled in this paper is that of finding all possible configurations of these elements that satisfy the constraints. Many problems in robotics (such as the position analysis of serial and parallel manipulators) and CAD/CAM (such as the interactive placement of objects) can be formulated in this way. The strategy herein proposed consists of looking for some of the a priori unknown distances, whose derivation permits solving the problem rather trivially. Finding these distances relies on a branch-and-prune technique, which iteratively eliminates from the space of distances entire regions which cannot contain any solution. This elimination is accomplished by applying redundant necessary conditions derived from the theory of distance geometry. The experimental results qualify this approach as a promising one.
Publisher version (URL):http://dx.doi.org/10.1109/TRO.2004.835450
Appears in Collections:(IRII) Artículos

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