Generalized Linear Product Homotopy Algorithms and the Computation of Reachable Surfaces

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dc.contributor.authorSu, Hai-Junen
dc.contributor.authorMcCarthy, J. Michaelen
dc.contributor.authorWatson, Layne T.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:35:54Zen
dc.date.available2013-06-19T14:35:54Zen
dc.date.issued2003en
dc.description.abstractIn this paper, we apply a homotopy algorithm to the problem of finding points in a moving body that lie on specific algebraic surfaces for a given set of spatial configurations of the body. This problem is a generalization of Burmester's determination of points in a body that lie on a circle for five planar positions. We focus on seven surfaces that we term "reachable" because they correspond to serial chains with two degree-of-freedom positioning structures combined with a three degree-of-freedom spherical wrist. A homotopy algorithm based on generalized linear products is used to provide a convenient estimate of the number of solutions of these polynomial systems. A parallelized version of this algorithm was then used to numerically determine all of the solutions.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00000669/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000669/01/Homotopy7.pdfen
dc.identifier.trnumberTR-03-24en
dc.identifier.urihttp://hdl.handle.net/10919/20102en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectParallel computationen
dc.titleGeneralized Linear Product Homotopy Algorithms and the Computation of Reachable Surfacesen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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