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dc.contributor.advisorNeveu, Bertrand
dc.coverage.spatialParís
dc.creatorGrandón, Carlos
dc.date.accessioned2017-03-24T18:07:50Z
dc.date.available2017-03-24T18:07:50Z
dc.date.issued2007
dc.identifierhttp://creativecommons.org/licenses/by-nc-nd/3.0/cl/
dc.identifier.urihttp://hdl.handle.net/10533/179094
dc.description.abstractIn this thesis we are interested in a particular class of problems which frequently appear in robotics (and many other areas as chemistry, molecular biology, Computer-Aided Design (CAD), and aeronautics). They are systems of distance equations with uncertainties. Uncertain values mean values which are not exactly determined but are bounded by well-known limits. These values are represented as intervais, and frequently come from measurements. In a model, these values appear as existentially quantified parameters. Solving such a problem with uncertainties means to find a set of solutions taking into account these inaccuracies in order to obtain certified answers (in the way that no solution is lost). The aim of the works contained in this thesis is to solve systems of distance equations with uncertainties in their parameters as accurately as possible, combining techniques from Constraint Programming and Interval Analysis communities. A common approximation for the solutions for these types of problems is to replace parameters with interval values by real numbers, and to solve the problem without considering the inaccuracies. We show that this approximation is not convenient, especially when certified solutions are required (for example for safely reasons for a Surgical Robot). In a first phase, we propose a special Branch and Prune algorithm with conditional bisection which is able to compute a rough approximation of each continuum of solutions for a given problem. A rough approximation (a box) is not enough in all the cases, thus a sharp approximation (a set of boxes) describing continuous solution sets is often required. We show that this approximation must consider an inne- bor te.st in order to detect large parts of the search space containing only solutions to the problem. Using inner box tests not only reduces the number of generated boxes but also provides more information about the geometry of the solutions set. We propose and compare various inner box tests for distance equations with uncertainties. When a single solution point belonging to a continuum of solutions is given, an inner box around this point and totally included within the continuum of solutions may be very interesting for tolerance issues. For this reason we propose a strategy for building such a box based on theoretical results of Modal Interval Analysis combined with a well-known technique of Constraint Programming called projection. Finaily, the developed techniques are illustrated on a real problern of Robotics in which we solve the direct kinematics of a special class of parallel robot.
dc.language.isoeng
dc.relationinstname: Conicyt
dc.relationreponame: Repositorio Digital RI2.0
dc.relationinstname: Conicyt
dc.relationreponame: Repositorio Digital RI2.0
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 Chile
dc.titleResolutión de systemes d equatións de distance avec incertitudes.
dc.typeTesis Doctorado
dc.description.degreeDocteur en Sciences
dc.contributor.institutionL'universite de Nice
dc.description.statusTERMINADA
dc.country.isofra
dc.description.conicytprogramPFCHA-Becas
dc.description.pages186p.
dc.relation.projectidinfo:eu-repo/grantAgreement/PFCHA-Becas/RI20
dc.relation.setinfo:eu-repo/semantics/dataset/hdl.handle.net/10533/93488
dc.rights.driverinfo:eu-repo/semantics/openAccess
dc.type.driverinfo:eu-repo/semantics/doctoralThesis
dc.relation.programhandle/10533/108040
dc.description.shortconicytprogramPFCHA-Becas
dc.type.tesisTesis
dc.type.openaireinfo:eu-repo/semantics/publishedVersion


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