DSpace Collection:
http://hdl.handle.net/10261/359
2016-02-14T05:56:24ZA distance geometry approach to the ingularity analysis of 3R robots
http://hdl.handle.net/10261/127518
Title: A distance geometry approach to the ingularity analysis of 3R robots
Authors: Thomas, Federico
Abstract: This paper shows how the computation of the singularity locus of a 3R robot can be reduced to the analysis of the relative position of two coplanar ellipses. Since the relative position of two conics is a projective invariant and the basic projective geometric invariants are determinants, it is not surprising that, using distance geometry, the computation of the singularity locus of a 3R robot can be fully expressed in terms of determinants. Geometric invariants have the benefit of simplifying symbolic manipulations. This paper shows how their use leads to a simpler characterization, compared to previous approaches, of the cusps and nodes in the singularity loci of 3R robots.2016-01-12T14:28:06ZVariable symmetry breaking in numerical constraint problems
http://hdl.handle.net/10261/127517
Title: Variable symmetry breaking in numerical constraint problems
Authors: Goldsztejn, Alexandre; Jermann, Christophe; Ruiz de Angulo, Vicente; Torras, Carme
Abstract: Symmetry breaking has been a hot topic of research in the past years, leading to many theoretical developments as well as strong scaling strategies for dealing with hard applications. Most of the research has however focused on discrete, combinatorial, problems, and only few considered also continuous, numerical, problems. While part of the theory applies in both contexts, numerical problems have specificities that make most of the technical developments inadequate. In this paper, we present the rlex constraints, partial symmetry-breaking inequalities corresponding to a relaxation of the famous lex constraints extensively studied in the discrete case. They allow (partially) breaking any variable symmetry and can be generated in polynomial time. Contrarily to lex constraints that are impractical in general (due to their overwhelming number) and inappropriate in the continuous context (due to their form), rlex constraints can be efficiently handled natively by numerical constraint solvers. Moreover, we demonstrate their pruning power on continuous domains is almost as strong as that of lex constraints, and they subsume several previous work on breaking specific symmetry classes for continuous problems. Their experimental behavior is assessed on a collection of standard numerical problems and the factors influencing their impact are studied. The results confirm rlex constraints are a dependable counterpart to lex constraints for numerical problems.2016-01-12T14:24:01ZAutomated generation and comparison of Takagi-Sugeno and polytopic quasi-LPV models
http://hdl.handle.net/10261/127516
Title: Automated generation and comparison of Takagi-Sugeno and polytopic quasi-LPV models
Authors: Rotondo, Damiano; Puig, VicenĂ§; Nejjari, Fatiha; Witczak, Marcin
Abstract: In the last decades, gain-scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non-linear systems. Among the approaches proposed in the literature, the linear parameter varying (LPV) and Takagi-Sugeno (TS) paradigms have proved to be successful in dealing with the different trials that the analyzer, or the designer, of a gain-scheduled control system has to face. Despite the strong similarities between the two paradigms, research on LPV and TS systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them. However, in recent works, some clues that there is a very close connection between LPV and TS worlds have been presented. The present paper openly addresses the presence of strong analogies between LPV and TS models, in an attempt to establish a bridge between these two worlds, so far considered different. In particular, this paper addresses the modeling problem, presenting two methods for the automated generation of LPV and TS systems, and introducing some measures in order to compare the obtained models. A mathematical example is used to illustrate the proposed methods.2016-01-12T14:18:07ZA unified position analysis of the Dixon and the generalized Peaucellier linkages
http://hdl.handle.net/10261/127515
Title: A unified position analysis of the Dixon and the generalized Peaucellier linkages
Authors: Rojas, NicolĂˇs; Dollar, Aaron M.; Thomas, Federico
Abstract: This paper shows how, using elementary Distance Geometry, a closure polynomial of degree 8 for the Dixon linkage can be derived without any trigonometric substitution, variable elimination, or artifice to collapse mirror configurations. The formulation permits the derivation of the geometric conditions required in order for each factor of the leading coefficient of this polynomial to vanish. These conditions either correspond to the case in which the quadrilateral defined by four joints is orthodiagonal, or to the case in which the center of the circle defined by three joints is on the line defined by two other joints. This latter condition remained concealed in previous formulations. Then, particular cases satisfying some of the mentioned geometric conditions are analyzed. Finally, the obtained polynomial is applied to derive the coupler curve of the generalized Peaucellier linkage, a linkage with the same topology as that of the celebrated Peaucellier straight-line linkage but with arbitrary link lengths. It is shown that this curve is 11-circular of degree 22 from which the bicircular quartic curve of the Cayley's scalene cell is derived as a particular case.2016-01-12T14:11:24Z