A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages

Porta, Josep M.; Ros, Lluís; Thomas, Federico

doi:10.1109/tro.2008.2012337

Cited by 51 publications

(84 citation statements)

References 47 publications

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“…Both methods exhibit similar convergence times on the reported experiments, but further tests should be carried out to elucidate how their performance scales comparatively, on linkages of increasing complexity. On the other hand, the method in [2] can be generalized to deal with spatial linkages [3], while the method presented here is generalizable to spherical linkages and a restricted class of spatial linkages using the results in [8,19]. The extension of the presented technique to deal with general spatial linkages is a point deserving further attention.…”

Section: Discussionmentioning

confidence: 99%

“…In recent years there has been a growing interest in the use of interval methods in Kinematics, specially for the task of finding the feasible configurations of complex linkages-the so-called position analysis problem-which, when performed analytically, may involve a large number of equations or high-degree polynomials [1][2][3]. When the solution space is continuous, interval methods can provide a discrete approximation of such space as a set of enclosing boxes, which can, at least in principle, be refined as much as desired [4].…”

Section: Introductionmentioning

confidence: 99%

“…When the box cannot be further reduced, it is split, usually into two halves (or branches), each of which is treated recursively by the same process. The pruning method may be a general interval propagation algorithm applied to the kinematic equations of the linkage [1,[4][5][6][7], or a more specific method suited to the problem [2,3,8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact interval propagation for the efficient solution of position analysis problems on planar linkages

Celaya

Creemers

Ros

2012

Mechanism and Machine Theory

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This paper presents an interval propagation algorithm for variables in planar single-loop linkages. Given intervals of allowed values for all variables, the algorithm provides, for every variable, the whole set of values, without overestimation, for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branch-and-prune search scheme, in order to solve the position analysis of general planar multi-loop linkages. Experimental results are included, comparing the method's performance with that of previous techniques given for the same task.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact interval propagation for the efficient solution of position analysis problems on planar linkages

Celaya

Creemers

Ros

2012

Mechanism and Machine Theory

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“…(1) by refining successive box approximations of C . We outline them for planar mechanisms, but general spatial mechanisms can also be treated with the proper extensions [16].…”

Section: Branch-and-prune Methodsmentioning

confidence: 99%

An Open-Source Toolbox for Motion Analysis of Closed-Chain Mechanisms

Porta

Ros

Bohigas

et al. 2013

Computational Kinematics

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Many situations in Robotics require an effective analysis of the motions of a closed-chain mechanism. Despite appearing very often in practice (e.g. in parallel manipulators, reconfigurable robots, or molecular compounds), there is a lack of general tools to effectively analyze the complex configuration spaces of such systems. This paper describes the CUIK suite, an open-source toolbox for motion analysis of general closed-chain mechanisms. The package can determine the motion range of the whole mechanism or of some of its parts, detect singular configurations leading to control or dexterity issues, or find collision-and singularity-free paths between given configurations. The toolbox is the result of several years of research and development within the Kinematics and Robot Design group at IRI, Barcelona, and is available under GPLv3 license from http://www.iri.upc.edu/cuik.

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“…It started to receive a lot of attention twenty years ago with the advent of molecular magnetic resonance experiments to obtain distances between atoms in rigid molecules [24], and more recently in Robotics to obtain intrinsic formulations of different kinematics problems, thus avoiding the introduction of arbitrary reference frames [77,98], or the problems derived from the tangent half-angle substitution [59,85]. Interval analysis and linear relaxation techniques have also been used for general position analysis solvers, giving box approximation solutions for general serial and parallel manipulators [69,71,80,97].…”

Section: Kinematics and Singularities Of Stewart-gough Platformsmentioning

confidence: 99%

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

Borràs

Thomas

Torras

2010

Advances in Robot Kinematics: Motion in Man and Machine

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A la meva família, pel seu recolzament incondicional. AgraïmentsM'agradaria expressar la meva sincera gratitud al professor Federico Thomas.La seva inestimable guia al llarg d'aquests 4 anys m'ha permès no només realitzar aquesta tesi, sinó aprendre queés la recerca i a estimar la professió a través del seu entusiasme en els projectes però també de la seva mirada crítica, sempre constructiva.També voldria agrair a la professora Carme Torras el temps que m'ha dedicat, al llarg de tots els treballs que hem fet junts, pels seus punts de vista sovint diferents que m'han donat més perspectiva i per deixar-me aprendre de la seva professionalitat i versatilitat.La Maria Alberich també mereix el meu agraïment, per haver-me presentat al Federico, i mostrar-me el camí cap a l'Institut i el món de la investigació, així com també pels seus consells al llarg d'aquest temps, des de la carrera fins avui. Finalment, també vull agrair a tots els companys de l'Institut de Robòtica i Informàtica Industrial, pel bon ambient, els bons moments, les opinions compartides i el recolzament moral i professional. I a la meva família i al Joan, per estar sempre al meu costat. AbstractThe Stewart-Gough platform was first introduced by E. Gough in 1954 and, since then, it has been used for many applications thanks to its great stiffness, accuracy and robustness in comparison with serial manipulators. It has triggered the research on parallel manipulators and continues to be the center of many researches because, despite its simple geometry, its analysis translates into challenging mathematical problems. One of the most challenging ones is the geometric interpretation of its singularities, that is, those positions where the platform loses stiffness. A complete geometric characterization of these unstable poses is still an open problem.The present thesis provides new insight into this problem from a completely new approach: finding singularity-invariant leg rearrangements.Finding all the transformations that leave the solution of a problem invariant does not solve it, but it provides a lot of information that contribute to its resolution. In the Stewart-Gough platform context, this indirect approach consists in the characterization of all the leg rearrangements that leave the platform singularity locus invariant. Such singularity-invariant leg rearrangements are shown to be a powerful tool to obtain kinematically equivalent manipulators, to help to visualize at a glance the complexity of its kinematics and to provide a common and original framework for the study of both pose-dependent singularities and architectural singularities of Stewart-Gough platforms.The thesis analyzes all the rigid components that a Stewart-Gough platform can contain on a case-by-case basis. Then, it is shown how some of the most simple components admit any leg rearrangement that preserves the lines and planes that their attachments define. On the contrary, other more complex components only admit rearrangements that preserve some extra geometric constrains. This appare...

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A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages

Cited by 51 publications

References 47 publications

Exact interval propagation for the efficient solution of position analysis problems on planar linkages

Exact interval propagation for the efficient solution of position analysis problems on planar linkages

An Open-Source Toolbox for Motion Analysis of Closed-Chain Mechanisms

Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms

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