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The univariate closure conditions of all fully parallel planar robots derived from a single polynomial
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 2013
Journal article
Read the abstract View Share Reference managersThe real roots of the univariate polynomial closure condition of a planar parallel robot determine the solutions of its forward kinematics. This paper shows how the univariate polynomials of all fully parallel planar robots can be derived directly from that of the widely known 3RPR robot by simply formulating these polynomials in terms of distances and oriented areas. This is a relevant result because it avoids the casebycase treatment that requires different sets of variable eliminations to obtain the univariate polynomial of each fullyparallel planar robot. 
The univariate closure conditions of all fully parallel planar robots derived from a single polynomial
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 201306
Journal article
Read the abstract View Share Reference managersThe real roots of the univariate polynomial closure condition of a planar parallel robot determine the solutions of its forward kinematics. This paper shows how the univariate polynomials of all fully parallel planar robots can be derived directly from that of the widely known 3RPR robot by simply formulating these polynomials in terms of distances and oriented areas. This is a relevant result because it avoids the casebycase treatment that requires different sets of variable eliminations to obtain the univariate polynomial of each fully parallel planar robot.
The real roots of the univariate polynomial closure condition of a planar parallel robot determine the solutions of its forward kinematics. This paper shows how the univariate polynomials of all fully parallel planar robots can be derived directly from that of the widely known 3RPR robot by simply formulating these polynomials in terms of distances and oriented areas. This is a relevant result because it avoids the casebycase treatment that requires different sets of variable eliminations to obtain the univariate polynomial of each fully parallel planar robot. 
Application of distance geometry to tracing coupler curves of pinjointed linkages
Thomas Arroyo, Federico; Rojas Libreros, Nicolás Enrique
Journal of mechanisms and robotics
Date of publication: 2013
Journal article
Read the abstract View Share Reference managersIn general, highorder coupler curves of singledegreeoffreedom plane linkages cannot be properly traced by standard predictor–corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple method that first traces the configuration space of planar linkages in a distance space and then maps it onto the mechanism workspace, to obtained the desired coupler curves, is proposed. Tracing the configuration space of a linkage in the proposed distance space is simple because the equation that implicitly defines this space can be straightforwardly obtained from a sequence of bilaterations, and the configuration space embedded in this distance space naturally decomposes into components corresponding to different combinations of signs for the oriented areas of the triangles involved in the bilaterations. The advantages of this twostep method are exemplified by tracing the coupler curves of a double butterfly linkage. 
A bilinear formulation for the motion planning of nonholonomic parallel orienting platforms
Grosch Obregon, Patrick John; Thomas Arroyo, Federico
IEEE/RSJ International Conference on Intelligent Robots and Systems
Presentation's date: 2013
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThis paper deals with the motion planning problem for parallel orienting platforms with one nonholonomic joint and two prismatic actuators which can maneuver to reach any threedegreeoffreedom pose of the moving platform. Since any system with two inputs and up to four generalized coordinates can always be transformed into chained form, this path planning problem can be solved using wellestablished procedures. Nevertheless, the use of these procedures requires a good understanding of Lie algebraic methods whose technicalities have proven a challenge to many practitioners who are not familiar with them. As an alternative, we show how by (a) properly locating the actuators, and (b) representing the platform orientation using Euler parameters, the studied path planning problem admits a closedform solution whose derivation requires no other tools than ordinary linear algebra.
This paper deals with the motion planning problem for parallel orienting platforms with one nonholonomic joint and two prismatic actuators which can maneuver to reach any threedegreeoffreedom pose of the moving platform. Since any system with two inputs and up to four generalized coordinates can always be transformed into chained form, this path planning problem can be solved using wellestablished procedures. Nevertheless, the use of these procedures requires a good understanding of Lie algebraic methods whose technicalities have proven a challenge to many practitioners who are not familiar with them. As an alternative, we show how by (a) properly locating the actuators, and (b) representing the platform orientation using Euler parameters, the studied path planning problem admits a closedform solution whose derivation requires no other tools than ordinary linear algebra.
Postprint (author’s final draft) 
On the primal and dual forms of the Stewart platform pure condition
Borras Sol, Julia; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 2012
Journal article
Read the abstract Access to the full text Share Reference managersThe algebraic characterization of the singularities of a Stewart platform is usually presented as a 6 × 6 determinant, whose rows correspond to the line coordinates of its legs, equated to zero. This expression can be rewritten in a more amenable way, known as the pure condition, as sums and products of 4×4 determinants whose rows correspond to the point coordinates of the legs attachments. Researchers usually rely on one of these two expressions to find the geometric conditions associated with the singularities of a particular Stewart platform. Although both are equivalent, it is advantageous to use either line or point coordinates depending on the platform topology. In this context, an equivalent expression involving only plane coordinates, a dual expression to that using point coordinates, seems to be missing. This paper is devoted to its derivation and to show how its use is advantageous in many practical cases mainly because of its surprising simplicity: it only involves the addition of 4 × 4 determinants whose rows are plane coordinates defined by sets of three attachments. 
Formulating Assur kinematic chains as projective extensions of Baranov trusses
Rojas, Nicolás; Thomas Arroyo, Federico
Mechanism and machine theory
Date of publication: 201210
Journal article
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On closedform solutions to the position analysis of Baranov trusses
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
Mechanism and machine theory
Date of publication: 2012
Journal article
Read the abstract Access to the full text Share Reference managersThe exact position analysis of a planar mechanism reduces to compute the roots of its characteristic polynomial. Obtaining this polynomial usually involves, as a first step, obtaining a system of equations derived from the independent kinematic loops of the mechanism. Although conceptually simple, the use of kinematic loops for deriving characteristic polynomials leads to complex variable eliminations and, in most cases, trigonometric substitutions. As an alternative, a method based on bilateration has recently been shown to permit obtaining the characteristic polynomials of the threeloop Baranov trusses without relying on variable eliminations or trigonometric substitutions. This paper shows how this technique can be applied to solve the position analysis of all catalogued Baranov trusses. The characteristic polynomials of them all have been derived and, as a result, the maximum number of their assembly modes has been obtained. A comprehensive literature survey is also included. 
Simplified Voronoi diagrams for motion planning of quadraticallysolvable GoughStewart platforms
Vaca Alzate, Ruben Hernando; Aranda López, Juan; Thomas Arroyo, Federico
International Symposium on Advances in Robot Kinematics
Presentation's date: 2012
Presentation of work at congresses
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The octahedral manipulator revisited
Rojas Libreros, Nicolás Enrique; Borras Sol, Julia; Thomas Arroyo, Federico
IEEE International Conference on Robotics and Automation
Presentation's date: 2012
Presentation of work at congresses
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Motion planning for parallel robots with nonholonomic joints
Tchon, Krzysztof; Jakubiak, Janusz; Grosch Obregon, Patrick John; Thomas Arroyo, Federico
International Symposium on Advances in Robot Kinematics
Presentation's date: 2012
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersDesigning a robot manipulator with fewer actuators than the dimension of its configuration space —to reduce bulk, weight and cost— becomes feasible by introducing mechanical elements that lead to nonholonomic constraints. Unfortunately, the mechanical advantages of these nonholonomic designs are usually darkened by the complexity of their control. This paper deals with motion planning for parallel robots with nonholonomic joints shedding new light on their control strategies. As a case study, the motion planning problem is solved for a 3˘UPU parallel robot,where ˘U stands for a nonholonomic joint whose instantaneous kinematics are equivalent to that of a universal joint. It is thus shown how the three prismatic actuators can maneuver to reach any sixdegreeoffreedompose of the moving platform. The motion planning has been addressed as a control problem in the control system representation of the robot’s kinematics and a motion planning algorithm has been devised based on a Jacobian inversion of the endpoint map of the representation. Performance of the algorithm is illustrated with numeric computations. 
Honorable mention, ASME Mechanisms and Robotics Committee Best Paper Award
Thomas Arroyo, Federico; Rojas, Nicolas
Award or recognition
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DistanceBased Formulations For The Position Analysis Of Kinematic Chains
Rojas Libreros, Nicolás Enrique
Defense's date: 20120620
Institute of Industrial and Control Engineering (IOC), Universitat Politècnica de Catalunya
Theses
Read the abstract Access to the full text Share Reference managersThis thesis addresses the kinematic analysis of mechanisms, in particular, the position analysis of kinematic chains, or linkages, that is, mechanisms with rigid bodies (links) interconnected by kinematic pairs (joints). This problem, of completely geometrical nature, consists in finding the feasible assembly modes that a kinematic chain can adopt. An assembly mode is a possible relative transformation between the links of a kinematic chain. When an assignment of positions and orientations is made for all links with respect to a given reference frame, an assembly mode is called a configuration. The methods reported in the literature for solving the position analysis of kinematic chains can be classified as graphical, analytical, or numerical. The graphical approaches are mostly geometrical and designed to solve particular problems. The analytical and numerical methods deal, in general, with kinematic chains of any topology and translate the original geometric problem into a system of kinematic analysis of all the Assur kinematic chains resulting from replacing some of its revolute joints by slider joints. Thus, it is concluded that the polynomials of all fullyparallel planar robots can be derived directly from that of the widely known 3RPR robot. In addition to these results, this thesis also presents an efficient procedure, based on distance and oriented area constraints, and geometrical arguments, to trace coupler curves of pinjointed Gr¨ubler kinematic chains. All these techniques and results together are contributions to theoretical kinematics of mechanisms, robot kinematics, and distance plane geometry. equations that defines the location of each link based, mainly, on independent loop equations. In the analytical approaches, the system of kinematic equations is reduced to a polynomial, known as the characteristic polynomial of the linkage, using different elimination methods —e.g., Gr¨obner bases or resultant techniques. In the numerical approaches, the system of kinematic equations is solved using, for instance, polynomial continuation or intervalbased procedures. In any case, the use of independent loop equations to solve the position analysis of kinematic chains, almost a standard in kinematics of mechanisms, has seldom been questioned despite the resulting system of kinematic equations becomes quite involved even for simple linkages. Moreover, stating the position analysis of kinematic chains directly in terms of poses, with or without using independent loop equations, introduces two major disadvantages: arbitrary reference frames has to be included, and all formulas involve translations and rotations simultaneously. This thesis departs from this standard approach by, instead of directly computing Cartesian locations, expressing the original position problem as a system of distancebased constraints that are then solved using analytical and numerical procedures adapted to their particularities. In favor of developing the basics and theory of the proposed approach, this thesis focuses on the study of the most fundamental planar kinematic chains, namely, Baranov trusses, Assur kinematic chains, and pinjointed Gr¨ubler kinematic chains. The results obtained have shown that the novel developed techniques are promising tools for the position analysis of kinematic chains and related problems. For example, using these techniques, the characteristic polynomials of most of the cataloged Baranov trusses can be obtained without relying on variable eliminations or trigonometric substitutions and using no other tools than elementary algebra. An outcome in clear contrast with the complex variable eliminations require when independent loop equations are used to tackle the problem. The impact of the above result is actually greater because it is shown that the characteristic polynomial of a Baranov truss, derived using the proposed distancebased techniques, contains all the necessary and sufficient information for solving the position
Esta tesis aborda el problema de análisis de posición de cadenas cinemáticas, mecanismos con cuerpos rígidos (enlaces) interconectados por pares cinemáticos (articulaciones). Este problema, de naturaleza geométrica, consiste en encontrar los modos de ensamblaje factibles que una cadena cinemática puede adoptar. Un modo de ensamblaje es una transformación relativa posible entre los enlaces de una cadena cinemática. Los métodos reportados en la literatura para la solución del análisis de posición de cadenas cinemáticas se pueden clasificar como gráficos, analíticos o numéricos. Los enfoques gráficos son geométricos y se diseñan para resolver problemas particulares. Los métodos analíticos y numéricos tratan con cadenas cinemáticas de cualquier topología y traducen el problema geométrico original en un sistema de ecuaciones cinemáticas que define la ubicación de cada enlace, basado generalmente en ecuaciones de bucle independientes. En los enfoques analíticos, el sistema de ecuaciones cinemáticas se reduce a un polinomio, conocido como el polinomio característico de la cadena cinemática, utilizando diferentes métodos de eliminación. En los métodos numéricos, el sistema se resuelve utilizando, por ejemplo, la continuación polinomial o procedimientos basados en intervalos. En cualquier caso, el uso de ecuaciones de bucle independientes, un estándar en cinemática de mecanismos, rara vez ha sido cuestionado a pesar de que el sistema resultante de ecuaciones es bastante complicado, incluso para cadenas simples. Por otra parte, establecer el análisis de la posición de cadenas cinemáticas directamente en términos de poses, con o sin el uso de ecuaciones de bucle independientes, presenta dos inconvenientes: sistemas de referencia arbitrarios deben ser introducidos, y todas las fórmulas implican traslaciones y rotaciones de forma simultánea. Esta tesis se aparta de este enfoque estándar expresando el problema de posición original como un sistema de restricciones basadas en distancias, en lugar de directamente calcular posiciones cartesianas. Estas restricciones son posteriormente resueltas con procedimientos analíticos y numéricos adaptados a sus particularidades. Con el propósito de desarrollar los conceptos básicos y la teoría del enfoque propuesto, esta tesis se centra en el estudio de las cadenas cinemáticas planas más fundamentales, a saber, estructuras de Baranov, cadenas cinemáticas de Assur, y cadenas cinemáticas de Grübler. Los resultados obtenidos han demostrado que las técnicas desarrolladas son herramientas prometedoras para el análisis de posición de cadenas cinemáticas y problemas relacionados. Por ejemplo, usando dichas técnicas, los polinomios característicos de la mayoría de las estructuras de Baranov catalogadas se puede obtener sin realizar eliminaciones de variables o sustituciones trigonométricas, y utilizando solo álgebra elemental. Un resultado en claro contraste con las complejas eliminaciones de variables que se requieren cuando se utilizan ecuaciones de bucle independientes. El impacto del resultado anterior es mayor porque se demuestra que el polinomio característico de una estructura de Baranov, derivado con las técnicas propuestas, contiene toda la información necesaria y suficiente para resolver el análisis de posición de las cadenas cinemáticas de Assur que resultan de la sustitución de algunas de sus articulaciones de revolución por articulaciones prismáticas. De esta forma, se concluye que los polinomios de todos los robots planares totalmente paralelos se pueden derivar directamente del polinomio característico del conocido robot 3RPR. Adicionalmente, se presenta un procedimiento eficaz, basado en restricciones de distancias y áreas orientadas, y argumentos geométricos, para trazar curvas de acoplador de cadenas cinemáticas de Grübler. En conjunto, todas estas técnicas y resultados constituyen contribuciones a la cinemática teórica de mecanismos, la cinemática de robots, y la geometría plana de distancias. Barcelona 13 
Computational Kinematics 2013 (CK2013)
Thomas Arroyo, Federico
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The forward kinematics of 3RPR planar robots: a review and a distancebased formulation
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 2011
Journal article
Read the abstract Access to the full text Share Reference managersThe standard forward kinematics analysis of 3RPR planar parallel robots boils down to computing the roots of a sextic polynomial. There are many different ways to obtain this polynomial but most of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience by translating the forward kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic —which is not linked to a particular reference frame— is straightforwardly obtained without the need of variable eliminations nor tangenthalfangle substitutions. The presented formulation is valid, without any modification, for any planar 3RPR parallel robot, including the special architectures and configurations —which ultimately lead to numerical instabilities— that cannot be directly handled by previous formulations.
Postprint (author’s final draft) 
Singularityinvariant families of lineplane 5SPU platforms
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
IEEE transactions on robotics
Date of publication: 201110
Journal article
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Closedform solution to the position analysis of Watt¿Baranov trusses using the bilateration method
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
Journal of mechanisms and robotics
Date of publication: 2011
Journal article
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Architectural singularities of a class of pentapods
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
Mechanism and machine theory
Date of publication: 2011
Journal article
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Distancebased position analysis of the three sevenlink Assur kinematic chains
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
Mechanism and machine theory
Date of publication: 201102
Journal article
Read the abstract Access to the full text Share Reference managersThe position analysis of planar linkages has been dominated by resultant elimination and tangenthalfangle substitution techniques applied to sets of kinematic loop equations. This analysis is thus reduced to finding the roots of a polynomial in one variable, the characteristic polynomial of the linkage. In this paper, by using a new distancebased technique, it is shown that this standard approach becomes unnecessarily involved when applied to the position analysis of the three sevenlink Assur kinematic chains. Indeed, it is shown that the characteristic polynomials of these linkages can be straightforwardly derived without relying on variable eliminations nor trigonometric substitutions, and using no others tools than elementary algebra. 
New geometric approaches to the singularity analysis of parallel platforms
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
Workshop Español de Robótica
Presentation's date: 2011
Presentation of work at congresses
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A coordinatefree approach to tracing the coupler curves of pinjointed linkages
Rojas Libreros, Nicolás Enrique; Thomas Arroyo, Federico
ASME International Design Engineering Technical Conferences
Presentation's date: 2011
Presentation of work at congresses
Read the abstract View Share Reference managersIn general, highorder coupler curves of plane mechanisms cannot be properly traced by standard predictorcorrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinatefree method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this twostep method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.
Honorable mention, ASME Mechanisms and Robotics Committee Best Paper Award 
Desplegament de l'exposició RSME imaginari a Catalunya. Fase 2011
Xambó Descamps, Sebastian; Plans Berenguer, Bernat; Borras Sol, Julia; Barja Yañez, Miguel Angel; Thomas Arroyo, Federico; Quer Bosor, Jordi; Torras, Carme; Alberich Carramiñana, Maria
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Superficies programables
Rull Sanahuja, Aleix; Pérez Gracia, María Alba; Grosch Obregon, Patrick John; Thomas Arroyo, Federico
Participation in a competitive project
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Singularityinvariant leg rearrangements in stewartgouch platforms
Borras Sol, Julia
Defense's date: 20110415
Institute of Industrial and Control Engineering (IOC), Universitat Politècnica de Catalunya
Theses
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Generation of underactuated manipulators with nonholonomic joints from ordinary manipulators
Grosch Obregon, Patrick John; Di Gregorio, Silvana; Thomas Arroyo, Federico
Journal of mechanisms and robotics
Date of publication: 2010
Journal article
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Motion Planning for a Novel Recon¿gurable Parallel Manipulator with Lockable Revolute Joints
Grosch Obregon, Patrick John; Di Gregorio, Silvana; López, Javier; Thomas Arroyo, Federico
IEEE International conference on robotics and automation
Date of publication: 201005
Journal article
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Singularityinvariant leg substitutions in pentapods
Borras Sol, Julia; Thomas Arroyo, Federico
IEEE/RSJ International Conference on Intelligent Robots and Systems
Presentation's date: 2010
Presentation of work at congresses
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Motion planning for a novel reconfigurable parallel manipulator with lockable revolute joints
Grosch Obregon, Patrick John; Di Gregorio, Silvana; López, Javier; Thomas Arroyo, Federico
IEEE International Conference on Robotics and Automation
Presentation's date: 2010
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThis paper introduces a class of reconfigurable parallel robots consisting of a fixed base and a moving platform connected by serial chains having RRPS (RevoluteRevolutePrismaticSpherical) topology. Only the prismatic joint is actuated and the first revolute joint in the chain can be locked or released online. The introduction of these lockable joints allow the prismatic actuators to maneuver to approximate 6DoF motions for the moving platform. An algorithm for generating these maneuvers is first described. Then, a motion planner, based on the generation of a Probabilistic RoadMap (PRM) whose nodes are connected using the described maneuvers, is presented. The generated trajectories avoid singularities and possible collisions between legs. (See accompanying video)
Postprint (author’s final draft) 
A distancebased formulation of the octahedral manipulator kinematics
Rojas Libreros, Nicolás Enrique; Borras Sol, Julia; Thomas Arroyo, Federico
IFToMM Symposium on Mechanism Design for Robotics
Presentation's date: 2010
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A family of quadraticallysolvable 5SPU parallel robots
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
IEEE International Conference on Robotics and Automation
Presentation's date: 2010
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersA 5SPU robot with collinear universal joints is well suited to handling an axisymmetric tool, since it has 5 controllable DoFs and the remaining one is a free rotation around the tool. The kinematics of such a robot having also coplanar spherical joints has previously been studied as a rigid subassembly of a StewartGough platform, it being denoted a lineplane component. It was shown that this component has 8 assembly modes corresponding to the roots of a biquartic polynomial. Here we identify a whole family of these 5SPU robots having only 4 assembly modes, which are obtained by solving two quadratic equations. This family is defined by a simple proportionality constraint relating the coordinates of the base and platform attachments. A geometric interpretation of the architectural singularities of this type of robots in terms of conics is provided, which facilitates their avoidance at the design stage. Parallel singularities obey also a neat geometric structure, which permits deriving a cell decomposition of configuration space. Two practical features of these quadraticallysolvable robots are the large maneuverability within each connected component and the fact that, for a fixed orientation of the tool, the singularity locus reduces to a plane. Index Terms—Parallel manipulators, StewartGough platforms, robot kinematics, kinematics singularities.
Postprint (author’s final draft) 
A robust forward kinematics analysis of 3RPR planar platforms
Rojas, Nicolás; Thomas Arroyo, Federico
International Symposium on Advances in Robot Kinematics
Presentation's date: 2010
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThe standard forward kinematics analysis of 3RPR planar parallel platforms boils down to computing the roots of a sextic polynomial. There are many different ways to obtain this polynomial but all of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience by translating the forward kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic —which is not linked to a particular reference frame— is straightforwardly obtained without the need of variable eliminations nor tangenthalfangle substitutions. The presented formulation is valid, without any modification, for any planar 3RPR parallel platform, including the special architectures and configurations —which ultimately lead to numerical instabilities— that cannot be directly handled by previous formulations.
Postprint (author’s final draft) 
Singularityinvariant leg rearrangements in doublyplanar StewartGough platforms
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
Robotics: Science and Systems
Presentation's date: 2010
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersIn general, rearranging the legs of a StewartGough platform, i.e., changing the locations of its leg attachments, modifies the platform singularity locus in a rather unexpected way. Nevertheless, some leg rearrangements have been recently found to leave singularities invariant but, unfortunately, these rearrangements are only valid for StewartGough platforms containing rigid components. In this work, the authors go a step further presenting singularityinvariant leg rearrangements that can be applied to any StewartGough platform whose base and platform attachments are coplanar. The practical consequences of the presented theoretical results are illustrated with several examples including wellknown architectures.
Postprint (author’s final draft) 
Singularityinvariant leg rearrangements in StewartGough platforms
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
International Symposium on Advances in Robot Kinematics
Presentation's date: 2010
Presentation of work at congresses
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A onemotor fullmobility 6PUS manipulator
Grosch Obregon, Patrick John; Di Gregorio, Silvana; Thomas Arroyo, Federico
CISMIFToMM Symposium on Robot Design, Dynamics and Control
Presentation's date: 2010
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThis paper presents the feasibility study of an underactuated parallel manipulator with 6PUS topology, destined to handle worktables in CNC machine tools. The proposed device exploits the fact that, in such an application, the path between the initial and final poses of the mobile platform is not assigned to reduce the number of actuators to only one.
Postprint (author’s final draft) 
Factories del futur pel sector manufacturer a Catalunya (manucat)
Casado Lopez, Ramon; Rodriguez Sendra, Rosa Maria; Buj Corral, Irene; Gomà Ayats, Joan Ramon; Fenollosa Artes, Felip; Napoles Alberro, Amelia Emelina; Martinez Miralles, Jordi Ramon; Fruitos Bickham, Oscar Alejandro; Travieso Rodríguez, José Antonio; Maspoch Ruldua, Maria Lluïsa; Martinez Velasco, Antonio Benito; TortMartorell Llabres, Javier; Vivancos Calvet, Joan; Roure Fernandez, Francisco; Puigjaner Corbella, Luis; Espuña Camarasa, Antonio; Thomas Arroyo, Federico; Pastor Artigues, M. Magdalena; Minguella Canela, Joaquim
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DESPLEGAMENT DE L'EXPOSICIÓ RSMEIMAGINARY A CATALUNYA  FASE 2010
Xambó Descamps, Sebastian; Torras, Carme; Thomas Arroyo, Federico; Barja Yañez, Miguel Angel; Plans Berenguer, Bernat; Borras Sol, Julia; Quer Bosor, Jordi; Alberich Carramiñana, Maria
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GARNICS: Gardening with a Cognitive System (FP7ICT247947)
Torras, Carme; Moreno Noguer, Francesc d'Assis; Agostini, Alejandro Gabriel; Dellen, Babette Karla Margarete; Alenyà Ribas, Guillem; Jimenez Schlegl, Pablo; Thomas Arroyo, Federico; Rozo Castañeda, Leonel; Husain, Syed Farzad; Foix Salmeron, Sergi
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On ¿transforms
Thomas Arroyo, Federico; Torras, Carme; Borras Sol, Julia
IEEE transactions on robotics
Date of publication: 2009
Journal article
Read the abstract Access to the full text Share Reference managersAnyset of two legs in a Gough–Stewart platform sharing an attachment is defined as a Δcomponent. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a Δ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough–Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as Δtransforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous Δtransforms does not necessarily lead to leg configurations containing a Δcomponent. As a consequence, the application of Δtransforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough–Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated selfmotions. 
Concise proof of Tienstra's formula
Porta Pleite, Josep M.; Thomas Arroyo, Federico
Journal of surveying engineering (ASCE)
Date of publication: 2009
Journal article
Read the abstract Access to the full text Share Reference managersThe resection problem consists in finding the location of an observer by measuring the angles subtended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. Un fortunately, all available proofs for this remarkable formula are intricate. This paper shows how, by using barycentric coordinates for the observer in terms of the locations of the stations, a neat and short proof is straightforwardly derived. 
Stratifications of the Euclidean motion group with applications to robotics
Alberich Carramiñana, Maria; Gonzalez, V.; Thomas Arroyo, Federico; Torras, Carme
Geometricae dedicata
Date of publication: 200908
Journal article
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Partially flagged parallel manipulators: singularity charting and avoidance
Alberich Carramiñana, Maria; Garolera, M; Thomas Arroyo, Federico; Torras, Carme
IEEE transactions on robotics
Date of publication: 200908
Journal article
Read the abstract Access to the full text Share Reference managersThere are only three 6SPS parallelmanipulatorswith triangular base and platform, i.e., the octahedral, the flagged, and the partially flagged, which are studied in this paper. The forward kinematics of the octahedralmanipulator is algebraically intricate, while those of the other two can be solved by three trilaterations. As an additional nice feature, the flagged manipulator is the only parallel platform for which a cell decomposition of its singularity locus has been derived. Here, we prove that the partially flagged manipulator also admits a wellbehaved decomposition, technically called a stratification, some of whose strata are not topological cells, however. Remarkably, the adjacency diagram of the 5D and 6D strata (which shows what 5D strata are contained in the closure of a 6D one) is the same as for the flaggedmanipulator. The availability of such a decomposition permits devising a redundant 7SPS manipulator, combining two partially flagged ones, which admits a control strategy that completely avoids singularities. Simulation results support these claims. 
On DeltaTransforms
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
IEEE transactions on robotics
Date of publication: 200912
Journal article
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A linear relaxation technique for the position analysis of multiloop linkages
Porta Pleite, Josep M.; Ros Giralt, Lluis; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 2009
Journal article
Read the abstract Access to the full text Share Reference managersThis paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branchandprune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile. 
"Adaptive Neural Control of Nonlinear Systems"
Thomas Arroyo, Federico; Baruch, I; Flores, JM; Garrido, R
Date of publication: 20090612
Book chapter
Read the abstract Access to the full text Share Reference managersThe present paper addresses pedestrian detection using local boosted features that are learned from a small set of training images. Our contribution is to use two boosting steps. The first one learns discriminant local features corresponding to pedestrian parts and the second one selects and combines these boosted features into a robust class classifier. In contrast of other works, our features are based on local differences over Histograms of Oriented Gradients (HoGs). Experiments carried out to a public dataset of pedestrian images show good performance with high classification rates 
Generation of underactuated parallel robots with nonholonomic joints and kinetostatic analysis of a casestudy
Grosch Obregon, Patrick John; Di Gregorio, Silvana; Thomas Arroyo, Federico
ASME International Design Engineering Technical Conferences
Presentation's date: 2009
Presentation of work at congresses
Read the abstract View Share Reference managersIt will be shown how to generate underactuated manipulators by substituting nonholonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in fullyparallel manipulators (FPMs). Through this pair substitution, an underactuated manipulator, previously proposed by one of the authors, will be demonstrated to be generated from an inversion of the 63 FPM. Moreover, the kinetostatic analysis of this manipulator will be reconsidered to obtain a simple and compact formulation. This reformulated analysis can be used both in the design of the underactuated manipulator, and in its control. 
Straighteningfree algorithm for the singularity analysis of StewartGough platforms with collinear/coplanar attachments
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
Computational Kinematics
Presentation's date: 20090508
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersAn algorithm to derive the pure condition of any doubleplanar StewartGough platform in a standard form suitable for comparison is presented. By applying the multilinear properties of brackets directly to the superbracket encoding of the pure condition, no straightening is required. It is then shown that any 33 platform has a corresponding 66 platform having its same superbracket, meaning that they have identical singularity loci. In general, the superbracket of any doubleplanar platform can be written as a linear combination of the superbrackets of 33 platforms, leading to a direct singularity assessment by inspecting the resulting decomposition.
Postprint (author’s final draft) 
Kinematics of lineplane subassemblies in Stewart platforms
Borras Sol, Julia; Thomas Arroyo, Federico
IEEE International Conference on Robotics and Automation
Presentation's date: 2009
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersWhen the attachments of five legs in a Stewart platform are collinear on one side and coplanar on the other, the platform is said to contain a lineplane subassembly. This paper is devoted to the kinematics analysis of this subassembly paying particular attention to the problem of moving the aforementioned attachments without altering the singularity locus of the platform. It is shown how this is always possible provided that some crossratios between lines defined by points in the plane are kept equal to other crossratios between points in the line. This result leads to two simple motion rules upon which complex changes in the location of the attachments can be performed. These rules have interesting practical consequences as they permit a designer to optimize aspects of a parallel robot containing the analyzed subassembly, such as its manipulability in a given region, without altering its singularity locus. 
A reconfigurable 5DoF 5SPU parallel platform
Borras Sol, Julia; Thomas Arroyo, Federico; Ottaviano, Erika; Ceccarelli, Marco
ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots
Presentation's date: 2009
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersThis paper presents a 5SPU platform whose base leg attachments can be easily reconfigured, statically or dynamically, without altering its singularity locus. This permits to adapt the platform’s geometry to particular tasks without increasing the complexity of its control. The allowed reconfigurations permit to reduce the risk of collisions between legs, or even improving the stiffness of the platform, in a given region of its configuration space. It is also shown that no architectural singularities are introduced by the proposed reconfigurations. 
A short account of Leonardo Torres' endless spindle
Thomas Arroyo, Federico
Mechanism and machine theory
Date of publication: 2008
Journal article
Read the abstract View Share Reference managersAt the end of the 19th century, several analog machines had been proposed for solving algebraic equations. These machines – based not only on kinematics principles but also on dynamic or hydrostatic balances, electric or electromagnetic devices, etc. – had one important drawback: lack of accuracy. Leonardo Torres was the first to beat the challenge of designing and implementing a machine able to compute the roots of algebraic equations that, in the case of polynomials of degree eight, attained a precision down to 1/1000. The key element of Torres’ machine was the endless spindle, an analog mechanical device designed to compute log(a + b) from log(a) and log(b). This short account gives a detailed description of this mechanism. 
A wirebased active tracker
Andrade Cetto, Juan; Thomas Arroyo, Federico
IEEE transactions on robotics
Date of publication: 200806
Journal article
Read the abstract Access to the full text Share Reference managersWirebased tracking devices are an affordable alternative to costly tracking devices. They consist of a fixed base and a platform, attached to the moving object, connected by six wires whose tension is maintained along the tracked trajectory. One important shortcoming of these devices is that they are forced to operate in reduced workspaces so as to avoid singular configurations. Singularities can be eliminated by adding more wires, but this causes more wire interferences, and a higher force exerted on the moving object by the measuring device itself. This paper shows how, by introducing a rotating base, the number of wires can be reduced to three, and singularities can be avoided by using an active sensing strategy. This also permits reducing wire interference problems and the pulling force exerted by the device. 
Analysing the singularities of 6SPS parallel robots using virtual legs
Borras Sol, Julia; Thomas Arroyo, Federico; Torras, Carme
International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
Presentation's date: 2008
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersA virtual leg in a 6SPS parallel robot is defined as a leg whose length is determined by the lengths of a subset of the actual legs of the robot. This necessarily implies that this subset of legs defines a rigid subassembly. In this paper, we consider four different rigid subassemblies, and show how the singularities of a robot containing one or several of these subassemblies are modified when substituting its actual legs by virtual legs.
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