Ponències/Comunicacions de congressos
http://hdl.handle.net/2117/99676
Sun, 28 Feb 2021 10:37:49 GMT
20210228T10:37:49Z

Clifford’s identity and generalized CayleyMenger determinants
http://hdl.handle.net/2117/339729
Clifford’s identity and generalized CayleyMenger determinants
Thomas, Federico; Porta Pleite, Josep Maria
Distance geometry is usually defined as the characterization and study of point sets in Rk, the kdimensional Euclidean space, based on the pairwise distances between their points. In this paper, we use Clifford’s identity to extend this kind of characterization to sets of n hyperspheres embedded in ¿n3 or Rn3 where the role of the Euclidean distance between two points is replaced by the socalled power between two hyperspheres. By properly choosing the value of n and the radii of these hyperspheres, Clifford’s identity reduces to conditions in terms of generalized CayleyMenger determinants which has been previously obtained on the basis of a casebycase analysis.
The final publication is available at link.springer.com
Tue, 16 Feb 2021 10:35:01 GMT
http://hdl.handle.net/2117/339729
20210216T10:35:01Z
Thomas, Federico
Porta Pleite, Josep Maria
Distance geometry is usually defined as the characterization and study of point sets in Rk, the kdimensional Euclidean space, based on the pairwise distances between their points. In this paper, we use Clifford’s identity to extend this kind of characterization to sets of n hyperspheres embedded in ¿n3 or Rn3 where the role of the Euclidean distance between two points is replaced by the socalled power between two hyperspheres. By properly choosing the value of n and the radii of these hyperspheres, Clifford’s identity reduces to conditions in terms of generalized CayleyMenger determinants which has been previously obtained on the basis of a casebycase analysis.

A space decomposition method for path planning of loop linkages
http://hdl.handle.net/2117/328737
A space decomposition method for path planning of loop linkages
Porta Pleite, Josep Maria; Cortés, Juan; Ros Giralt, Lluís; Thomas, Federico
This paper introduces box approximations as a new tool for path planning of closedloop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for openchain robots  they capture the freespace connectivity in a multiresolutive fashion and yield rectangloid channels enclosing collisionfree paths  but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolutioncomplete path planners can be devised using them. To the authors' knowledge, this is the first spacedecomposition approach to closedloop linkage path planning proposed in the literature.
Tue, 15 Sep 2020 08:06:52 GMT
http://hdl.handle.net/2117/328737
20200915T08:06:52Z
Porta Pleite, Josep Maria
Cortés, Juan
Ros Giralt, Lluís
Thomas, Federico
This paper introduces box approximations as a new tool for path planning of closedloop linkages. Box approximations are finite collections of rectangloids that tightly envelop the robot's free space at a desired resolution. They play a similar role to that of approximate cell decompositions for openchain robots  they capture the freespace connectivity in a multiresolutive fashion and yield rectangloid channels enclosing collisionfree paths  but have the additional property of enforcing the satisfaction of loop closure constraints frequently arising in articulated linkages. We present an efficient technique to compute such approximations and show how resolutioncomplete path planners can be devised using them. To the authors' knowledge, this is the first spacedecomposition approach to closedloop linkage path planning proposed in the literature.

Visuallyguided robot navigation: from artificial to natural landmarks
http://hdl.handle.net/2117/192622
Visuallyguided robot navigation: from artificial to natural landmarks
Celaya Llover, Enric; Albarral Garcia, Jose Luis; Jimenez Schlegl, Pablo; Torras, Carme
Landmarkbased navigation in unknown unstructured environments is far from solved. The bottleneck nowadays seems to be the fast detection of reliable visual references in the image stream as the robot moves. In our research, we have decoupled the navigation issues from this visual bottleneck, by first using artificial landmarks that could be easily detected and identified. Once we had a navigation system working, we developed a strategy to detect and track salient regions along image streams by just performing online pixel sampling. This strategy continuously updates the mean and covariances of the salient regions, as well as creates, deletes and merges regions according to the sample flow. Regions detected as salient can be considered as potential landmarks to be used in the navigation task.
The final publication is available at link.springer.com
Wed, 08 Jul 2020 11:30:56 GMT
http://hdl.handle.net/2117/192622
20200708T11:30:56Z
Celaya Llover, Enric
Albarral Garcia, Jose Luis
Jimenez Schlegl, Pablo
Torras, Carme
Landmarkbased navigation in unknown unstructured environments is far from solved. The bottleneck nowadays seems to be the fast detection of reliable visual references in the image stream as the robot moves. In our research, we have decoupled the navigation issues from this visual bottleneck, by first using artificial landmarks that could be easily detected and identified. Once we had a navigation system working, we developed a strategy to detect and track salient regions along image streams by just performing online pixel sampling. This strategy continuously updates the mean and covariances of the salient regions, as well as creates, deletes and merges regions according to the sample flow. Regions detected as salient can be considered as potential landmarks to be used in the navigation task.

Natural landmark detection for visuallyguided robot navigation
http://hdl.handle.net/2117/191345
Natural landmark detection for visuallyguided robot navigation
Celaya Llover, Enric; Albarral Garcia, Jose Luis; Jimenez Schlegl, Pablo; Torras, Carme
The main difficulty to attain fully autonomous robot navigation outdoors is the fast detection of reliable visual references, and their subsequent characterization as landmarks for immediate and unambiguous recognition. Aimed at speed, our strategy has been to track salient regions along image streams by just performing online pixel sampling. Persistent regions are considered good candidates for landmarks, which are then characterized by a set of subregions with given color and normalized shape. They are stored in a database for posterior recognition during the navigation process. Some experimental results showing landmarkbased navigation of the legged robot Lauron III in an outdoor setting are provided.
The final publication is available at link.springer.com
Tue, 23 Jun 2020 07:45:44 GMT
http://hdl.handle.net/2117/191345
20200623T07:45:44Z
Celaya Llover, Enric
Albarral Garcia, Jose Luis
Jimenez Schlegl, Pablo
Torras, Carme
The main difficulty to attain fully autonomous robot navigation outdoors is the fast detection of reliable visual references, and their subsequent characterization as landmarks for immediate and unambiguous recognition. Aimed at speed, our strategy has been to track salient regions along image streams by just performing online pixel sampling. Persistent regions are considered good candidates for landmarks, which are then characterized by a set of subregions with given color and normalized shape. They are stored in a database for posterior recognition during the navigation process. Some experimental results showing landmarkbased navigation of the legged robot Lauron III in an outdoor setting are provided.

Exploiting singlecycle symmetries in branchandprune algorithms
http://hdl.handle.net/2117/191176
Exploiting singlecycle symmetries in branchandprune algorithms
Ruiz de Angulo García, Vicente; Torras, Carme
As a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a BranchandPrune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a ndimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice.
The final publication is available at link.springer.com
Fri, 19 Jun 2020 10:36:29 GMT
http://hdl.handle.net/2117/191176
20200619T10:36:29Z
Ruiz de Angulo García, Vicente
Torras, Carme
As a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a BranchandPrune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a ndimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice.

Singularityfree computation of quaternions from rotation matrices in E4 and E3
http://hdl.handle.net/2117/182619
Singularityfree computation of quaternions from rotation matrices in E4 and E3
Sarabandi, Soheil; Pérez Gracia, Alba; Thomas, Federico
A real orthogonal matrix representing a rotation in E4 can be decomposed into the commutative product of a leftisoclinic and a rightisoclinic rotation matrix. The double quaternion representation of rotations in E4 follows directly from this decomposition. In this paper, it is shown how this decomposition can be performed without divisions. This avoids the common numerical issues attributed to the computation of quaternions from rotation matrices. The map from the 4×4 rotation matrices to the set of double unit quaternions is a 2to1 covering map. Thus, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clari¿ed. When particularized to three dimensions, it is shown how the resulting formulation outperforms, from the numerical point of view, the celebrated Shepperd’s method.
Wed, 01 Apr 2020 08:07:25 GMT
http://hdl.handle.net/2117/182619
20200401T08:07:25Z
Sarabandi, Soheil
Pérez Gracia, Alba
Thomas, Federico
A real orthogonal matrix representing a rotation in E4 can be decomposed into the commutative product of a leftisoclinic and a rightisoclinic rotation matrix. The double quaternion representation of rotations in E4 follows directly from this decomposition. In this paper, it is shown how this decomposition can be performed without divisions. This avoids the common numerical issues attributed to the computation of quaternions from rotation matrices. The map from the 4×4 rotation matrices to the set of double unit quaternions is a 2to1 covering map. Thus, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clari¿ed. When particularized to three dimensions, it is shown how the resulting formulation outperforms, from the numerical point of view, the celebrated Shepperd’s method.

A fast branchandprune algorithm for the position analysis of spherical mechanisms
http://hdl.handle.net/2117/180995
A fast branchandprune algorithm for the position analysis of spherical mechanisms
Shabani, Arya; Sarabandi, Soheil; Porta Pleite, Josep Maria; Thomas, Federico
Different branchandprune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multiaffine polynomials. Multiaffinity has an important impact on how the propagation of motion intervals can be performed because a multiaffine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.
The final publication is available at link.springer.com
Tue, 24 Mar 2020 08:40:47 GMT
http://hdl.handle.net/2117/180995
20200324T08:40:47Z
Shabani, Arya
Sarabandi, Soheil
Porta Pleite, Josep Maria
Thomas, Federico
Different branchandprune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multiaffine polynomials. Multiaffinity has an important impact on how the propagation of motion intervals can be performed because a multiaffine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.

Forward kinematics of the general triplearm robot using a distancebased formulation
http://hdl.handle.net/2117/132085
Forward kinematics of the general triplearm robot using a distancebased formulation
Rojas, Nicolas; Thomas, Federico
Distancebased formulations have successfully been used to obtain closure polynomialsfor planar mechanisms without relying, in most cases, on variable eliminations. The methods resulting from previous attempts to generalize these techniques to spatial mechanisms exhibit somelimitations such as the impossibility of incorporating orientation constraints. For the first time, thispaper presents a complete satisfactory generalization. As an example, it is applied to obtain a closure polynomial for the the general triplearm parallel robot (that is, the 3RPS 3DOF robot). Thispolynomial, not linked to any particular reference frame, is obtained without variable eliminationsor tangenthalfangle substitutions
The final publication is available at link.springer.com
Fri, 26 Apr 2019 07:21:05 GMT
http://hdl.handle.net/2117/132085
20190426T07:21:05Z
Rojas, Nicolas
Thomas, Federico
Distancebased formulations have successfully been used to obtain closure polynomialsfor planar mechanisms without relying, in most cases, on variable eliminations. The methods resulting from previous attempts to generalize these techniques to spatial mechanisms exhibit somelimitations such as the impossibility of incorporating orientation constraints. For the first time, thispaper presents a complete satisfactory generalization. As an example, it is applied to obtain a closure polynomial for the the general triplearm parallel robot (that is, the 3RPS 3DOF robot). Thispolynomial, not linked to any particular reference frame, is obtained without variable eliminationsor tangenthalfangle substitutions

A new insight into the coupler curves of the RCCC fourbar linkage
http://hdl.handle.net/2117/131805
A new insight into the coupler curves of the RCCC fourbar linkage
Thomas, Federico; Pérez Gracia, Alba
Based on the condition for four points to lie on the unit sphere, derived using Distance Geometry, a new mathematical formulation for the coupler curves of the RCCC linkage is presented. The relevance of this formulation is not only its simplicity, but the elegant way in which we can obtain the derivative of any variable with respect to any other, and the simple way in which intervals of monotonicity can be detected. All these results are compactly expressed in terms of Gramians and, as a consequence, they have a direct geometric meaning contrarily to what happens with previous approaches based on kinematic loop equations.
The final publication is available at link.springer.com
Tue, 23 Apr 2019 08:50:44 GMT
http://hdl.handle.net/2117/131805
20190423T08:50:44Z
Thomas, Federico
Pérez Gracia, Alba
Based on the condition for four points to lie on the unit sphere, derived using Distance Geometry, a new mathematical formulation for the coupler curves of the RCCC linkage is presented. The relevance of this formulation is not only its simplicity, but the elegant way in which we can obtain the derivative of any variable with respect to any other, and the simple way in which intervals of monotonicity can be detected. All these results are compactly expressed in terms of Gramians and, as a consequence, they have a direct geometric meaning contrarily to what happens with previous approaches based on kinematic loop equations.

A singularityrobust LQR controller for parallel robots
http://hdl.handle.net/2117/130001
A singularityrobust LQR controller for parallel robots
Bordalba Llaberia, Ricard; Porta Pleite, Josep Maria; Ros Giralt, Lluís
Parallel robots exhibit the socalled forward singularities, which complicate substantially the planning and control of their motions. Often, such complications are circumvented by restricting the motions to singularityfree regions of the workspace. However, this comes at the expense of reducing the motion range of the robot substantially. It is for this reason that, recently, efforts are underway to control singularity crossing trajectories. This paper proposes a reliable controller to stabilize such kind of trajectories. The controller is based on the classical theory of linear quadratic regulators, which we adapt appropriately to the case of parallel robots. As opposed to traditional computedtorque methods, the obtained controller does not rely on expensive inverse dynamics computations. Instead, it uses an optimal control law that is easy to evaluate, and does not generate instabilities at forward singularities. The performance of the controller is exemplified on a fivebar parallel robot accomplishing two tasks that require the traversal of singularities.
© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
Fri, 01 Mar 2019 13:35:12 GMT
http://hdl.handle.net/2117/130001
20190301T13:35:12Z
Bordalba Llaberia, Ricard
Porta Pleite, Josep Maria
Ros Giralt, Lluís
Parallel robots exhibit the socalled forward singularities, which complicate substantially the planning and control of their motions. Often, such complications are circumvented by restricting the motions to singularityfree regions of the workspace. However, this comes at the expense of reducing the motion range of the robot substantially. It is for this reason that, recently, efforts are underway to control singularity crossing trajectories. This paper proposes a reliable controller to stabilize such kind of trajectories. The controller is based on the classical theory of linear quadratic regulators, which we adapt appropriately to the case of parallel robots. As opposed to traditional computedtorque methods, the obtained controller does not rely on expensive inverse dynamics computations. Instead, it uses an optimal control law that is easy to evaluate, and does not generate instabilities at forward singularities. The performance of the controller is exemplified on a fivebar parallel robot accomplishing two tasks that require the traversal of singularities.