Ponències/Comunicacions de congressos
http://hdl.handle.net/2117/99676
2024-03-29T15:00:59ZCollocation methods for second order systems
http://hdl.handle.net/2117/375134
Collocation methods for second order systems
Moreno Martín, Siro; Ros Giralt, Lluís; Celaya Llover, Enric
Collocation methods for numerical optimal control commonly assume that the system dynamics is expressed as a first order ODE of the form x¿ = f(x, u, t), where x is the state and u the control vector. However, in many systems in robotics, the dynamics adopts the second order form q¨ = g(q, q¿, u, t), where q is the configuration. To preserve the first order form, the usual procedure is to introduce the velocity variable v = q¿ and define the state as x = (q, v), where q and v are treated as independent in the collocation method. As a consequence, the resulting trajectories do not fulfill the mandatory relationship v(t) = q¿(t) for all times, and even violate q¨ = g(q, q¿, u, t) at the collocation points. This prevents the possibility of reaching a correct solution for the problem, and makes the trajectories less compliant with the system dynamics. In this paper we propose a formulation for the trapezoidal and Hermite-Simpson collocation methods that is able to deal with second order dynamics and grants the mutual consistency of the trajectories for q and v while ensuring q¨ = g(q, q¿, u, t) at the collocation points. As a result, we obtain trajectories with a much smaller dynamical error in similar computation times, so the robot will behave closer to what is predicted by the solution. We illustrate these points by way of examples, using well-established benchmark problems from the literature.
2022-10-27T10:16:14ZMoreno Martín, SiroRos Giralt, LluísCelaya Llover, EnricCollocation methods for numerical optimal control commonly assume that the system dynamics is expressed as a first order ODE of the form x¿ = f(x, u, t), where x is the state and u the control vector. However, in many systems in robotics, the dynamics adopts the second order form q¨ = g(q, q¿, u, t), where q is the configuration. To preserve the first order form, the usual procedure is to introduce the velocity variable v = q¿ and define the state as x = (q, v), where q and v are treated as independent in the collocation method. As a consequence, the resulting trajectories do not fulfill the mandatory relationship v(t) = q¿(t) for all times, and even violate q¨ = g(q, q¿, u, t) at the collocation points. This prevents the possibility of reaching a correct solution for the problem, and makes the trajectories less compliant with the system dynamics. In this paper we propose a formulation for the trapezoidal and Hermite-Simpson collocation methods that is able to deal with second order dynamics and grants the mutual consistency of the trajectories for q and v while ensuring q¨ = g(q, q¿, u, t) at the collocation points. As a result, we obtain trajectories with a much smaller dynamical error in similar computation times, so the robot will behave closer to what is predicted by the solution. We illustrate these points by way of examples, using well-established benchmark problems from the literature.Kinematics of a gear-based spherical mechanism
http://hdl.handle.net/2117/372095
Kinematics of a gear-based spherical mechanism
Thomas, Federico
Kazuki Abe and his collaborators have recently presented an actuated gear-based spherical mechanism called ABENICS. It has received a lot of attention, not only because of its eye-catching motions during operation, but also and mostly, because it can successfully be used when large motion ranges and a high stiffness are required. Nevertheless, the main disadvantage of Abe et al.'s design is that it is an over-actuated mechanism: it requires four instead of only three actuators. In this paper, we propose a variation on this mechanism which requires three actuators, thus simplifying its control and its potential cost. The kinematics of this new mechanism is studied in detail, including its forward and inverse kinematics, as well as its singularities.
This book is the compilation of proceedings presented at the 18th International Symposium on Advances in Robot Kinematics held in Bilbao (Spain) in 2022.
2022-08-31T12:39:56ZThomas, FedericoKazuki Abe and his collaborators have recently presented an actuated gear-based spherical mechanism called ABENICS. It has received a lot of attention, not only because of its eye-catching motions during operation, but also and mostly, because it can successfully be used when large motion ranges and a high stiffness are required. Nevertheless, the main disadvantage of Abe et al.'s design is that it is an over-actuated mechanism: it requires four instead of only three actuators. In this paper, we propose a variation on this mechanism which requires three actuators, thus simplifying its control and its potential cost. The kinematics of this new mechanism is studied in detail, including its forward and inverse kinematics, as well as its singularities.The distance geometry of the generalized lobster’s arm
http://hdl.handle.net/2117/372092
The distance geometry of the generalized lobster’s arm
Thomas, Federico; Porta Pleite, Josep Maria
This paper proposes a distance-based formulation to solve the inverse kinematics of what is known as the generalized Lobster's arm: a 6R serial chain in which all consecutive revolute axes intersect. Since the solution of the inverse kinematics of a general 6R serial chain comes down to finding the roots of a 16th-degree polynomial, one might think that this polynomial also contains the solutions to the inverse kinematics of 6R serial chains with special geometric parameters as a mere particular case. Nevertheless, under certain geometric circumstances various problems can appear. Some are of numerical nature, but others are fundamental problems of the used method. For that reason, it is still useful to study 6R chains with special geometric parameters, especially when the new formulation leads to a simpler solution, gives new insights, and provides new connections with other problems, as is the case in this paper.
This book is the compilation of proceedings presented at the 18th International Symposium on Advances in Robot Kinematics held in Bilbao (Spain) in 2022.
2022-08-31T12:32:09ZThomas, FedericoPorta Pleite, Josep MariaThis paper proposes a distance-based formulation to solve the inverse kinematics of what is known as the generalized Lobster's arm: a 6R serial chain in which all consecutive revolute axes intersect. Since the solution of the inverse kinematics of a general 6R serial chain comes down to finding the roots of a 16th-degree polynomial, one might think that this polynomial also contains the solutions to the inverse kinematics of 6R serial chains with special geometric parameters as a mere particular case. Nevertheless, under certain geometric circumstances various problems can appear. Some are of numerical nature, but others are fundamental problems of the used method. For that reason, it is still useful to study 6R chains with special geometric parameters, especially when the new formulation leads to a simpler solution, gives new insights, and provides new connections with other problems, as is the case in this paper.Model predictive control for a Mecanum-wheeled robot navigating among obstacles
http://hdl.handle.net/2117/367011
Model predictive control for a Mecanum-wheeled robot navigating among obstacles
Moreno Caireta, Iñigo; Celaya Llover, Enric; Ros Giralt, Lluís
Mecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.
2022-05-06T12:39:00ZMoreno Caireta, IñigoCelaya Llover, EnricRos Giralt, LluísMecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.Clifford’s identity and generalized Cayley-Menger determinants
http://hdl.handle.net/2117/339729
Clifford’s identity and generalized Cayley-Menger determinants
Thomas, Federico; Porta Pleite, Josep Maria
Distance geometry is usually defined as the characterization and study of point sets in Rk, the k-dimensional 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 ¿n-3 or Rn-3 where the role of the Euclidean distance between two points is replaced by the so-called 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 Cayley-Menger determinants which has been previously obtained on the basis of a case-by-case analysis.
The final publication is available at link.springer.com
2021-02-16T10:35:01ZThomas, FedericoPorta Pleite, Josep MariaDistance geometry is usually defined as the characterization and study of point sets in Rk, the k-dimensional 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 ¿n-3 or Rn-3 where the role of the Euclidean distance between two points is replaced by the so-called 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 Cayley-Menger determinants which has been previously obtained on the basis of a case-by-case 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 closed-loop 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 open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free 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 resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.
2020-09-15T08:06:52ZPorta Pleite, Josep MariaCortés, JuanRos Giralt, LluísThomas, FedericoThis paper introduces box approximations as a new tool for path planning of closed-loop 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 open-chain robots - they capture the free-space connectivity in a multi-resolutive fashion and yield rectangloid channels enclosing collision-free 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 resolution-complete path planners can be devised using them. To the authors' knowledge, this is the first space-decomposition approach to closed-loop linkage path planning proposed in the literature.Visually-guided robot navigation: from artificial to natural landmarks
http://hdl.handle.net/2117/192622
Visually-guided robot navigation: from artificial to natural landmarks
Celaya Llover, Enric; Albarral Garcia, Jose Luis; Jiménez Schlegl, Pablo; Torras, Carme
Landmark-based 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 on-line 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
2020-07-08T11:30:56ZCelaya Llover, EnricAlbarral Garcia, Jose LuisJiménez Schlegl, PabloTorras, CarmeLandmark-based 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 on-line 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 visually-guided robot navigation
http://hdl.handle.net/2117/191345
Natural landmark detection for visually-guided robot navigation
Celaya Llover, Enric; Albarral Garcia, Jose Luis; Jiménez 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 on-line 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 landmark-based navigation of the legged robot Lauron III in an outdoor setting are provided.
The final publication is available at link.springer.com
2020-06-23T07:45:44ZCelaya Llover, EnricAlbarral Garcia, Jose LuisJiménez Schlegl, PabloTorras, CarmeThe 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 on-line 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 landmark-based navigation of the legged robot Lauron III in an outdoor setting are provided.Exploiting single-cycle symmetries in branch-and-prune algorithms
http://hdl.handle.net/2117/191176
Exploiting single-cycle symmetries in branch-and-prune 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 Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional 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
2020-06-19T10:36:29ZRuiz de Angulo García, VicenteTorras, CarmeAs 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 Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional 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.Singularity-free computation of quaternions from rotation matrices in E4 and E3
http://hdl.handle.net/2117/182619
Singularity-free 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 left-isoclinic and a right-isoclinic 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 2-to-1 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.
2020-04-01T08:07:25ZSarabandi, SoheilPérez Gracia, AlbaThomas, FedericoA real orthogonal matrix representing a rotation in E4 can be decomposed into the commutative product of a left-isoclinic and a right-isoclinic 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 2-to-1 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.