Dispersion relation for hadronic light-by-light scattering: two-pion contributions

In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_\mu$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $\gamma^*\gamma^*\to\pi\pi$. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_\mu^{\pi\text{-box}}=-15.9(2)\times 10^{-11}$. As an application of the partial-wave formalism, we present a first calculation of $\pi\pi$-rescattering effects in HLbL scattering, with $\gamma^*\gamma^*\to\pi\pi$ helicity partial waves constructed dispersively using $\pi\pi$ phase shifts derived from the inverse-amplitude method. In this way, the isospin-$0$ part of our calculation can be interpreted as the contribution of the $f_0(500)$ to HLbL scattering in $(g-2)_\mu$. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its $S$-wave rescattering corrections reads $a_\mu^{\pi\text{-box}} + a_{\mu,J=0}^{\pi\pi,\pi\text{-pole LHC}}=-24(1)\times 10^{-11}$.Comment: 70 pages, 14 figures, Mathematica notebook with full expressions for the basis change included as supplementary material. Version accepted for publication in JHE

Inverse Kinematics without matrix inversion

This paper presents a new singularity robust and computationally efficient method for solving the inverse kinematics (IK) problem. In this method, the transformation from Cartesian space to joint space is performed in a feedback loop and as a result the new feedback inverse kinematics (FIK) law operates as a filter and does not require matrix manipulations (inversion, singular value decomposition or a computation of a damping factor). While the computational demand is greatly reduced, the performance is comparable to the one delivered by the damped least squares (DLS) law. The new algorithm is capable of escaping and avoiding kinematic singularities and in this respect it outperforms pseudo-inverse based formulations

Vision-Based Hybrid Controller to Release a 4-DOF Parallel Robot from a Type II Singularity

[EN] The high accuracy and dynamic performance of parallel robots (PRs) make them suitable to ensure safe operation in human¿robot interaction. However, these advantages come at the expense of a reduced workspace and the possible appearance of type II singularities. The latter is due to the loss of control of the PR and requires further analysis to keep the stiffness of the PR even after a singular configuration is reached. All or a subset of the limbs could be responsible for a type II singularity, and they can be detected by using the angle between two output twist screws (OTSs). However, this angle has not been applied in control because it requires an accurate measure of the pose of the PR. This paper proposes a new hybrid controller to release a 4-DOF PR from a type II singularity based on a real time vision system. The vision system data are used to automatically readapt the configuration of the PR by moving the limbs identified by the angle between two OTSs. This controller is intended for a knee rehabilitation PR, and the results show how this release is accomplished with smooth controlled movements where the patient¿s safety is not compromised.This research was funded by the FEDER-CICYT project with reference PID2020-119522RBI00 (ROBOTS PARALELOS DE REHABILITACION: DETECCION Y CONTROL DE SINGULARIDADES EN PRESENCIA DE ERRORES DE MANUFACTURA), Spain.Pulloquinga-Zapata, J.; Escarabajal-Sánchez, RJ.; Ferrándiz, J.; Vallés Miquel, M.; Mata Amela, V.; Urízar, M. (2021). Vision-Based Hybrid Controller to Release a 4-DOF Parallel Robot from a Type II Singularity. Sensors. 21(12):1-21. https://doi.org/10.3390/s21124080121211

Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas

The main interest of this thesis consists of the study and implementation of postprocessors to adapt the toolpath generated by a Computer Aided Manufacturing (CAM) system to a complex robotic workcell of eight joints, devoted to the rapid prototyping of 3D CAD-defined products. It consists of a 6R industrial manipulator mounted on a linear track and synchronized with a rotary table. To accomplish this main objective, previous work is required. Each task carried out entails a methodology, objective and partial results that complement each other, namely: - It is described the architecture of the workcell in depth, at both displacement and joint-rate levels, for both direct and inverse resolutions. The conditioning of the Jacobian matrix is described as kinetostatic performance index to evaluate the vicinity to singular postures. These ones are analysed from a geometric point of view. - Prior to any machining, the additional external joints require a calibration done in situ, usually in an industrial environment. A novel Non-contact Planar Constraint Calibration method is developed to estimate the external joints configuration parameters by means of a laser displacement sensor. - A first control is originally done by means of a fuzzy inference engine at the displacement level, which is integrated within the postprocessor of the CAM software. - Several Redundancy Resolution Schemes (RRS) at the joint-rate level are compared for the configuration of the postprocessor, dealing not only with the additional joints (intrinsic redundancy) but also with the redundancy due to the symmetry on the milling tool (functional redundancy). - The use of these schemes is optimized by adjusting two performance criterion vectors related to both singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done during the path tracking. Two innovative fuzzy inference engines actively adjust the weight of each joint in these tasks.Andrés De La Esperanza, FJ. (2011). Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10627Palanci

Multi-robot cooperative platform : a task-oriented teleoperation paradigm

This thesis proposes the study and development of a teleoperation system based on multi-robot cooperation under the task oriented teleoperation paradigm: Multi-Robot Cooperative Paradigm, MRCP. In standard teleoperation, the operator uses the master devices to control the remote slave robot arms. These arms reproduce the desired movements and perform the task. With the developed work, the operator can virtually manipulate an object. MRCP automatically generates the arms orders to perform the task. The operator does not have to solve situations arising from possible restrictions that the slave arms may have. The research carried out is therefore aimed at improving the accuracy teleoperation tasks in complex environments, particularly in the field of robot assisted minimally invasive surgery. This field requires patient safety and the workspace entails many restrictions to teleoperation. MRCP can be defined as a platform composed of several robots that cooperate automatically to perform a teleoperated task, creating a robotic system with increased capacity (workspace volume, accessibility, dexterity ...). The cooperation is based on transferring the task between robots when necessary to enable a smooth task execution. The MRCP control evaluates the suitability of each robot to continue with the ongoing task and the optimal time to execute a task transfer between the current selected robot and the best candidate to continue with the task. From the operator¿s point of view, MRCP provides an interface that enables the teleoperation though the task-oriented paradigm: operator orders are translated into task actions instead of robot orders. This thesis is structured as follows: The first part is dedicated to review the current solutions in the teleoperation of complex tasks and compare them with those proposed in this research. The second part of the thesis presents and reviews in depth the different evaluation criteria to determine the suitability of each robot to continue with the execution of a task, considering the configuration of the robots and emphasizing the criterion of dexterity and manipulability. The study reviews the different required control algorithms to enable the task oriented telemanipulation. This proposed teleoperation paradigm is transparent to the operator. Then, the Thesis presents and analyses several experimental results using MRCP in the field of minimally invasive surgery. These experiments study the effectiveness of MRCP in various tasks requiring the cooperation of two hands. A type task is used: a suture using minimally invasive surgery technique. The analysis is done in terms of execution time, economy of movement, quality and patient safety (potential damage produced by undesired interaction between the tools and the vital tissues of the patient). The final part of the thesis proposes the implementation of different virtual aids and restrictions (guided teleoperation based on haptic visual and audio feedback, protection of restricted workspace regions, etc.) using the task oriented teleoperation paradigm. A framework is defined for implementing and applying a basic set of virtual aids and constraints within the framework of a virtual simulator for laparoscopic abdominal surgery. The set of experiments have allowed to validate the developed work. The study revealed the influence of virtual aids in the learning process of laparoscopic techniques. It has also demonstrated the improvement of learning curves, which paves the way for its implementation as a methodology for training new surgeons.Aquesta tesi doctoral proposa l'estudi i desenvolupament d'un sistema de teleoperació basat en la cooperació multi-robot sota el paradigma de la teleoperació orientada a tasca: Multi-Robot Cooperative Paradigm, MRCP. En la teleoperació clàssica, l'operador utilitza els telecomandaments perquè els braços robots reprodueixin els seus moviments i es realitzi la tasca desitjada. Amb el treball realitzat, l'operador pot manipular virtualment un objecte i és mitjançant el MRCP que s'adjudica a cada braç les ordres necessàries per realitzar la tasca, sense que l'operador hagi de resoldre les situacions derivades de possibles restriccions que puguin tenir els braços executors. La recerca desenvolupada està doncs orientada a millorar la teleoperació en tasques de precisió en entorns complexos i, en particular, en el camp de la cirurgia mínimament invasiva assistida per robots. Aquest camp imposa condicions de seguretat del pacient i l'espai de treball comporta moltes restriccions a la teleoperació. MRCP es pot definir com a una plataforma formada per diversos robots que cooperen de forma automàtica per dur a terme una tasca teleoperada, generant un sistema robòtic amb capacitats augmentades (volums de treball, accessibilitat, destresa,...). La cooperació es basa en transferir la tasca entre robots a partir de determinar quin és aquell que és més adequat per continuar amb la seva execució i el moment òptim per realitzar la transferència de la tasca entre el robot actiu i el millor candidat a continuar-la. Des del punt de vista de l'operari, MRCP ofereix una interfície de teleoperació que permet la realització de la teleoperació mitjançant el paradigma d'ordres orientades a la tasca: les ordres es tradueixen en accions sobre la tasca en comptes d'estar dirigides als robots. Aquesta tesi està estructurada de la següent manera: Primerament es fa una revisió de l'estat actual de les diverses solucions desenvolupades actualment en el camp de la teleoperació de tasques complexes, comparant-les amb les proposades en aquest treball de recerca. En el segon bloc de la tesi es presenten i s'analitzen a fons els diversos criteris per determinar la capacitat de cada robot per continuar l'execució d'una tasca, segons la configuració del conjunt de robots i fent especial èmfasi en el criteri de destresa i manipulabilitat. Seguint aquest estudi, es presenten els diferents processos de control emprats per tal d'assolir la telemanipulació orientada a tasca de forma transparent a l'operari. Seguidament es presenten diversos resultats experimentals aplicant MRCP al camp de la cirurgia mínimament invasiva. En aquests experiments s'estudia l'eficàcia de MRCP en diverses tasques que requereixen de la cooperació de dues mans. S'ha escollit una tasca tipus: sutura amb tècnica de cirurgia mínimament invasiva. L'anàlisi es fa en termes de temps d'execució, economia de moviment, qualitat i seguretat del pacient (potencials danys causats per la interacció no desitjada entre les eines i els teixits vitals del pacient). Finalment s'ha estudiat l'ús de diferents ajudes i restriccions virtuals (guiat de la teleoperació via retorn hàptic, visual o auditiu, protecció de regions de l'espai de treball, etc) dins el paradigma de teleoperació orientada a tasca. S'ha definint un marc d'aplicació base i implementant un conjunt de restriccions virtuals dins el marc d'un simulador de cirurgia laparoscòpia abdominal. El conjunt d'experiments realitzats han permès validar el treball realitzat. Aquest estudi ha permès determinar la influencia de les ajudes virtuals en el procés d'aprenentatge de les tècniques laparoscòpiques. S'ha evidenciat una millora en les corbes d'aprenentatge i obre el camí a la seva implantació com a metodologia d'entrenament de nous cirurgians.Postprint (published version