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© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/)., The roots of the closure polynomial associated with a given mechanism determine its assembly modes. In the case of 6R closed-loop mechanisms, these polynomials are usually expressed in the half-angle tangent of one of its joints. In this paper, we derive closure polynomials of 6R robots in terms of distances, not angles. The use of a distance-based formulation provides, in general, a fundamental advantage since it leads to closure conditions without requiring neither variable eliminations nor variable substitutions. We restrict our attention, though, to robots with coplanar consecutive joint axes, i.e., robots whose consecutive axes intersect at either proper or improper points. We show that this particular arrangement of joints does not result in a reduction in the maximum number of the inverse kinematic solutions with respect to the general case. Moreover, this family of robots include broadly used offset-wrist arms. For instance, in this paper, we obtain closure polynomials for robots such as the FANUC CRX-10iA/L, the UR10e, and the KUKA LBR iiwa R800 robot in generic form (i.e., as a function of their end-effector locations)., acknowledge the financial support of the Spanish National Plan for Scientific and Technical Research and Innovation through project PID2020-117509GB-I00/MCIN/AEI/10.13039/50110001103, Peer Reviewed, Postprint (published version)

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd., In this paper, we address the problem of restoring the orthogonality of a numerically noisy 4D rotation matrix by finding its nearest (in Frobenius norm) correct rotation matrix. This problem can be straightforwardly solved using the Singular Value Decomposition (SVD). Nevertheless, to avoid numerical methods, we present two new closed-form methods. One relies on the direct minimization of the mentioned Frobenius norm, and the other on the passage to double quaternion representation. A comparison of these two methods with respect to the SVD reveals that the method based on a double quaternion representation is superior in all aspects., Spanish Ministry of Economy andCompetitiveness, Grant/Award Number:PID2020-117509GB-I00/AEI/10.13039/50110001103, Peer Reviewed, Postprint (published version)

Background: The noninflammatory immunoglobulin G4 (IgG4) is linked to tolerance and is unique to humans. Although poorly understood, prolonged antigenic stimulation and IL-4-signaling along the T helper 2-axis may be instrumental in IgG4 class switching. Recently, repeated SARS-CoV-2 mRNA vaccination has been linked to IgG4 skewing. Although widely used immunosuppressive drugs have been shown to only moderately affect humoral responses to SARS-CoV-2 mRNA vaccination, the effect on IgG4 switching has not been investigated. Methods: Here we study the impact of such immunosuppressive drugs, including the IL-4 receptor-blocking antibody dupilumab, on IgG4 skewing upon repeated SARS-CoV-2 mRNA vaccination. Receptor-binding domain (RBD) specific antibody responses were longitudinally measured in 600 individuals, including patients with immune-mediated inflammatory diseases treated with a TNF inhibitor (TNFi) and/or methotrexate (MTX), dupilumab, and healthy/untreated controls, after repeated mRNA vaccination. Results: We observed a substantial increase in the proportion of RBD-specific IgG4 antibodies (median 21%) in healthy/untreated controls after third vaccination. This IgG4 skewing was profoundly reduced in dupilumab-treated patients (<1%). Unexpectedly, an equally strong suppression of IgG4 skewing was observed in TNFi-treated patients (<1%), whereas MTX caused a modest reduction (7%). RBD-specific total IgG levels were hardly affected by these immunosuppressive drugs. Minimal skewing was observed, when primary vaccination was adenoviral vector-based. Conclusions: Our results imply a critical role for IL-4/IL-13 as well as TNF in vivo IgG4 class switching. These novel findings advance our understanding of IgG4 class switch dynamics, and may benefit humoral tolerance induction strategies, treatment of IgG4 pathologies and mRNA vaccine optimization.

It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are often governed by a second or higher order ODE involving configuration variables and their time derivatives. To apply a collocation method, therefore, the usual practice is to resort to the well known procedure of casting an Mth order ODE into M first order ones. This manipulation, which in the continuous domain is perfectly valid, leads to inconsistencies when the problem is discretized. Since the configuration variables and their time derivatives are approximated with polynomials of the same degree, their differential dependencies cannot be fulfilled, and the actual dynamics is not satisfied, not even at the collocation points. This paper draws attention to this problem, and develops improved versions of the trapezoidal and Hermite-Simpson collocation methods that do not present these inconsistencies. In many cases, the new methods reduce the dynamic transcription error in one order of magnitude, or even more, without noticeably increasing the cost of computing the solutions., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been partially funded by Agencia Estatal de Investigación under project Kinodyn+, with reference PID2020-117509GB-I00/AEI /10.13039/50110001103, and by a Ph.D. contract supporting the first author, with reference PRE2018-085582., Peer Reviewed, Postprint (published version)

© 2023 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., It is well known that the singularities of a Gough-Stewart platform arise when the determinant of the Plücker coordinates of the robot leg lines vanish. The direct expansion of this determinant in terms of the configuration of the moving platform leads to an intimidating algebraic expression which is difficult to organize in a manner that facilitates extracting geometric conditions for singularities to occur. The use of Grassmann-Cayley algebra has permitted expressing this determinant as a bracket polynomial which is easier to manipulate symbolically. Each monomial in this polynomial is the product of three brackets, 4×4 determinants involving the homogeneous coordinates of four leg attachments. In this paper, we show how to derive, using elementary linear algebra arguments, bracket polynomials where all brackets can be interpreted as reciprocal products between lines. Contrarily to what one might expect, these new bracket polynomials are simpler in general than those previously obtained using Grassmann-Cayley algebra., This work was partially supported by the Spanish Government through project PID2020-117509GB-I00/AEI/10.13039/50110001103., Peer Reviewed, Postprint (author's final draft)

© 2023 by the authors, Several clinical trials are working on drug development for Duchenne and Becker muscular dystrophy (DMD and BMD) treatment, and, since the expected increase in dystrophin is relatively subtle, high-sensitivity quantification methods are necessary. There is also a need to quantify dystrophin to reach a definitive diagnosis in individuals with mild BMD, and in female carriers. We developed a method for the quantification of dystrophin in DMD and BMD patients using spectral confocal microscopy. It offers the possibility to capture the whole emission spectrum for any antibody, ensuring the selection of the emission peak and allowing the detection of fluorescent emissions of very low intensities. Fluorescence was evaluated first on manually selected regions of interest (ROIs), proving the usefulness of the methodology. Later, ROI selection was automated to make it operator-independent. The proposed methodology correctly classified patients according to their diagnosis, detected even minimal traces of dystrophin, and the results obtained automatically were statistically comparable to the manual ones. Thus, spectral imaging could be implemented to measure dystrophin expression and it could pave the way for detailed analysis of how its expression relates to the clinical course. Studies could be further expanded to better understand the expression of dystrophin-associated protein complexes (DAPCs)., This research was partially founded by “Somriures Valents” (private grant)., Peer Reviewed, Postprint (published version)

Recognition of the untapped potential of photosynthesis to improve crop yields has spurred research to identify targets for breeding. The CO2-fixing enzyme Rubisco is characterised by a number of inefficiencies and frequently limits carbon assimilation at the top of the canopy, representing a clear target for wheat improvement. Two bread wheat lines with similar genetic backgrounds and contrasting in vivo maximum carboxylation activity of Rubisco per unit leaf nitrogen (Vc,max,25/Narea) determined using high throughput phenotyping methods were selected for detailed study from a panel of 80 spring wheat lines. Detailed phenotyping of photosynthetic traits in the two lines using glasshouse-grown plants showed no difference in Vc,max,25/Narea determined directly via in vivo and in vitro methods. Detailed phenotyping of glasshouse-grown plants of the 80 wheat lines also showed no correlation between photosynthetic traits measured via high throughput phenotyping of field-grown plants. Our findings suggest that the complex interplay between traits determining crop productivity and the dynamic environments experienced by field-grown plants needs to be considered when designing strategies for effective wheat crop yield improvement when breeding for particular environments

© 2022 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., Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained mechanical systems, i.e., those whose state coordinates are subject to holonomic or nonholonomic constraints, such as loop-closure or rolling-contact constraints. These constraints confine the robot trajectories to an implicitly-defined manifold, which complicates the computation of accurate solutions. Discretization errors inherent to the transcription of the problem easily make the trajectories drift away from this manifold, which results in physically inconsistent motions that are difficult to track with a controller. This article reviews existing methods to deal with this problem and proposes new ones to overcome their limitations. Current approaches either disregard the kinematic constraints (which leads to drift accumulation) or modify the system dynamics to keep the trajectory close to the manifold (which adds artificial forces or energy dissipation to the system). The methods we propose, in contrast, achieve full drift elimination on the discrete trajectory, or even along the continuous one, without artificial modifications of the system dynamics. We illustrate and compare the methods using various examples of different complexity., This work was supported in part by the Spanish Ministry of Science, Innovation, and Universities under Project DPI2017-88282-P and Project PID2020-117509GBI00/AEI/10.13039/50110001103 and in part by the German Federal Ministry for Economic Affairs and Energy (BMWi) via DyConPV (0324166B), Peer Reviewed, Postprint (author's final draft)

© 2022 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, Pseudospectral collocation methods have proven to be powerful tools to solve optimal control problems. While these methods generally assume the dynamics is given in the first order form xdot = f(x, u, t), where x is the state and u is the control vector, robotic systems are typically governed by second order ODEs of the form qddot = g(q, qdot, u, t), where q is the configuration. To convert the second order ODE into a first order one, the usual approach is to introduce a velocity variable v and impose its coincidence with the time derivative of q. Lobatto methods grant this constraint by construction, as their polynomials describing the trajectory for v are the time derivatives of those for q, but the same cannot be said for the Gauss and Radau methods. This is problematic for such methods, as then they cannot guarantee that qddot = g(q, qdot, u, t) at the collocation points. On their negative side, Lobatto methods cannot be used to solve initial value problems, as given the values of u at the collocation points they generate an overconstrained system of equations for the states. In this paper, we propose a Legendre-Gauss collocation method that retains the advantages of the usual Lobatto, Gauss, and Radau methods, while avoiding their shortcomings. The collocation scheme we propose is applicable to solve initial value problems, preserves the consistency between the polynomials for v and q, and ensures that qddot = g(q, qdot, u, t) at the collocation points., Peer Reviewed, Postprint (author's final draft)

© 2022 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, No proper norm exists to measure the distance between two object poses essentially because a general pose is defined by a rotation and a translation, and thus it involves magnitudes with different units. As a means to solve this dimensional-inhomogeneity problem, the concept of characteristic length has been put forward in the area of kinematics. The idea consists in scaling translations according to this characteristic length and then approximating the corresponding displacement defining the object pose in R^3 by a rotation in R^4, for which a norm exists. This paper sheds new light on this kind of approximations which permits simplifying optimization problem whose cost functions involve translations and rotations simultaneously. A good example of this kind of problems is the pointcloud registration problem in which the optimal rotation and translation between two sets of corresponding 3D point data, so that they are aligned/registered, have to be found. As a result, a simple closed-form formula for solving this problem is presented which is shown to be an attractive alternative to the previous approaches., Peer Reviewed, Postprint (author's final draft)