Aerial Cable Towed Systems (ACTS) are composed of several Unmanned Aerial Vehicles (UAVs) connected to a payload by cables. Compared to towing objects from individual aerial vehicles, an ACTS has significant advantages such as heavier payload capacity, modularity, and full control of the payload pose. They are however generally large with limited ability to meet geometric constraints while avoiding collisions between UAVs. This paper presents the modelling, performance analysis, design, and a proposed controller for a novel ACTS with variable cable lengths, named Variable Aerial Cable Towed System (VACTS).Winches are embedded on the UAVs for actuating the cable lengths similar to a Cable-Driven Parallel Robot to increase the versatility of the ACTS. The general geometric, kinematic and dynamic models of the VACTS are derived, followed by the development of a centralized feedback linearization controller. The design is based on a wrench analysis of the VACTS, without constraining the cables to pass through the UAV center of mass, as in current works. Additionally, the performance of the VACTS and ACTS are compared showing that the added versatility comes at the cost of payload and configuration flexibility. A prototype confirms the feasibility of the system.

The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material points onto their closest states in the material data set. In this study, we compare and develop several possible data structures for solving the nearest-neighbor problem. We show that approximate nearest-neighbor (ANN) algorithms can accelerate material data searches by several orders of magnitude relative to exact searching algorithms. The approximations are suggested by--and adapted to--the structure of the data-driven iterative solver and result in no significant loss of solution accuracy. We assess the performance of the ANN algorithm with respect to material data set size with the aid of a 3D elasticity test case. We show that computations on a single processor with up to one billion material data points are feasible within a few seconds execution time with a speedup of more than 106 with respect to exact k-d trees.

This paper investigates a situation pointed out in a recent paper, in which a non-singular change of assembly mode of a planar 2-RPR-PR parallel manipulator was realized by encircling a point of multiplicity 4. It is shown that this situation is, in fact, a non-generic one and gives rise to cusps under a small perturbation. Furthermore , we show that, for a large class of singularities of multiplicity 4, there are only two types of stable singularities occurring in a small perturbation: these two types are given by the complex square mapping and the quarto mapping. Incidentally , this paper confirms the fact that, generically, a local non-singular change of solution must be accomplished by encircling a cusp point.

This paper establishes a complete framework for infinitely nested logarithmic improvements to regularity criteria for the three-dimensional incompressible Navier-Stokes equations. Building upon our previous works on logarithmically improved and multi-level logarithmically improved criteria, we demonstrate that the limiting case of infinitely nested logarithms fully bridges the gap between subcritical and critical regularity. Specifically, we prove that if the initial data $u_0 \in L^2(\mathbb{R}^3)$ satisfies the condition $\|(-\Delta)^{1/4}u_0\|_{L^q(\mathbb{R}^3)} \leq C_0\Psi(\|u_0\|_{\dot{H}^{1/2}})$, where$\Psi$ incorporates infinitely nested logarithmic factors with appropriate decay conditions, then there exists a unique global-in-time smooth solution to the Navier-Stokes equations. This result establishes global well-posedness at the critical regularity threshold $s = 1/2$. The proof relies on infinitely nested commutator estimates, precise characterization of the critical exponent function in the limiting case, and careful analysis of the energy cascade. We also derive the exact Hausdorff dimension bound for potential singular sets in this limiting case, proving that the dimension reduces to zero. Through systematic construction of the limiting function spaces and detailed analysis of the associated ODEs, we demonstrate that infinitely nested logarithmic improvements provide a pathway to resolving the global regularity question for the Navier-Stokes equations.

Quadruped robots are currently a widespread platform for robotics research, thanks to powerful Reinforcement Learning controllers and the availability of cheap and robust commercial platforms. However, to broaden the adoption of the technology in the real world, we require robust navigation stacks relying only on low-cost sensors such as depth cameras. This paper presents a first step towards a robust localization, mapping, and navigation system for low-cost quadruped robots. In pursuit of this objective we combine contact-aided kinematic, visual-inertial odometry, and depth-stabilized vision, enhancing stability and accuracy of the system. Our results in simulation and two different real-world quadruped platforms show that our system can generate an accurate 2D map of the environment, robustly localize itself, and navigate autonomously. Furthermore, we present in-depth ablation studies of the important components of the system and their impact on localization accuracy. Videos, code, and additional experiments can be found on the project website: this https URL

This paper addresses the domain shift problem for segmentation. As a solution, we propose OLVA, a novel and lightweight unsupervised domain adaptation method based on a Variational Auto-Encoder (VAE) and Optimal Transport (OT) theory. Thanks to the VAE, our model learns a shared cross-domain latent space that follows a normal distribution, which reduces the domain shift. To guarantee valid segmentations, our shared latent space is designed to model the shape rather than the intensity variations. We further rely on an OT loss to match and align the remaining discrepancy between the two domains in the latent space. We demonstrate OLVA's effectiveness for the segmentation of multiple cardiac structures on the public Multi-Modality Whole Heart Segmentation (MM-WHS) dataset, where the source domain consists of annotated 3D MR images and the unlabelled target domain of 3D CTs. Our results show remarkable improvements with an additional margin of 12.5\% dice score over concurrent generative training approaches.

The rat race between user-generated data and data-processing systems is currently won by data. The increased use of machine learning leads to further increase in processing requirements, while data volume keeps growing. To win the race, machine learning needs to be applied to the data as it goes through the network. In-network classification of data can reduce the load on servers, reduce response time and increase scalability. In this paper, we introduce IIsy, implementing machine learning classification models in a hybrid fashion using off-the-shelf network devices. IIsy targets three main challenges of in-network classification: (i) mapping classification models to network devices (ii) extracting the required features and (iii) addressing resource and functionality constraints. IIsy supports a range of traditional and ensemble machine learning models, scaling independently of the number of stages in a switch pipeline. Moreover, we demonstrate the use of IIsy for hybrid classification, where a small model is implemented on a switch and a large model at the backend, achieving near optimal classification results, while significantly reducing latency and load on the servers.

We present an accurate, fast and efficient method for segmentation and muscle mask propagation in 3D freehand ultrasound data, towards accurate volume quantification. A deep Siamese 3D Encoder-Decoder network that captures the evolution of the muscle appearance and shape for contiguous slices is deployed. We uses it to propagate a reference mask annotated by a clinical expert. To handle longer changes of the muscle shape over the entire volume and to provide an accurate propagation, we devise a Bidirectional Long Short Term Memory module. Also, to train our model with a minimal amount of training samples, we propose a strategy combining learning from few annotated 2D ultrasound slices with sequential pseudo-labeling of the unannotated slices. We introduce a decremental update of the objective function to guide the model convergence in the absence of large amounts of annotated data. After training with a small number of volumes, the decremental update transitions from a weakly-supervised training to a few-shot setting. Finally, to handle the class-imbalance between foreground and background muscle pixels, we propose a parametric Tversky loss function that learns to adaptively penalize false positives and false negatives. We validate our approach for the segmentation, label propagation, and volume computation of the three low-limb muscles on a dataset of 61600 images from 44 subjects. We achieve a Dice score coefficient of over $95~\%$ and a volumetric error \textcolor{black}{of} $1.6035 \pm 0.587~\%$.

Cloud-to-ground lightning strikes observed in a specific geographical domain over time can be naturally modeled by a spatio-temporal point process. Our focus lies in the parametric estimation of its intensity function, incorporating both spatial factors (such as altitude) and spatio-temporal covariates (such as field temperature, precipitation, etc.). The events are observed in France over a span of three years. Spatio-temporal covariates are observed with resolution $0.1^\circ \times 0.1^\circ$ ($\approx 100$km$^2$) and six-hour periods. This results in an extensive dataset, further characterized by a significant excess of zeroes (i.e., spatio-temporal cells with no observed events). We reexamine composite likelihood methods commonly employed for spatial point processes, especially in situations where covariates are piecewise constant. Additionally, we extend these methods to account for zero-deflated subsampling, a strategy involving dependent subsampling, with a focus on selecting more cells in regions where events are observed. A simulation study is conducted to illustrate these novel methodologies, followed by their application to the dataset of lightning strikes.

Occlusion presents a significant challenge for safety-critical applications such as autonomous driving. Collaborative perception has recently attracted a large research interest thanks to the ability to enhance the perception of autonomous vehicles via deep information fusion with intelligent roadside units (RSU), thus minimizing the impact of occlusion. While significant advancement has been made, the data-hungry nature of these methods creates a major hurdle for their real-world deployment, particularly due to the need for annotated RSU data. Manually annotating the vast amount of RSU data required for training is prohibitively expensive, given the sheer number of intersections and the effort involved in annotating point clouds. We address this challenge by devising a label-efficient object detection method for RSU based on unsupervised object discovery. Our paper introduces two new modules: one for object discovery based on a spatial-temporal aggregation of point clouds, and another for refinement. Furthermore, we demonstrate that fine-tuning on a small portion of annotated data allows our object discovery models to narrow the performance gap with, or even surpass, fully supervised models. Extensive experiments are carried out in simulated and real-world datasets to evaluate our method.

This work presents the development of a parallel manipulator used for otological surgery from the perspective of co-design. Co-design refers to the simultaneous involvement of the end-users (surgeons), stakeholders (designers, ergonomic experts, manufacturers), and experts from the fields of optimization and mechanisms. The role of each member is discussed in detail and the interactions between the stakeholders are presented. Co-design facilitates a reduction in the parameter space considered during mechanism optimization, leading to a more efficient design process. Additionally, the co-design principles help avoid unforeseen errors and help in quicker adaptation of the proposed solution.

We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.

This paper introduces a novel class of initial data for which the three-dimensional incompressible Navier--Stokes equations yield unique global-in-time solutions. Building on a logarithmically improved regularity criterion, we impose a logarithmically subcritical condition on the initial data. Specifically, if \[ u_0 \in L^2(\mathbb{R}^3) \quad \text{and} \quad \|(-\Delta)^{s/2}u_0\|_{L^q(\mathbb{R}^3)} \le \frac{C_0}{\Bigl(1+\log\bigl(e+\|u_0\|_{\dot{H}^s}\bigr)\Bigr)^{\delta}}, \] for some $s \in (1/2,1)$ under appropriate scaling, then the corresponding solution exists globally and is unique. The proof employs refined commutator estimates for the fractional Laplacian together with new energy methods that exploit this logarithmic improvement to prevent singularity formation. Furthermore, we establish links between these improved criteria and turbulence theory. We derive precise relationships connecting the regularity conditions with turbulent intermittency, showing that the logarithmic enhancements correspond to anomalous scaling exponents in the turbulent energy spectrum. Additionally, we characterize the local structure of potential singularities and provide tight bounds on the energy flux in turbulent cascades. This approach bridges the gap between subcritical and critical regularity for the Navier--Stokes equations and offers a robust mathematical foundation for key phenomena observed in turbulence.

This paper extends our previous results on logarithmically improved regularity criteria for the three-dimensional Navier-Stokes equations by establishing a comprehensive framework of multi-level logarithmic improvements. We prove that if the initial data $u_0 \in L^2(\mathbb{R}^3)$ satisfies a nested logarithmically weakened condition $\|(-\Delta)^{s/2}u_0\|_{L^q(\mathbb{R}^3)} \leq \frac{C_0}{\prod_{j=1}^{n} (1 + L_j(\|u_0\|_{\dot{H}^s}))^{\delta_j}}$for some$s \in (1/2, 1)$, where$L_j$ represents $j$-fold nested logarithms, then the corresponding solution exists globally in time and is unique. The proof introduces a novel sequence of increasingly precise commutator estimates incorporating multiple layers of logarithmic corrections. We establish the existence of a critical threshold function $\Phi(s,q,\{\delta_j\}_{j=1}^n)$ that completely characterizes the boundary between global regularity and potential singularity formation, with explicit asymptotics as $s$ approaches the critical value $1/2$. This paper further provides a rigorous geometric characterization of potential singular structures through refined multi-fractal analysis, showing that any singular set must have Hausdorff dimension bounded by $1 - \sum_{j=1}^n \frac{\delta_j}{1+\delta_j} \cdot \frac{1}{j+1}$. Our results constitute a significant advancement toward resolving the global regularity question for the Navier-Stokes equations, as we demonstrate that with properly calibrated sequences of nested logarithmic improvements, the gap to the critical case can be systematically reduced.

Muscle fatigue is defined as the point at which the muscle is no longer able to sustain the required force or work output level. The overexertion of muscle force and muscle fatigue can induce acute pain and chronic pain in human body. When muscle fatigue is accumulated, the functional disability can be resulted as musculoskeletal disorders (MSD). There are several posture exposure analysis methods useful for rating the MSD risks, but they are mainly based on static postures. Even in some fatigue evaluation methods, muscle fatigue evaluation is only available for static postures, but not suitable for dynamic working process. Meanwhile, some existing muscle fatigue models based on physiological models cannot be easily used in industrial ergonomic evaluations. The external dynamic load is definitely the most important factor resulting muscle fatigue, thus we propose a new fatigue model under a framework for evaluating fatigue in dynamic working processes. Under this framework, virtual reality system is taken to generate virtual working environment, which can be interacted with the work with haptic interfaces and optical motion capture system. The motion information and load information are collected and further processed to evaluate the overall work load of the worker based on dynamic muscle fatigue models and other work evaluation criterions and to give new information to characterize the penibility of the task in design process.

Automated verification of living organism models allows us to gain previously unknown knowledge about underlying biological processes. In this paper, we show the benefits to use parametric time Petri nets in order to analyze precisely the dynamic behavior of biological oscillatory systems. In particular, we focus on the resilience properties of such systems. This notion is crucial to understand the behavior of biological systems (e.g. the mammalian circadian rhythm) that are reactive and adaptive enough to endorse major changes in their environment (e.g. jet-lags, day-night alternating work-time). We formalize these properties through parametric TCTL and demonstrate how changes of the environmental conditions can be tackled to guarantee the resilience of living organisms. In particular, we are able to discuss the influence of various perturbations, e.g. artificial jet-lag or components knock-out, with regard to quantitative delays. This analysis is crucial when it comes to model elicitation for dynamic biological systems. We demonstrate the applicability of this technique using a simplified model of circadian clock.

In autonomous robotics, a critical challenge lies in developing robust solutions for Active Collaborative SLAM, wherein multiple robots collaboratively explore and map an unknown environment while intelligently coordinating their movements and sensor data acquisitions. In this article, we present an efficient centralized frontier sharing approach that maximizes exploration by taking into account information gain in the merged map, distance, and reward computation among frontier candidates and encourages the spread of agents into the environment. Eventually, our method efficiently spreads the robots for maximum exploration while keeping SLAM uncertainty low. Additionally, we also present two coordination approaches, synchronous and asynchronous to prioritize robot goal assignments by the central server. The proposed method is implemented in ROS and evaluated through simulation and experiments on publicly available datasets and similar methods, rendering promising results.

Cable-Driven Parallel Robots (CDPRs) offer high payload capacities, large translational workspace and high dynamic performances. The rigid base frame of the CDPR is connected in parallel to the moving platform using cables. However, their orientation workspace is usually limited due to cable/cable and cable/moving platform collisions. This paper deals with the design, modelling and prototyping of a hybrid robot. This robot, which is composed of a CDPR mounted in series with a Parallel Spherical Wrist (PSW), has both a large translational workspace and an unlimited orientation workspace. It should be noted that the six degrees of freedom (DOF) motions of the moving platform of the CDPR, namely, the base of the PSW, and the three-DOF motion of the PSW are actuated by means of eight actuators fixed to the base. As a consequence, the overall system is underactuated and its total mass and inertia in motion is reduced.

This paper is about the stabilization of a cascade system composed by an infinite-dimensional system, that we suppose to be exponentially stable, and an ordinary differential equation (ODE), that we suppose to be marginally stable. The system is controlled through the infinite-dimensional system. Such a structure is particularly useful when applying the internal model approach on infinite-dimensional systems. Our strategy relies on the forwarding method, which uses a Lyapunov functional and a Sylvester equation to build a feedback-law. Under some classical assumptions in the output regulation theory, we prove that the closed-loop system is globally exponentially stable.

We consider flows of ordinary differential equations (ODEs) driven by path differentiable vector fields. Path differentiable functions constitute a proper subclass of Lipschitz functions which admit conservative gradients, a notion of generalized derivative compatible with basic calculus rules. Our main result states that such flows inherit the path differentiability property of the driving vector field. We show indeed that forward propagation of derivatives given by the sensitivity differential inclusions provide a conservative Jacobian for the flow. This allows to propose a nonsmooth version of the adjoint method, which can be applied to integral costs under an ODE constraint. This result constitutes a theoretical ground to the application of small step first order methods to solve a broad class of nonsmooth optimization problems with parametrized ODE constraints. This is illustrated with the convergence of small step first order methods based on the proposed nonsmooth adjoint.