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Visual Odometry (VO) and Visual SLAM (V-SLAM) systems often struggle in low-light and dark environments due to the lack of robust visual features. In this paper, we propose a novel active illumination framework to enhance the performance of VO and V-SLAM algorithms in these challenging conditions. The developed approach dynamically controls a moving light source to illuminate highly textured areas, thereby improving feature extraction and tracking. Specifically, a detector block, which incorporates a deep learning-based enhancing network, identifies regions with relevant features. Then, a pan-tilt controller is responsible for guiding the light beam toward these areas, so that to provide information-rich images to the ego-motion estimation algorithm. Experimental results on a real robotic platform demonstrate the effectiveness of the proposed method, showing a reduction in the pose estimation error up to 75% with respect to a traditional fixed lighting technique.

The study of algebraic curves $\cX$ with numerous automorphisms in relation to their genus $g(\cX)$ is a well-established area in Algebraic Geometry. In 1995, Irokawa and Sasaki \cite{Sasaki} gave a complete classification of curves over $\mathbb{C}$ with an automorphism of order $N \geq 2g(\mathcal{X}) + 1$. Precisely, such curves are either hyperelliptic with $N=2g(\cX)+2$ with $g(\cX)$ even, or are quotients of the Fermat curve of degree $N$ by a cyclic group of order $N$. Such a classification does not hold in positive characteristic $p$, the curve with equation $y^2=x^p-x$ being a well-studied counterexample. This paper successfully classifies curves with a cyclic automorphism group of order $N$ at least $2g(\mathcal{X}) + 1$ in positive characteristic $p \neq 2$, offering the positive characteristic counterpart to the Irokawa-Sasaki result. The possibility of wild ramification in positive characteristic has presented a few challenges to the investigation.

In the last decade, data-driven approaches have become popular choices for quadrotor control, thanks to their ability to facilitate the adaptation to unknown or uncertain flight conditions. Among the different data-driven paradigms, Deep Reinforcement Learning (DRL) is currently one of the most explored. However, the design of DRL agents for Micro Aerial Vehicles (MAVs) remains an open challenge. While some works have studied the output configuration of these agents (i.e., what kind of control to compute), there is no general consensus on the type of input data these approaches should employ. Multiple works simply provide the DRL agent with full state information, without questioning if this might be redundant and unnecessarily complicate the learning process, or pose superfluous constraints on the availability of such information in real platforms. In this work, we provide an in-depth benchmark analysis of different configurations of the observation space. We optimize multiple DRL agents in simulated environments with different input choices and study their robustness and their sim-to-real transfer capabilities with zero-shot adaptation. We believe that the outcomes and discussions presented in this work supported by extensive experimental results could be an important milestone in guiding future research on the development of DRL agents for aerial robot tasks.

In multi-robot systems, relative localization between platforms plays a crucial role in many tasks, such as leader following, target tracking, or cooperative maneuvering. State of the Art (SotA) approaches either rely on infrastructure-based or on infrastructure-less setups. The former typically achieve high localization accuracy but require fixed external structures. The latter provide more flexibility, however, most of the works use cameras or lidars that require Line-of-Sight (LoS) to operate. Ultra Wide Band (UWB) devices are emerging as a viable alternative to build infrastructure-less solutions that do not require LoS. These approaches directly deploy the UWB sensors on the robots. However, they require that at least one of the platforms is static, limiting the advantages of an infrastructure-less setup. In this work, we remove this constraint and introduce an active method for infrastructure-less relative localization. Our approach allows the robot to adapt its position to minimize the relative localization error of the other platform. To this aim, we first design a specialized anchor placement for the active localization task. Then, we propose a novel UWB Relative Localization Loss that adapts the Geometric Dilution Of Precision metric to the infrastructure-less scenario. Lastly, we leverage this loss function to train an active Deep Reinforcement Learning-based controller for UWB relative localization. An extensive simulation campaign and real-world experiments validate our method, showing up to a 60% reduction of the localization error compared to current SotA approaches.

Many of the existing works on quadrotor control address the trajectory tracking problem by employing a cascade design in which the translational and rotational dynamics are stabilized by two separate controllers. The stability of the cascade is often proved by employing trajectory-based arguments, most notably, integral input-to-state stability. In this paper, we follow a different route and present a control law ensuring that a composite function constructed from the translational and rotational tracking errors is a Lyapunov function for the closed-loop cascade. In particular, starting from a generic control law for the double integrator, we develop a suitable attitude control extension, by leveraging a backstepping-like procedure. Using this construction, we provide an almost global stability certificate. The proposed design employs the unit sphere $\mathcal{S}^2$ to describe the rotational degrees of freedom required for position control. This enables a simpler controller tuning and an improved tracking performance with respect to previous global solutions. The new design is demonstrated via numerical simulations and on real-world experiments.

A problem of current interest, also motivated by applications to Coding theory, is to find explicit equations for \textit{maximal} curves, that are projective, geometrically irreducible, non-singular curves defined over a finite field $\mathbb{F}_{q^2}$ whose number of $\mathbb{F}_{q^2}$-rational points attains the Hasse-Weil upper bound of $q^2+2\mathfrak{g}q+1$ where $\mathfrak{g}$ is the genus of the curve $\mathcal{X}$. For curves which are Galois covered of the Hermitian curve, this has been done so far ad hoc, in particular in the cases where the Galois group has prime order and also when has order the square of the characteristic. In this paper we obtain explicit equations of all Galois covers of the Hermitian curve with Galois group of order $dp$ where $p$ is the characteristic of $\mathbb{F}_{q^2}$ and $d$ is prime other than $p$. We also compute the generators of the Weierstrass semigroup at a special $\mathbb{F}_{q^2}$-rational point of some of the curves, and discuss some possible positive impacts on the minimum distance problems of AG-codes., Comment: arXiv admin note: text overlap with arXiv:2307.15192

The capability to autonomously track a non-cooperative target is a key technological requirement for micro aerial vehicles. In this paper, we propose an output feedback control scheme based on deep reinforcement learning for controlling a micro aerial vehicle to persistently track a flying target while maintaining visual contact. The proposed method leverages relative position data for control, relaxing the assumption of having access to full state information which is typical of related approaches in literature. Moreover, we exploit classical robustness indicators in the learning process through domain randomization to increase the robustness of the learned policy. Experimental results validate the proposed approach for target tracking, demonstrating high performance and robustness with respect to mass mismatches and control delays. The resulting nonlinear controller significantly outperforms a standard model-based design in numerous off-nominal scenarios.

We analyse the largest eigenvalue of the adjacency matrix of the configuration model with large degrees, where the latter are treated as hard constraints. In particular, we compute the expectation of the largest eigenvalue for degrees that diverge as the number of vertices $n$ tends to infinity, uniformly on a scale between $1$ and $\sqrt{n}$, and show that a weak law of large numbers holds. We compare with what was derived in our earlier paper "Central limit theorem for the principal eigenvalue and eigenvector of Chung-Lu random graphs" for the Chung-Lu model, which in the regime considered represents the corresponding configuration model with soft constraints, and show that the expectation is shifted down by $1$ asymptotically. This shift is a signature of breaking of ensemble equivalence between the hard and soft (also known as micro-canonical and canonical) versions of the configuration model. The latter result generalizes a previous finding in "A spectral signature of breaking of ensemble equivalence for constrained random graphs" obtained in the case when all degrees are equal., Comment: 21 pages, 3 figures

Visual active tracking is a growing research topic in robotics due to its key role in applications such as human assistance, disaster recovery, and surveillance. In contrast to passive tracking, active tracking approaches combine vision and control capabilities to detect and actively track the target. Most of the work in this area focuses on ground robots, while the very few contributions on aerial platforms still pose important design constraints that limit their applicability. To overcome these limitations, in this paper we propose D-VAT, a novel end-to-end visual active tracking methodology based on deep reinforcement learning that is tailored to micro aerial vehicle platforms. The D-VAT agent computes the vehicle thrust and angular velocity commands needed to track the target by directly processing monocular camera measurements. We show that the proposed approach allows for precise and collision-free tracking operations, outperforming different state-of-the-art baselines on simulated environments which differ significantly from those encountered during training. Moreover, we demonstrate a smooth real-world transition to a quadrotor platform with mixed-reality.

A Chung-Lu random graph is an inhomogeneous Erd\H{o}s-R\'enyi random graph in which vertices are assigned average degrees, and pairs of vertices are connected by an edge with a probability that is proportional to the product of their average degrees, independently for different edges. We derive a central limit theorem for the principal eigenvalue and the components of the principal eigenvector of the adjacency matrix of a Chung-Lu random graph. Our derivation requires certain assumptions on the average degrees that guarantee connectivity, sparsity and bounded inhomogeneity of the graph.

In the last decades, visual target tracking has been one of the primary research interests of the Robotics research community. The recent advances in Deep Learning technologies have made the exploitation of visual tracking approaches effective and possible in a wide variety of applications, ranging from automotive to surveillance and human assistance. However, the majority of the existing works focus exclusively on passive visual tracking, i.e., tracking elements in sequences of images by assuming that no actions can be taken to adapt the camera position to the motion of the tracked entity. On the contrary, in this work, we address visual active tracking, in which the tracker has to actively search for and track a specified target. Current State-of-the-Art approaches use Deep Reinforcement Learning (DRL) techniques to address the problem in an end-to-end manner. However, two main problems arise: i) most of the contributions focus only on discrete action spaces and the ones that consider continuous control do not achieve the same level of performance; and ii) if not properly tuned, DRL models can be challenging to train, resulting in a considerably slow learning progress and poor final performance. To address these challenges, we propose a novel DRL-based visual active tracking system that provides continuous action policies. To accelerate training and improve the overall performance, we introduce additional objective functions and a Heuristic Trajectory Generator (HTG) to facilitate learning. Through an extensive experimentation, we show that our method can reach and surpass other State-of-the-Art approaches performances, and demonstrate that, even if trained exclusively in simulation, it can successfully perform visual active tracking even in real scenarios.

For random systems subject to a constraint, the microcanonical ensemble requires the constraint to be met by every realisation ("hard constraint"), while the canonical ensemble requires the constraint to be met only on average ("soft constraint"). It is known that for random graphs subject to topological constraints breaking of ensemble equivalence may occur when the size of the graph tends to infinity, signalled by a non-vanishing specific relative entropy of the two ensembles. We investigate to what extent breaking of ensemble equivalence is manifested through the largest eigenvalue of the adjacency matrix of the graph. We consider two examples of constraints in the dense regime: (1) fix the degrees of the vertices (= the degree sequence); (2) fix the sum of the degrees of the vertices (= twice the number of edges). Example (1) imposes an extensive number of local constraints and is known to lead to breaking of ensemble equivalence. Example (2) imposes a single global constraint and is known to lead to ensemble equivalence. Our working hypothesis is that breaking of ensemble equivalence corresponds to a non-vanishing difference of the expected values of the largest eigenvalue under the two ensembles. We verify that, in the limit as the size of the graph tends to infinity, the difference between the expected values of the largest eigenvalue in the two ensembles does not vanish for (1) and vanishes for (2). A key tool in our analysis is a transfer method that uses relative entropy to determine whether probabilistic estimates can be carried over from the canonical ensemble to the microcanonical ensemble, and illustrates how breaking of ensemble equivalence may prevent this from being possible., Comment: 16 pages. Updated version of the previous work: the result is generalized to broader density regimes for the considered random graph models

Solid-state dewetting phenomenon in silver thin films offers a straightforward method to obtain structures having controlled shape or size -this latter in principle spanning several orders of magnitudes -- with potentially strong interest in many applications involving high-tech industry and biomedicine. In this work nanostructured silver is deposited by pulsed electron ablation technique and its surface modified upon thermal treatments in air at increasing temperatures. Surface chemistry and morphology are then monitored simultaneously by X-ray photoemission spectroscopy and atomic force microscopy; in particular, the power spectral density of surface heights is used to analyze the alteration of morphology induced by annealing. It is shown that this approach adds a level of information about the dewetting process since it allows to separate between long- and short-range surface behavior and to retrieve statistical quantities relevant to a description of the features in view of applications. Our results are presented in the framework of a multidisciplinary approach, advantages and limits of which are deepened and discussed.

Motivated by the development of on-going optomechanical experiments aimed at constraining non-local effects inspired by some quantum gravity scenarios, the Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to a cavity field mode(s), is investigated. In particular, we consider the previously studied model of non-local oscillators obtained as the non-relativistic limit of a class of non-local Klein-Gordon operators, $f(\Box)$, with $f$ an analytical function. The results of previous works, in which the interaction was not included, are recovered and extended by way of standard perturbation theory. At the same time, the perturbed energy spectrum becomes available in this formulation, and we obtain the Langevin's equations characterizing the interacting system., Comment: 7+3 pages, 2 figures. This version matches the published one

In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2,3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set's retarded nonlocal d'Alembertians parametrised by a length scale $l_k$. In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in arXiv:hep-th/1611.10281 is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for why these two cutoff are necessary, and the different roles they play in making the entanglement entropy on causal sets finite., Comment: 36 pages, 14 figures

In this paper, a technique for accurate estimation of the moment of magnetic dipole is proposed. The achievable accuracy is investigated, as a function of measurement noise affecting estimation of magnetic field cartesian components. The proposed technique is validated both via simulations and experimentally., Comment: Preprint

This paper presents the development of a system for realizing interactive exhibitions in the context of a science and technology center. The core functionality of the system is provided by a positioning subsystem comprised of a fixed infrastructure of transmitters and a sensor worn by a user. The operating principle of the positioning system is based on inductive coupling of resonators. Information about the position of the user is transferred to an information system for processing and displaying. Possible use cases include interactive games, information retrieval interfaces and educational scenarios., Comment: Preprint

In this paper, simultaneous estimation of 3D position and attitude of a single coil using a set of anchors, with known position and magnetic dipole, is analyzed. Effect of noise and geometric properties of the anchors' constellation is considered. Several parameters are analyzed and discussed, including placement of anchors in a single or in multiple orthogonal planes. It is shown that adding space and orientation diversity anchors may lead to a more robust performance when the mobile node attitude changes in time., Comment: Preprint version. Conference accepted paper

The signaling between two observers in 3+1 dimensional flat spacetime coupled locally to a non-local field is considered. We show that in the case where two observers are purely timelike related -- so that an exchange of on-shell massless quanta cannot occur -- signaling is still possible because of a violation of Huygens' principle. In particular, we show that the signaling is exponentially suppressed by the non-locality scale. Furthermore, we consider the case in which the two observers are light-like related and show that the non-local modification to the local result is polynomially suppressed in the non-locality scale. This may have implications for phenomenological tests of non-local theories., Comment: 9 pages, 3 Figures. RevTeX 4.1