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Accurate satellite pose estimation is crucial for autonomous guidance, navigation, and control (GNC) systems in in-orbit servicing (IOS) missions. This paper explores the impact of different tasks within a multi-task learning (MTL) framework for satellite pose estimation using monocular images. By integrating tasks such as direct pose estimation, keypoint prediction, object localization, and segmentation into a single network, the study aims to evaluate the reciprocal influence between tasks by testing different multi-task configurations thanks to the modularity of the convolutional neural network (CNN) used in this work. The trends of mutual bias between the analyzed tasks are found by employing different weighting strategies to further test the robustness of the findings. A synthetic dataset was developed to train and test the MTL network. Results indicate that direct pose estimation and heatmap-based pose estimation positively influence each other in general, while both the bounding box and segmentation tasks do not provide significant contributions and tend to degrade the overall estimation accuracy.

Designing accurate yet robust tracking controllers with tight performance guarantees for Lagrangian systems is challenging due to nonlinear modeling uncertainties and conservative stability criteria. This article proposes a structure-preserving projector-based tracking control law for uncertain Euler-Lagrange (EL) systems using physically consistent Lagrangian-Gaussian Processes (L-GPs). We leverage the uncertainty quantification of the L-GP for adaptive feedforward-feedback balancing. In particular, an accurate probabilistic guarantee for exponential stability is derived by leveraging matrix analysis results and contraction theory, where the benefit of the proposed controller is proven and shown in the closed-form expressions for convergence rate and radius. Extensive numerical simulations not only demonstrate the controller's efficacy based on a two-link and a soft robotic manipulator but also all theoretical results are explicitly analyzed and validated., Comment: author-submitted electronic preprint version

Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic passivity as one of the significant characteristics of friction is rarely considered in these methods. To address this issue, we propose a Gaussian Process based model that preserves the inherent structural properties such as passivity. A matrix-vector physical structure is considered in our approaches to ensure physical consistency, in particular, enabling a guarantee of positive semi-definiteness of the damping matrix. An aircraft benchmark simulation is employed to demonstrate the efficacy of our methodology. Estimation accuracy and data efficiency are increased substantially by considering and enforcing more structured physical knowledge. Also, the fulfillment of the dissipative nature of the aerodynamics is validated numerically., Comment: accepted by L4DC 2024

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal.

We report on the dielectric and electrocaloric properties of Ba$_{1-y}$Ca$_y$Ti$_{1-x}$Hf$_x$O$_3$ for compositions $0.12

In its original version, the Thomson problem consists of the search for the minimum-energy configuration of a set of point-like electrons that are confined to the surface of a two-dimensional sphere (${\cal S}^2$) that repel each other according to Coulomb's law, in which the distance is the Euclidean distance in the embedding space of the sphere, {\em i.e.}, $\mathbb{R}^3$. In this work, we consider the analogous problem where the electrons are confined to an $n$-dimensional flat Clifford torus ${\cal T}^n$ with $n = 1, 2, 3$. Since the torus ${\cal T}^n$ can be embedded in the complex manifold $\mathbb{C}^n$, we define the distance in the Coulomb law as the Euclidean distance in $\mathbb{C}^n$, in analogy to what is done for the Thomson problem on the sphere. The Thomson problem on a Clifford torus is of interest because super-cells with the topology of Clifford torus can be used to describe periodic systems such as Wigner crystals. In this work we numerically solve the Thomson problem on a square Clifford torus. To illustrate the usefulness of our approach we apply it to Wigner crystals. We demonstrate that the equilibrium configurations we obtain for a large numbers of electrons are consistent with the predicted structures of Wigner crystals. Finally, in the one-dimensional case we analytically obtain the energy spectrum and the phonon dispersion law.

The electric polarizability and the spread of the total position tensors are used to characterize the metallic vs insulator nature of large (finite) systems. Finite clusters are usually treated within the open boundary condition formalism. This introduces border effects, which prevents a fast convergence to the thermodynamic limit and which can be eliminated within the formalism of periodic boundary conditions. Recently, we have introduced an original approach to periodic boundary conditions, named Clifford Boundary Conditions. It considers a finite fragment extracted from a periodic system and the modification of its topology into that of a Clifford Torus. The quantity representing the position is modified in order to fulfill the system periodicity. In this work, we apply the formalism of Clifford Boundary Conditions to the case of Carbon Nanotubes, whose treatment results to be particularly simple for the Zigzag geometry. Indeed, we demonstrate that at the H\"uckel level these nanotubes, either finite or periodic, are formally equivalent to a collection of {\em non-interacting dimerized linear chains}, thus simplifying their treatment. This equivalence is used to describe some nanotube properties as the sum of the contributions of the independent chains and to identify the origin of peculiar behaviors (such as the conductivity). Indeed, if the number of hexagons along the circumference is a multiple of three a metallic behavior is found, namely a divergence of both the (per electron) polarizability and total position spread of at least one linear chain. These results are in agreement with those in the literature from Tight-Binding calculations.