Fault-tolerant formation driving mechanism designed for heterogeneous MAVs-UGVs groups

A fault-tolerant method for stabilization and navigation of 3D heterogeneous formations is proposed in this paper. The presented Model Predictive Control (MPC) based approach enables to deploy compact formations of closely cooperating autonomous aerial and ground robots in surveillance scenarios without the necessity of a precise external localization. Instead, the proposed method relies on a top-view visual relative localization provided by the micro aerial vehicles flying above the ground robots and on a simple yet stable visual based navigation using images from an onboard monocular camera. The MPC based schema together with a fault detection and recovery mechanism provide a robust solution applicable in complex environments with static and dynamic obstacles. The core of the proposed leader-follower based formation driving method consists in a representation of the entire 3D formation as a convex hull projected along a desired path that has to be followed by the group. Such an approach provides non-collision solution and respects requirements of the direct visibility between the team members. The uninterrupted visibility is crucial for the employed top-view localization and therefore for the stabilization of the group. The proposed formation driving method and the fault recovery mechanisms are verified by simulations and hardware experiments presented in the paper

A new Algorithm Based on Factorization for Heterogeneous Domain Decomposition

Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection reaction diffusion type a heterogeneous domain decomposition algorithm which allows us to recover a solution that is very close to the solution of the fully viscous problem, but solves only an inviscid problem in parts of the domain. Our new algorithm is based on the factorization of the underlying differential operator, and we therefore call it factorization algorithm. We give a detailed error analysis, and show that we can obtain approximations in the viscous region which are much closer to the viscous solution in the entire domain of simulation than approximations obtained by other heterogeneous domain decomposition algorithms from the literature.Comment: 23 page

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

A multiscale-multiphysics strategy for numerical modeling of thin piezoelectric sheets

Flexible piezoelectric devices made of polymeric materials are widely used for micro- and nano-electro-mechanical systems. In particular, numerous recent applications concern energy harvesting. Due to the importance of computational modeling to understand the influence that microscale geometry and constitutive variables exert on the macroscopic behavior, a numerical approach is developed here for multiscale and multiphysics modeling of piezoelectric materials made of aligned arrays of polymeric nanofibers. At the microscale, the representative volume element consists in piezoelectric polymeric nanofibers, assumed to feature a linear piezoelastic constitutive behavior and subjected to electromechanical contact constraints using the penalty method. To avoid the drawbacks associated with the non-smooth discretization of the master surface, a contact smoothing approach based on B\'ezier patches is extended to the multiphysics framework providing an improved continuity of the parameterization. The contact element contributions to the virtual work equations are included through suitable electric, mechanical and coupling potentials. From the solution of the micro-scale boundary value problem, a suitable scale transition procedure leads to the formulation of a macroscopic thin piezoelectric shell element.Comment: 11 pages, 6 pages, 21 reference

Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.Comment: 12 pages, 3 figure

Mechano-electric heterogeneity of the myocardium as a paradigm of its function

Myocardial heterogeneity is well appreciated and widely documented, from sub-cellular to organ levels. This paper reviews significant achievements of the group, led by Professor Vladimir S. Markhasin, Russia, who was one of the pioneers in studying and interpreting the relevance of cardiac functional heterogeneity