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We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.
In this paper we present SMART-FACTORY, a setup for a research and teaching facility in industrial robotics that is based on the RoboCup Logistics League. It is driven by the need for developing and applying solutions for digital production. Digitization receives constantly increasing attention in many areas, especially in industry. The common theme is to make things smart by using intelligent computer technology. Especially in the last decade there have been many attempts to improve existing processes in factories, for example, in production logistics, also with deploying cyber-physical systems. An initiative that explores challenges and opportunities for robots in such a setting is the RoboCup Logistics League. Since its foundation in 2012 it is an international effort for research and education in an intra-warehouse logistics scenario. During seven years of competition a lot of knowledge and experience regarding autonomous robots was gained. This knowledge and experience shall provide the basis for further research in challenges of future production. The focus of our SMART-FACTORY is to create a stimulating environment for research on logistics robotics, for teaching activities in computer science and electrical engineering programmes as well as for industrial users to study and explore the feasibility of future technologies. Building on a very successful history in the RoboCup Logistics League we aim to provide stakeholders with a dedicated facility oriented at their individual needs.
This paper introduces a new maritime search and rescue system based on S-band illumination harmonic radar (HR). Passive and active tags have been developed and tested while attached to life jackets and a small boat. In this demonstration test carried out on the Baltic Sea, the system was able to detect and range the active tags up to a distance of 5800 m using an illumination signal transmit-power of 100 W. Special attention is given to the development, performance, and conceptual differences between passive and active tags used in the system. Guidelines for achieving a high HR dynamic range, including a system components description, are given and a comparison with other HR systems is performed. System integration with a commercial maritime X-band navigation radar is shown to demonstrate a solution for rapid search and rescue response and quick localization.