The Experts below are selected from a list of 2562 Experts worldwide ranked by ideXlab platform

Fred Van Keulen - One of the best experts on this subject based on the ideXlab platform.

  • explicit level set based topology optimization using an exact heaviside Function and consistent sensitivity analysis
    International Journal for Numerical Methods in Engineering, 2012
    Co-Authors: N P Dijk, Matthijs Langelaar, Fred Van Keulen
    Abstract:

    SUMMARY This paper presents a level-set-based topology optimization method based on numerically consistent sensitivity analysis. The proposed method uses a direct steepest-descent update of the design variables in a level-set method; the level-set nodal values. An exact Heaviside formulation is used to relate the level-set Function to element densities. The level-set Function is not required to be a Signed-Distance Function, and reinitialization is not necessary. Using this approach, level-set-based topology optimization problems can be solved consistently and multiple constraints treated simultaneously. The proposed method leads to more insight in the nature of level-set-based topology optimization problems. The level-set-based design parametrization can describe gray areas and numerical hinges. Consistency causes results to contain these numerical artifacts. We demonstrate that alternative parameterizations, level-set-based or density-based regularization can be used to avoid artifacts in the final results. The effectiveness of the proposed method is demonstrated using several benchmark problems. The capability to treat multiple constraints shows the potential of the method. Furthermore, due to the consistency, the optimizer can run into local minima; a fundamental difficulty of level-set-based topology optimization. More advanced optimization strategies and more efficient optimizers may increase the performance in the future. Copyright © 2012 John Wiley & Sons, Ltd.

Jua Nieto - One of the best experts on this subject based on the ideXlab platform.

  • freetures localization in Signed Distance Function maps
    arXiv: Robotics, 2020
    Co-Authors: Alexande Millane, Hele Oleynikova, Christia Lanegge, Jeff Delmerico, Jua Nieto, Roland Siegwa, Marc Pollefeys, Cesa Cadena
    Abstract:

    Localization of a robotic system within a previously mapped environment is important for reducing estimation drift and for reusing previously built maps. Existing techniques for geometry-based localization have focused on the description of local surface geometry, usually using pointclouds as the underlying representation. We propose a system for geometry-based localization that extracts features directly from an implicit surface representation: the Signed Distance Function (SDF). The SDF varies continuously through space, which allows the proposed system to extract and utilize features describing both surfaces and free-space. Through evaluations on public datasets, we demonstrate the flexibility of this approach, and show an increase in localization performance over state-of-the-art handcrafted surfaces-only descriptors. We achieve an average improvement of ~12% on an RGB-D dataset and ~18% on a LiDAR-based dataset. Finally, we demonstrate our system for localizing a LiDAR-equipped MAV within a previously built map of a search and rescue training ground.

  • voxgraph globally consistent volumetric mapping using Signed Distance Function submaps
    International Conference on Robotics and Automation, 2020
    Co-Authors: Victo Reijgwa, Alexande Millane, Hele Oleynikova, Roland Siegwa, Cesa Cadena, Jua Nieto
    Abstract:

    Globally consistent dense maps are a key requirement for long-term robot navigation in complex environments. While previous works have addressed the challenges of dense mapping and global consistency, most require more computational resources than may be available on-board small robots. We propose a framework that creates globally consistent volumetric maps on a CPU and is lightweight enough to run on computationally constrained platforms. Our approach represents the environment as a collection of overlapping Signed Distance Function (SDF) submaps and maintains global consistency by computing an optimal alignment of the submap collection. By exploiting the underlying SDF representation, we generate correspondence-free constraints between submap pairs that are computationally efficient enough to optimize the global problem each time a new submap is added. We deploy the proposed system on a hexacopter micro aerial vehicle (MAV) with an Intel i7-8650 U CPU in two realistic scenarios: mapping a large-scale area using a 3D LiDAR and mapping an industrial space using an RGB-D camera. In the large-scale outdoor experiments, the system optimizes a 120 × 80 m map in less than 4 s and produces absolute trajectory RMSEs of less than 1 m over 400 m trajectories. Our complete system, called voxgraph , is available as open source. 1 1 https://github.com/ethz-asl/voxgraph .

Charles Dapogny - One of the best experts on this subject based on the ideXlab platform.

  • geometric constraints for shape and topology optimization in architectural design
    Computational Mechanics, 2017
    Co-Authors: Charles Dapogny, Gregoire Allaire, Alexis Faure, Georgios Michailidis, Agnes Couvelas, Rafael Estevez
    Abstract:

    This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the Signed Distance Function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

  • shape optimization with a level set based mesh evolution method
    Computer Methods in Applied Mechanics and Engineering, 2014
    Co-Authors: Gregoire Allaire, Pascal Frey, Charles Dapogny
    Abstract:

    In this article, we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process - by means of a mesh amenable for mechanical analyses - while retaining the whole versatility of the level set method when it comes to accounting for their evolution. The key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one, and conversely; this notably brings into play an algorithm for generating the Signed Distance Function to an arbitrary discrete domain, and a mesh generation algorithm for implicitly-defined geometries.

  • multi phase structural optimization via a level set method
    ESAIM: Control Optimisation and Calculus of Variations, 2014
    Co-Authors: Gregoire Allaire, Charles Dapogny, Georgios Michailidis, Gabriel Delgado
    Abstract:

    We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves jump of discontinuous quantities at the interface which are difficult to numerically evaluate. Therefore we suggest an alternative smoothed interface approach which yields more convenient shape derivatives. We rely on the Signed Distance Function and we enforce a fixed width of the transition layer around the interface (a crucial property in order to avoid increasing "grey" regions of fictitious materials). It turns out that the optimization of a diffuse interface has its own interest in material science, for example to optimize Functionally graded materials. Several 2-d examples of compliance minimization are numerically tested which allow us to compare the shape derivatives obtained in the sharp or smoothed interface cases.

Pascal Frey - One of the best experts on this subject based on the ideXlab platform.

  • shape optimization with a level set based mesh evolution method
    Computer Methods in Applied Mechanics and Engineering, 2014
    Co-Authors: Gregoire Allaire, Pascal Frey, Charles Dapogny
    Abstract:

    In this article, we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process - by means of a mesh amenable for mechanical analyses - while retaining the whole versatility of the level set method when it comes to accounting for their evolution. The key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one, and conversely; this notably brings into play an algorithm for generating the Signed Distance Function to an arbitrary discrete domain, and a mesh generation algorithm for implicitly-defined geometries.

  • Computation of the Signed Distance Function to a discrete contour on adapted triangulation
    Calcolo, 2012
    Co-Authors: C. Dapogny, Pascal Frey
    Abstract:

    In this paper, we propose a numerical method for computing the Signed Distance Function to a discrete domain, on an arbitrary triangular background mesh. It mainly relies on the use of some theoretical properties of the unsteady Eikonal equation. Then we present a way of adapting the mesh on which computations are held to enhance the accuracy for both the approximation of the Signed Distance Function and the approximation of the initial discrete contour by the induced piecewise affine reconstruction, which is crucial when using this Signed Distance Function in a context of level set methods. Several examples are presented to assess our analysis, in two or three dimensions.

Shinji Nishiwaki - One of the best experts on this subject based on the ideXlab platform.

  • a level set based topology optimization method using the discretized Signed Distance Function as the design variables
    Structural and Multidisciplinary Optimization, 2010
    Co-Authors: Shintaro Yamasaki, Tsuyoshi Nomura, Atsushi Kawamoto, Kazuo Sato, Kazuhiro Izui, Shinji Nishiwaki
    Abstract:

    This paper deals with a new topology optimization method based on the level set method. In the proposed method, the discretized Signed Distance Function, a kind of level set Function, is used as the design variables, and these are then updated using their sensitivities. The Signed Distance characteristic of the design variables are maintained by performing a re-initialization at every update during the iterated optimization procedure. In this paper, a minimum mean compliance problem and a compliant mechanism design problem are formulated based on the level set method. In the formulations of these design problems, a perimeter constraint is imposed to overcome the ill-posedness of the structural optimization problem. The sensitivity analysis for the above structural optimization problems is conducted based on the adjoint variable method. The augmented Lagrangian method is incorporated to deal with multiple constraints. Finally, several numerical examples that include multiple constraints are provided to confirm the validity of the method, and it is shown that appropriate optimal structures are obtained.