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A natural extension of point facility location problems are those problems in which facilities are extensive, i.e. those that can not be represented by isolated points but as some dimensional structures such as straight lines, segments of lines, polygonal curves or circles. In this paper a review of the existing work on the location of extensive facilities in continuous spaces is given. Gaps in the knowledge are identified and suggestions for further research are made.

In this article, we investigate the maximum entropy moment closure in gas dynamics. We show that the usual choice of polynomial weight functions may lead to hyperbolic systems with an unpleasant state space: equilibrium states are boundary points with possibly singular fluxes. In order to avoid singularities, the necessary arises to find weight functions which growing sub-quadratically at infinity. Unfortunately, this requirement leads to a conflict with Galilean invariance of the moment systems because we can show that rotational and translational invariant, finite dimensional function spaces necessarily consist of polynomials.

Mit der vorliegenden Veröffentlichung soll der Versuch unternommen werden, mathematischen Schulstoff aus konkreten Problemen herzuentwickeln. Im Mittelpunkt der vorliegenden Arbeit stehen betriebswirtschaftliche Planungs- und Entscheidungsprobleme, wie sie von fast allen Wirtschaftsunternehmen zu lösen sind. Dabei wird im besonderen auf folgende Optimierungsprobleme eingegangen: Berechnung des Rohstoffbedarfs bei gegebenen Bestellungen, Aufarbeitung von vorhandenen Lagerbeständen und das Stücklistenproblem.

Fragestellungen der Standortplanung sollen den Mathematikunterricht der Schule bereichern, dort behandelt und gelöst werden. In dieser Arbeit werden planare Standortprobleme vorgestellt, die im Mathematikunterricht behandelt werden können. Die Probleme Produktion von Halbleiterplatinen, Planung eines Feuerwehrhauses und das Zentrallagerproblem, die ausnahmlos real und nicht konstruiert sind, werden ausführlich durchgearbeitet, so dass es schnell möglich ist, daraus Unterrichtseinheiten zu entwickeln.

By means of the limit and jump relations of classical potential theory the framework of a wavelet approach on a regular surface is established. The properties of a multiresolution analysis are verified, and a tree algorithm for fast computation is developed based on numerical integration. As applications of the wavelet approach some numerical examples are presented, including the zoom-in property as well as the detection of high frequency perturbations. At the end we discuss a fast multiscale representation of the solution of (exterior) Dirichlet's or Neumann's boundary-value problem corresponding to regular surfaces.

Industrial Ecology's Hidden Philosophy of Nature. Fundamental Underpinning to Use Nature as Model
(2001)

In its scientific sense, industrial ecology represents an emerging transdisciplinary field of studying industrial systems and their fundamental linkage with natural ecosystems. As a short form, industrial ecology is called the "science of sustainability". At the bottom of industrial ecology there is a refreshingly different perspective of understanding nature as model in comparison with other scientific disciplines and concepts of understanding nature e.g. in terms of "sack of resources", "biophysical limit", "something outside", "surrounding", or just "environment" as opposed to industrial systems. The keynote of industrial ecology's specific perspective of understanding nature is to balance the development of industrial systems with the constraints of natural eco-systems, analogous to an "industrial symbiosis". The goal is to contribute for laying a fundamental underpinning for industrial ecology in its scientific sense, in this case especially for its use of nature as model. Therefore an impressive battery of philosophical arguments is provided bringing to bear against the sort of probably raised fallacies and facile or hasty proclaimed critics by sceptics, hard-liners, and mainstream-scientists who often overlook industrial ecology's stimulating role towards sustainability.

Point-to-Point Trajectory Planning of Flexible Redundant Robot Manipulators Using Genetic Algorithms
(2001)

The paper focuses on the problem of point-to-point trajectory planning for flexible redundant robot manipulators (FRM) in joint space. Compared with irredundant flexible manipulators, a FRM possesses additional possibilities during point-to-point trajectory planning due to its kinematics redundancy. A trajectory planning method to minimize vibration and/or executing time of a point-to-point motion is presented for FRM based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as planning variables. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate, and final points in joint space. The trajectory planning of FRM is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. Case studies show that the method is applicable.

This article presents contributions in the field of path planning for industrial robots with 6 degrees of freedom. This work presents the results of our research in the last 4 years at the Institute for Process Control and Robotics at the University of Karlsruhe. The path planning approach we present works in an implicit and discretized C-space. Collisions are detected in the Cartesian workspace by a hierarchical distance computation. The method is based on the A* search algorithm and needs no essential off-line computation. A new optimal discretization method leads to smaller search spaces, thus speeding up the planning. For a further acceleration, the search was parallelized. With a static load distribution good speedups can be achieved. By extending the algorithm to a bidirectional search, the planner is able to automatically select the easier search direction. The new dynamic switching of start and goal leads finally to the multi-goal path planning, which is able to compute a collision-free path between a set of goal poses (e.g., spot welding points) while minimizing the total path length.

The vibration induced in a deformable object upon automatic handling by robot manipulators can often be bothersome. This paper presents a force/torque sensor-based method for handling deformable linear objects (DLOs) in a manner suitable to eliminate acute vibration. An adjustment-motion that can be attached to the end of an arbitrary end-effector's trajectory is employed to eliminate vibration of deformable objects. Differently from model-based methods, the presented sensor-based method does not employ any information from previous motions. The adjustment-motion is generated automatically by analyzing data from a force/torque sensor mounted on the robot wrist. Template matching technique is used to find out the matching point between the vibrational signal of the DLO and a template. Experiments are conducted to test the new method under various conditions. Results demonstrate the effectiveness of the sensor-based adjustment-motion.

The task of handling non-rigid one-dimensional objects by a robot manipulation system is investigated. Especially, approaches to calculate motions with specific behavior in point contacts between the object and environment are regarded. For single point contacts, motions based on generalized rotations solving the direct and inverse manipulation problem are investigated. The latter problem is additionally tackled by simple rotation and translation motions. For double and multiple point contacts, motions based on Splines are suggested. In experimental results with steel springs, the predicted and measured effect for each approach are compared.

Manipulating Deformable Linear Objects: Attachable Adjustment-Motions for Vibration Reduction
(2001)

This paper addresses the problem of handling deformable linear objects (DLOs) in a suitable way to avoid acute vibration. Different types of adjustment-motions that eliminate vibration of deformable objects and can be attached to the end of an arbitrary end-effector trajectory are presented. For describing the dynamics of deformable linear objects, the finite element method is used to derive the dynamic differential equations. Genetic algorithm is used to find the optimal adjustment motion for each simulation example. Experiments are conducted to verify the presented manipulating method.

Manipulating Deformable Linear Objects: Model-Based Adjustment-Motion for Vibration Reduction
(2001)

This paper addresses the problem of handling deformable linear objects (DLOs) in a suitable way to avoid acute vibration. An adjustment-motion that eliminates vibration of DLOs and can be attached to the end of any arbitrary end-effector's trajectory is presented, based on the concept of open-loop control. The presented adjustment-motion is a kind of agile end-effector motion with limited scope. To describe the dynamics of deformable linear objects, the finite element method is used to derive the dynamic differential equations. Genetic algorithm is used to find the optimal adjustment-motion for each simulation example. In contrast to previous approaches, the presented method can be treated as one of the manipulation skills and can be applied to different cases without major changes to the method.