Solving polynomial systems via symbolic-numeric reduction to geometric involutive form

AbstractWe briefly survey several existing methods for solving polynomial systems with inexact coefficients, then introduce our new symbolic-numeric method which is based on the geometric (Jet) theory of partial differential equations. The method is stable and robust. Numerical experiments illustrate the performance of the new method

Solving geoinformatics parametric polynomial systems using the improved Dixon resultant

Improvements in computational and observational technologies in geoinformatics, e.g., the use of laser scanners that produce huge point cloud data sets, or the proliferation of global navigation satellite systems (GNSS) and unmanned aircraft vehicles (UAVs), have brought with them the challenges of handling and processing this “big data”. These call for improvement or development of better processing algorithms. One way to do that is integration of symbolically presolved sub-algorithms to speed up computations. Using examples of interest from real geoinformatic problems, we will discuss the Dixon-EDF resultant as an improved resultant method for the symbolic solution of parametric polynomial systems. We will briefly describe the method itself, then discuss geoinformatics problems arising in minimum distance mapping (MDM), parameter transformations, and pose estimation essential for resection. Dixon-EDF is then compared to older notions of “Dixon resultant”, and to several respected implementations of Gröbner bases algorithms on several systems. The improved algorithm, Dixon-EDF, is found to be greatly superior, usually by orders of magnitude, in both CPU usage and RAM usage. It can solve geoinformatics problems on which the other methods fail, making symbolic solution of parametric systems feasible for many problems

Attention-controlled acquisition of a qualitative scene model for mobile robots

Haasch A. Attention-controlled acquisition of a qualitative scene model for mobile robots. Bielefeld (Germany): Bielefeld University; 2007.Robots that are used to support humans in dangerous environments, e.g., in manufacture facilities, are established for decades. Now, a new generation of service robots is focus of current research and about to be introduced. These intelligent service robots are intended to support humans in everyday life. To achieve a most comfortable human-robot interaction with non-expert users it is, thus, imperative for the acceptance of such robots to provide interaction interfaces that we humans are accustomed to in comparison to human-human communication. Consequently, intuitive modalities like gestures or spontaneous speech are needed to teach the robot previously unknown objects and locations. Then, the robot can be entrusted with tasks like fetch-and-carry orders even without an extensive training of the user. In this context, this dissertation introduces the multimodal Object Attention System which offers a flexible integration of common interaction modalities in combination with state-of-the-art image and speech processing techniques from other research projects. To prove the feasibility of the approach the presented Object Attention System has successfully been integrated in different robotic hardware. In particular, the mobile robot BIRON and the anthropomorphic robot BARTHOC of the Applied Computer Science Group at Bielefeld University. Concluding, the aim of this work, to acquire a qualitative Scene Model by a modular component offering object attention mechanisms, has been successfully achieved as demonstrated on numerous occasions like reviews for the EU-integrated Project COGNIRON or demos