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Published in:
2020 | OriginalPaper | Chapter
Optimization Algorithm for Approximating the Solutions Set of Nonlinear Inequalities Systems in the Problem of Determining the Robot Workspace
Authors : Larisa Rybak, Dmitry Malyshev, Elena Gaponenko
Published in: Advances in Optimization and Applications
Publisher: Springer International Publishing
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Abstract
This paper is devoted to the problem of determining the workspace of robots. We consider an approach to the development of a numerical method for approximating the set of solutions of a system of nonlinear inequalities based on the concept of non-uniform coverings. An approach is proposed based on the transformation of non-uniform covering sets into a set of partially ordered sets of integers to reduce computational complexity. An algorithm for transforming boxes of a covering set is presented. The approach has been tested for a 3-RPS robot. The results of the mathematical simulation and analysis of the effectiveness of the proposed approach based on an estimate of the reduction in the amount of numbers describing the covering set are presented.