Mathematical Model and Solution Algorithm for Virtual Localization Problem
Introduction. The optimization placement problem refereed to virtual localization is studied. This problem is motivated by the need to optimize the production of parts from near-net shape blanks using CNC machines. The known algorithms for solving the virtual localization problem come down to determ...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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V.M. Glushkov Institute of Cybernetics
2022-12-01
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| Series: | Кібернетика та комп'ютерні технології |
| Subjects: | |
| Online Access: | http://cctech.org.ua/13-vertikalnoe-menyu-en/428-abstract-22-4-3-arte |
| _version_ | 1797870917119901696 |
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| author | Sergiy Plankovskyy Yevgen Tsegelnyk Oleksandr Pankratov Tetyana Romanova Serhiy Maximov Volodymyr Kombarov |
| author_facet | Sergiy Plankovskyy Yevgen Tsegelnyk Oleksandr Pankratov Tetyana Romanova Serhiy Maximov Volodymyr Kombarov |
| author_sort | Sergiy Plankovskyy |
| collection | DOAJ |
| description | Introduction. The optimization placement problem refereed to virtual localization is studied. This problem is motivated by the need to optimize the production of parts from near-net shape blanks using CNC machines. The known algorithms for solving the virtual localization problem come down to determining the location parameters of the part CAD model inside the point cloud obtained by scanning the workpiece surface. The main disadvantage of such algorithms is the use of criteria that are insensitive to the intersection of the surfaces of the part and the workpiece. In order to prevent such errors in production conditions, it is necessary to involve a human operator in conducting operations based on virtual localization. In this way, the virtual localization problem of complex shape objects is of paramount importance.
The purpose of the paper is to propose a new approach for solving the virtual localization problem.
Results. A new mathematical model of the virtual localization problem based on the phi-function technique is proposed. We developed a solution strategy that combines algorithm of generating feasible starting points with non-linear optimization procedure. The testing of the proposed approach was carried out for a two-dimensional case. The computational results illustrated with graphical illustrations are provided that show the efficiency of the proposed algorithm.
Conclusions. The obtained results show that the use of the phi-functions technique prevents the occurrence of erroneous solutions with the intersection of the workpiece surfaces. An algorithm for solving the problem of virtual localization in a two-dimensional formulation for the case when the part and the workpiece are convex polygons has been developed. For the considered test problems, the solution time did not exceed 2.5 sec, which fully meets the requirements of industrial use. In the future, it is planned to extend the proposed method to the cases when the CAD model of the part has an arbitrary shape and is formed by Boolean operations on geometric primitives. |
| first_indexed | 2024-04-10T00:36:01Z |
| format | Article |
| id | doaj.art-17b0b74ec963490ea7b138ab76086368 |
| institution | Directory Open Access Journal |
| issn | 2707-4501 2707-451X |
| language | English |
| last_indexed | 2024-04-10T00:36:01Z |
| publishDate | 2022-12-01 |
| publisher | V.M. Glushkov Institute of Cybernetics |
| record_format | Article |
| series | Кібернетика та комп'ютерні технології |
| spelling | doaj.art-17b0b74ec963490ea7b138ab760863682023-03-14T17:05:50ZengV.M. Glushkov Institute of CyberneticsКібернетика та комп'ютерні технології2707-45012707-451X2022-12-014334410.34229/2707-451X.22.4.310-34229-2707-451X-22-4-3Mathematical Model and Solution Algorithm for Virtual Localization ProblemSergiy Plankovskyy0https://orcid.org/0000-0003-2908-903XYevgen Tsegelnyk1https://orcid.org/0000-0003-1261-9890Oleksandr Pankratov2https://orcid.org/0000-0002-2958-8923Tetyana Romanova3https://orcid.org/0000-0002-8618-4917Serhiy Maximov4Volodymyr Kombarov5https://orcid.org/0000-0002-6158-0374O.M. Beketov National University of Urban Economy in Kharkiv, UkraineO.M. Beketov National University of Urban Economy in Kharkiv, UkraineAnatolii Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine, KharkivAnatolii Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine, KharkivAnatolii Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine, KharkivO.M. Beketov National University of Urban Economy in Kharkiv, UkraineIntroduction. The optimization placement problem refereed to virtual localization is studied. This problem is motivated by the need to optimize the production of parts from near-net shape blanks using CNC machines. The known algorithms for solving the virtual localization problem come down to determining the location parameters of the part CAD model inside the point cloud obtained by scanning the workpiece surface. The main disadvantage of such algorithms is the use of criteria that are insensitive to the intersection of the surfaces of the part and the workpiece. In order to prevent such errors in production conditions, it is necessary to involve a human operator in conducting operations based on virtual localization. In this way, the virtual localization problem of complex shape objects is of paramount importance. The purpose of the paper is to propose a new approach for solving the virtual localization problem. Results. A new mathematical model of the virtual localization problem based on the phi-function technique is proposed. We developed a solution strategy that combines algorithm of generating feasible starting points with non-linear optimization procedure. The testing of the proposed approach was carried out for a two-dimensional case. The computational results illustrated with graphical illustrations are provided that show the efficiency of the proposed algorithm. Conclusions. The obtained results show that the use of the phi-functions technique prevents the occurrence of erroneous solutions with the intersection of the workpiece surfaces. An algorithm for solving the problem of virtual localization in a two-dimensional formulation for the case when the part and the workpiece are convex polygons has been developed. For the considered test problems, the solution time did not exceed 2.5 sec, which fully meets the requirements of industrial use. In the future, it is planned to extend the proposed method to the cases when the CAD model of the part has an arbitrary shape and is formed by Boolean operations on geometric primitives.http://cctech.org.ua/13-vertikalnoe-menyu-en/428-abstract-22-4-3-artepolygonal domainphi-function techniquevirtual localizationcnc machining |
| spellingShingle | Sergiy Plankovskyy Yevgen Tsegelnyk Oleksandr Pankratov Tetyana Romanova Serhiy Maximov Volodymyr Kombarov Mathematical Model and Solution Algorithm for Virtual Localization Problem Кібернетика та комп'ютерні технології polygonal domain phi-function technique virtual localization cnc machining |
| title | Mathematical Model and Solution Algorithm for Virtual Localization Problem |
| title_full | Mathematical Model and Solution Algorithm for Virtual Localization Problem |
| title_fullStr | Mathematical Model and Solution Algorithm for Virtual Localization Problem |
| title_full_unstemmed | Mathematical Model and Solution Algorithm for Virtual Localization Problem |
| title_short | Mathematical Model and Solution Algorithm for Virtual Localization Problem |
| title_sort | mathematical model and solution algorithm for virtual localization problem |
| topic | polygonal domain phi-function technique virtual localization cnc machining |
| url | http://cctech.org.ua/13-vertikalnoe-menyu-en/428-abstract-22-4-3-arte |
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