Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies
In this paper, we consider a collision detection problem that frequently arises in the field of robotics. Given a set of bodies with their initial positions and trajectories, we wish to identify the first collision that occurs between any two bodies. or to determine that none exists. For the case of...
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| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | , , |
| التنسيق: | article |
| منشور في: |
2020
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://eprints.kfupm.edu.sa/id/eprint/2553/1/convex_hull_representations_of_models_fo_sherali_isi_000171551100004.pdf |
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| _version_ | 1864513391136079872 |
|---|---|
| author | Sherali, H.D. |
| author2 | Smith, J.C. Selim, S.Z. unknown |
| author2_role | author author author |
| author_facet | Sherali, H.D. Smith, J.C. Selim, S.Z. unknown |
| author_role | author |
| dc.creator.none.fl_str_mv | Sherali, H.D. Smith, J.C. Selim, S.Z. unknown |
| dc.date.*.fl_str_mv | 2020 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://eprints.kfupm.edu.sa/id/eprint/2553/1/convex_hull_representations_of_models_fo_sherali_isi_000171551100004.pdf Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 135. pp. 514-526. |
| dc.language.none.fl_str_mv | en |
| dc.publisher.none.fl_str_mv | ELSEVIER SCIENCE BV |
| dc.relation.none.fl_str_mv | https://eprints.kfupm.edu.sa/id/eprint/2553/ |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Computer |
| dc.title.none.fl_str_mv | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| dc.type.none.fl_str_mv | Article PeerReviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this paper, we consider a collision detection problem that frequently arises in the field of robotics. Given a set of bodies with their initial positions and trajectories, we wish to identify the first collision that occurs between any two bodies. or to determine that none exists. For the case of bodies having linear trajectories, we construct a convex hull representation of the integer programming model of S.Z. Selim and H.A. Almohamad [European Journal of Operational Research 119 (1) (1999) 121-129], and compare the relative effectiveness in solving this problem via the resultant linear program. We also extend this analysis to model a situation in which bodies move along piecewise linear trajectories, possibly rotating at the end of each linear segment. For this case, we again compare an integer programming approach with its linear programming convex hull representation, and exhibit the effectiveness of solving a sequence of mathematical programs for each time segment over a global programming scheme which considers all segments at once. We provide computational results to illustrate the effect of various numbers of bodies present in the collision scenarios, as well as the times at which the first collision occurs. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | KFUPM_6ed31023294d3be14ce6b9b699cf390a |
| identifier_str_mv | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 135. pp. 514-526. |
| language_invalid_str_mv | en |
| network_acronym_str | KFUPM |
| network_name_str | King Fahd University of Petroleum and Minerals |
| oai_identifier_str | oai::2553 |
| publishDate | 2020 |
| publisher.none.fl_str_mv | ELSEVIER SCIENCE BV |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Convex Hull Representations Of Models For Computing Collisions Between Multiple BodiesSherali, H.D.Smith, J.C.Selim, S.Z.unknownComputerIn this paper, we consider a collision detection problem that frequently arises in the field of robotics. Given a set of bodies with their initial positions and trajectories, we wish to identify the first collision that occurs between any two bodies. or to determine that none exists. For the case of bodies having linear trajectories, we construct a convex hull representation of the integer programming model of S.Z. Selim and H.A. Almohamad [European Journal of Operational Research 119 (1) (1999) 121-129], and compare the relative effectiveness in solving this problem via the resultant linear program. We also extend this analysis to model a situation in which bodies move along piecewise linear trajectories, possibly rotating at the end of each linear segment. For this case, we again compare an integer programming approach with its linear programming convex hull representation, and exhibit the effectiveness of solving a sequence of mathematical programs for each time segment over a global programming scheme which considers all segments at once. We provide computational results to illustrate the effect of various numbers of bodies present in the collision scenarios, as well as the times at which the first collision occurs.ELSEVIER SCIENCE BVArticlePeerReviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://eprints.kfupm.edu.sa/id/eprint/2553/1/convex_hull_representations_of_models_fo_sherali_isi_000171551100004.pdf Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 135. pp. 514-526. enhttps://eprints.kfupm.edu.sa/id/eprint/2553/2020info:eu-repo/semantics/openAccessoai::25532019-11-01T13:44:48Z |
| spellingShingle | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies Sherali, H.D. Computer |
| status_str | publishedVersion |
| title | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| title_full | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| title_fullStr | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| title_full_unstemmed | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| title_short | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| title_sort | Convex Hull Representations Of Models For Computing Collisions Between Multiple Bodies |
| topic | Computer |
| url | https://eprints.kfupm.edu.sa/id/eprint/2553/1/convex_hull_representations_of_models_fo_sherali_isi_000171551100004.pdf |