Reduction of placement problems using Minkowski decomposition
The problem of finding collision-free placements for an object amid obstacles has two well-known solutions: the task space approach and the configuration space approach. In this correspondence, we study the mathematical structure of the placement problem, and show that Minkowski decomposition of the...
| Veröffentlicht in: | IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society. - 1996. - 33(2003), 1 vom: 28., Seite 133-8 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2003
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society |
| Schlagworte: | Journal Article |
| Zusammenfassung: | The problem of finding collision-free placements for an object amid obstacles has two well-known solutions: the task space approach and the configuration space approach. In this correspondence, we study the mathematical structure of the placement problem, and show that Minkowski decomposition of the object produces a hierarchy of intermediate reformulations. This provides the mathematical foundation for common approximate solution methods already used in applications. In particular, it provides a recipe for discretizing rotations consistently. The methods discussed are particularly effective for simple shapes |
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| Beschreibung: | Date Completed 02.10.2012 Date Revised 01.02.2008 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1941-0492 |
| DOI: | 10.1109/TSMCB.2003.808180 |