On minimum-time paths of bounded curvature with position-dependent constraints
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multipl...
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| Format: | Artykuł |
| Język: | en_US |
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Elsevier
2017
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| Dostęp online: | http://hdl.handle.net/1721.1/109775 https://orcid.org/0000-0002-2104-3128 https://orcid.org/0000-0002-0505-1400 |
| _version_ | 1826216461957332992 |
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| author | Sanfelice, Ricardo G. Yong, Sze Zheng Frazzoli, Emilio |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Sanfelice, Ricardo G. Yong, Sze Zheng Frazzoli, Emilio |
| author_sort | Sanfelice, Ricardo G. |
| collection | MIT |
| description | We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a “refraction” law at the boundary of the regions that generalizes the so-called Snell’s law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results. |
| first_indexed | 2024-09-23T16:48:04Z |
| format | Article |
| id | mit-1721.1/109775 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:48:04Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1097752022-09-29T21:35:00Z On minimum-time paths of bounded curvature with position-dependent constraints Sanfelice, Ricardo G. Yong, Sze Zheng Frazzoli, Emilio Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Yong, Sze Zheng Frazzoli, Emilio We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a “refraction” law at the boundary of the regions that generalizes the so-called Snell’s law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results. 2017-06-09T18:46:41Z 2017-06-09T18:46:41Z 2013-12 2013-07 Article http://purl.org/eprint/type/JournalArticle 0005-1098 http://hdl.handle.net/1721.1/109775 Sanfelice, Ricardo G.; Yong, Sze Zheng and Frazzoli, Emilio. “On Minimum-Time Paths of Bounded Curvature with Position-Dependent Constraints.” Automatica 50, no. 2 (February 2014): 537–546 © 2013 Elsevier Ltd https://orcid.org/0000-0002-2104-3128 https://orcid.org/0000-0002-0505-1400 en_US http://dx.doi.org/10.1016/j.automatica.2013.11.016 Automatica Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier arXiv |
| spellingShingle | Sanfelice, Ricardo G. Yong, Sze Zheng Frazzoli, Emilio On minimum-time paths of bounded curvature with position-dependent constraints |
| title | On minimum-time paths of bounded curvature with position-dependent constraints |
| title_full | On minimum-time paths of bounded curvature with position-dependent constraints |
| title_fullStr | On minimum-time paths of bounded curvature with position-dependent constraints |
| title_full_unstemmed | On minimum-time paths of bounded curvature with position-dependent constraints |
| title_short | On minimum-time paths of bounded curvature with position-dependent constraints |
| title_sort | on minimum time paths of bounded curvature with position dependent constraints |
| url | http://hdl.handle.net/1721.1/109775 https://orcid.org/0000-0002-2104-3128 https://orcid.org/0000-0002-0505-1400 |
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