On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution
The paper presents methods to determine the time, positions, and distance of closest approach for two vehicles following arbitrary trajectories in two or three dimensions. The distance of closest approach of two vehicles following arbitrary curved trajectories is determined by two conditions: (i) th...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Advanced Transportation |
| Online Access: | http://dx.doi.org/10.1155/2018/2918026 |
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| _version_ | 1850168570875478016 |
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| author | Luís Braga Campos Joaquim Guerreiro Marques |
| author_facet | Luís Braga Campos Joaquim Guerreiro Marques |
| author_sort | Luís Braga Campos |
| collection | DOAJ |
| description | The paper presents methods to determine the time, positions, and distance of closest approach for two vehicles following arbitrary trajectories in two or three dimensions. The distance of closest approach of two vehicles following arbitrary curved trajectories is determined by two conditions: (i) the relative velocity must be orthogonal to the relative position in order for the distance to be a nonzero extremum; (ii) the radial acceleration including centripetal terms must have a direction that increases the separation for the extremum to be a minimum. This theorem on the distance of closest approach simplifies in the case of uniform motion along rectilinear trajectories. Three examples are given: (i) the two-dimensional motion of surface vehicles changing the velocity of one of them so as to enforce a given minimum separation distance; (ii) the three-dimensional motion of two aircraft, one flying horizontally and the other climbing, changing the vertical velocity of the latter to ensure a minimum separation distance set “a priori”; (iii) the case of an aircraft flying with constant velocity in a straight line so that its closest approach to another aircraft flying in a circular holding pattern in the same plane occurs at a given time chosen “a priori”. |
| format | Article |
| id | doaj-art-a78b9993efcc462683a6aee119e952ae |
| institution | OA Journals |
| issn | 0197-6729 2042-3195 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Advanced Transportation |
| spelling | doaj-art-a78b9993efcc462683a6aee119e952ae2025-08-20T02:20:56ZengWileyJournal of Advanced Transportation0197-67292042-31952018-01-01201810.1155/2018/29180262918026On the Kinematics of Vehicles Relevant to Conflict Detection and ResolutionLuís Braga Campos0Joaquim Guerreiro Marques1CCTAE (Center for Aeronautical and Space Science and Technology), IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalCCTAE (Center for Aeronautical and Space Science and Technology), IDMEC/LAETA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalThe paper presents methods to determine the time, positions, and distance of closest approach for two vehicles following arbitrary trajectories in two or three dimensions. The distance of closest approach of two vehicles following arbitrary curved trajectories is determined by two conditions: (i) the relative velocity must be orthogonal to the relative position in order for the distance to be a nonzero extremum; (ii) the radial acceleration including centripetal terms must have a direction that increases the separation for the extremum to be a minimum. This theorem on the distance of closest approach simplifies in the case of uniform motion along rectilinear trajectories. Three examples are given: (i) the two-dimensional motion of surface vehicles changing the velocity of one of them so as to enforce a given minimum separation distance; (ii) the three-dimensional motion of two aircraft, one flying horizontally and the other climbing, changing the vertical velocity of the latter to ensure a minimum separation distance set “a priori”; (iii) the case of an aircraft flying with constant velocity in a straight line so that its closest approach to another aircraft flying in a circular holding pattern in the same plane occurs at a given time chosen “a priori”.http://dx.doi.org/10.1155/2018/2918026 |
| spellingShingle | Luís Braga Campos Joaquim Guerreiro Marques On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution Journal of Advanced Transportation |
| title | On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution |
| title_full | On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution |
| title_fullStr | On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution |
| title_full_unstemmed | On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution |
| title_short | On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution |
| title_sort | on the kinematics of vehicles relevant to conflict detection and resolution |
| url | http://dx.doi.org/10.1155/2018/2918026 |
| work_keys_str_mv | AT luisbragacampos onthekinematicsofvehiclesrelevanttoconflictdetectionandresolution AT joaquimguerreiromarques onthekinematicsofvehiclesrelevanttoconflictdetectionandresolution |