Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints
This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obs...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2019/5158967 |
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| author | Dinesh B. Seenivasan Alberto Olivares Ernesto Staffetti |
| author_facet | Dinesh B. Seenivasan Alberto Olivares Ernesto Staffetti |
| author_sort | Dinesh B. Seenivasan |
| collection | DOAJ |
| description | This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the optimal control problem with logical constraints is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, and operational constraints. |
| format | Article |
| id | doaj-art-b5133df020764d65b8555b9131479982 |
| institution | Kabale University |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-b5133df020764d65b8555b91314799822025-02-03T05:45:58ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742019-01-01201910.1155/2019/51589675158967Multiaircraft Optimal 4D Trajectory Planning Using Logical ConstraintsDinesh B. Seenivasan0Alberto Olivares1Ernesto Staffetti2Department of Signal Theory and Communications and Telematic Systems and Computing, Universidad Rey Juan Carlos, Camino del Molino s/n 28943 Fuenlabrada, Madrid, SpainDepartment of Signal Theory and Communications and Telematic Systems and Computing, Universidad Rey Juan Carlos, Camino del Molino s/n 28943 Fuenlabrada, Madrid, SpainDepartment of Signal Theory and Communications and Telematic Systems and Computing, Universidad Rey Juan Carlos, Camino del Molino s/n 28943 Fuenlabrada, Madrid, SpainThis paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the optimal control problem with logical constraints is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, and operational constraints.http://dx.doi.org/10.1155/2019/5158967 |
| spellingShingle | Dinesh B. Seenivasan Alberto Olivares Ernesto Staffetti Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints International Journal of Aerospace Engineering |
| title | Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints |
| title_full | Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints |
| title_fullStr | Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints |
| title_full_unstemmed | Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints |
| title_short | Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints |
| title_sort | multiaircraft optimal 4d trajectory planning using logical constraints |
| url | http://dx.doi.org/10.1155/2019/5158967 |
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