Volume 20, Issue 5 (May 2020)
Modares Mechanical Engineering 2020, 20(5): 1187-1197 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Kosari A, Kassaei S, Rostampour A, Seyedzamani S. Use of Conformal Mapping in the Field of Flying Vehicle Route Planning. Modares Mechanical Engineering 2020; 20 (5) :1187-1197
URL: http://mme.modares.ac.ir/article-15-20652-en.html
URL: http://mme.modares.ac.ir/article-15-20652-en.html
1- Aerospace Department, New Sciences & Technologies Faculty, University of Tehran, Tehran, Iran , kosari_a@ut.ac.ir
2- Aerospace Department, New Sciences & Technologies Faculty, University of Tehran, Tehran, Iran
3- Satellite Research Institute, Iranian Space Research Center, Tehran, Iran
2- Aerospace Department, New Sciences & Technologies Faculty, University of Tehran, Tehran, Iran
3- Satellite Research Institute, Iranian Space Research Center, Tehran, Iran
Abstract: (3087 Views)
In this paper, a novel method for designing the flight paths of an aircraft is presented based on the concept of conformal mapping. Here, a low-altitude route-planning problem has been considered. In this problem, maintaining the control effort to reduce aircraft's altitude and increasing the speed with the limitations of Terrain Following (TF) and Terrain Avoidance (TA) issues, is the main strategy of this performance maneuver. In the proposed approach, attempts are made to convert the real space including terrains and obstacles, in which their data are provided using a digital elevation map, into a pseudo obstacle-free virtual space with no barriers and altitude constraints. In this regard, the concept of conformal mapping has been used as a facilitating mathematical tool for this problem-solving space transformation. The transformation of the problem-solving spaces under the mapping leads to solving the problem of dynamic reflection, the performance criterion, and the real altitude constraints in the virtual space. It is noteworthy that in designing a path in a newly converted space, the effect of barriers on the formation of flight routes is somehow included in the equations expressed in the virtual space. The results of multiple case studies and numerical optimizations performed for 2D geometrical terrains and obstacles show that the proposed approach is more consistent with the basic flight concepts as well as real-world applications.
Keywords: Trajectory Planning, Conformal Mapping, Terrain and Obstacle Avoidance Flight, Low Altitude Flight, Optimal Control
Article Type: Original Research |
Subject:
Control
Received: 2018/05/9 | Accepted: 2019/10/15 | Published: 2020/05/9
Received: 2018/05/9 | Accepted: 2019/10/15 | Published: 2020/05/9
References
1. Kyriakis P, Moustris G. Terrain following for fixed-wing unmanned aerial vehicles using feedback equivalence. IEEE Control Systems Letters. 2019;3(1):150-155. [Link] [DOI:10.1109/LCSYS.2018.2854239]
2. Kosari A, Kassaei SI. Using conformal mapping in developing a novel optimal obstacle-avoidance trajectory-planning for a flying robot. IEEE International Conference on Power, Control, Signals and Instrumentation Engineering. Chennai, India: IEEE; 2017. [Link] [DOI:10.1109/ICPCSI.2017.8392292]
3. Kosari A, Kassaei SI. Dynamic constrained low altitude flight maneuvers with constant energy. IEEE International Conference on Power, Control, Signals and Instrumentation Engineering. Chennai, India: IEEE; 2017. [Link] [DOI:10.1109/ICPCSI.2017.8392293]
4. Denton PL, Jones JE, Froeberg RV. A new technique for terrain following/terrain Avoidance guidance command generation. AGARD Conference Proceedings [Issue 138]. Tokyo: J Global; 1986. [Link]
5. Yang H. Zhao Y. Trajectory planning for autonomous aerospace vehicles amid known obstacles and conflicts. Journal of Guidance, Control, and Dynamics. 2004;27(6):997-1008. [Link] [DOI:10.2514/1.12514]
6. Menon PK, Cheng VH, Kim E. Optimal trajectory synthesis for terrain-following flight. Journal of Guidance, Control, and Dynamics. 1991;14(4):807-813. [Link] [DOI:10.2514/3.20716]
7. Malaek SM, Kosari A. Dynamic based cost functions for TF/TA flights. IEEE Transactions on Aerospace and Electronic Systems. 2012;48(1):44-63. [Link] [DOI:10.1109/TAES.2012.6129620]
8. Qing L. Aircraft route optimization using genetic algorithms. Second International Conference on Genetic Algorithms in Engineering Systems: Innovations And Applications. Glasgow, UK: IET; 1997. [Link] [DOI:10.1049/cp:19971212]
9. Mohanty PK, Parhi DR. Optimal path planning for a mobile robot using cuckoo search algorithm. Journal of Experimental & Theoretical Artificial Intelligence. 2016;28(1-2):35-52. [Link] [DOI:10.1080/0952813X.2014.971442]
10. Malaek SM, Kosari A. Novel minimum time trajectory planning in terrain following flights. IEEE Transactions on Aerospace and Electronic Systems. 2007;43(1):2-12. [Link] [DOI:10.1109/TAES.2007.357150]
11. Nikolos IK, Valavanis KP, Tsourveloudis NC, Kostaras AN. Evolutionary algorithm based offline/online path planner for uav navigation. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics). 2003;33(6):898-912. [Link] [DOI:10.1109/TSMCB.2002.804370]
12. Rahim M, Móhammad‐Bagher Malaek S. Aircraft terrain following flights based on fuzzy logic. Aircraft Engineering and Aerospace Technology. 2011;83(2):94-104. [Link] [DOI:10.1108/00022661111120980]
13. Kosari A, Maghsoudi H, Lavaei A, Ahmadi R. Optimal online trajectory generation for a flying robot for terrain following purposes using neural network. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. 2015;229(6):1124-1141. [Link] [DOI:10.1177/0954410014545797]
14. Kassaei SI, Kosari A. Aircraft trajectory planning with an altitude-bound in terrain-following flight. Modares Mechanical Engineering. 2017;17(12):135-144. [Persian] [Link]
15. Kosari A, Maghsoudi H, Lavaei A. Path generation for flying robots in mountainous regions. International Journal of Micro Air Vehicles. 2017;9(1):44-60. [Link] [DOI:10.1177/1756829316678877]
16. Kamyar R, Taheri E. Aircraft optimal terrain/threat-based trajectory planning and control. Journal of Guidance, Control, and Dynamics. 2014;37(2):466-483. [Link] [DOI:10.2514/1.61339]
17. Khademi I, Maleki B, Nasseri Mood A. Optimal three dimensional terrain following/terrain avoidance for aircraft using direct transcription method. 19th Mediterranean Conference on Control & Automation (MED). Corfu, Greece: IEEE; 2011. pp. 254-258. [Link] [DOI:10.1109/MED.2011.5983062]
18. Roskam J. Airplane flight dynamics and automatic flight controls: Part I (Volume 1). United States: DARcorporation; Reprint edition; 2001. [Link]
19. Abolwitz MJ, Fokas Athanassios S. Complex variables: Introduction and applications second edition (Cambridge texts in applied mathematics). 2nd Edition. Cambridge: Cambridge University Press, 2003. [Link]
20. Brown Ch. Complex variables and Applications, 8th ed. India: Mc Graw Hill India; 2008. [Link]
21. Rao AV. Survey of numerical methods for optimal control. Advances in the Astronautical Sciences. 2009;135(1):497-528. [Link]
22. Betts JT. Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics. 1998;21(2):193-207. [Link] [DOI:10.2514/2.4231]
23. Benson DA. A gauss pseudospectral transcription for optimal control [Dissertation]. Cambridge: Massachusetts Institute of Technology, 2005. [Link]
24. Huntington GT. Advancement and analysis of a Gauss pseudospectral transcription for optimal control problems [Dissertation]. Cambridge: Massachusetts Institute of Technology; 2007. [Link]
25. Gill PE, Murray W, Saunders MA. SNOPT: An SQP algorithm for large-scale constrained optimization. 2005;47(1):99-131. [Link] [DOI:10.1137/S0036144504446096]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |